October 2016 Evaluating Sovereign Disaster Risk Finance Strategies: Case Studies and Guidance © 2016 International Bank for Reconstruction and Development / International Development Association or THE WORLD BANK 1818 H Street NW Washington DC 20433 Telephone: 202-473-1000 Internet: www.worldbank.org This work is a product of the staff of The World Bank with external contributions. The findings, interpretations, and conclusions expressed in this work do not necessarily reflect the views of The World Bank, its Board of Executive Directors, or the governments they represent. The World Bank does not guarantee the accuracy of the data included in this work. The boundaries, colors, denominations, and other information shown on any map in this work do not imply any judgment on the part of The World Bank concerning the legal status of any territory or the endorsement or acceptance of such boundaries. Rights and Permissions The material in this work is subject to copyright. Because The World Bank encourages dissemination of its knowledge, this work may be reproduced, in whole or in part, for noncommercial purposes as long as full attribution to this work is given. Any queries on rights and licenses, including subsidiary rights, should be addressed to the Office of the Publisher, The World Bank, 1818 H Street NW, Washington, DC 20433, USA; fax: 202-522-2422; e-mail: pubrights@worldbank.org Evaluating Sovereign Disaster Risk Finance Strategies: Case Studies and Guidance ii EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE Acknowledgements This report was written by a joint team comprising Daniel Clarke and Naomi Cooney of the Disaster Risk Financing and Insurance Program of The World Bank Group and Anna Edwards and Andrew Jinks of the UK Government Actuary’s Department. Overall guidance was provided by Olivier Mahul (World Bank-GFDRR Disaster Risk Financing and Insurance Program) and Ian Rogers (UK Government Actuary’s Department). The report is an output of the Disaster Risk Finance Impact Analytics Project, and it greatly benefited from the inputs and reviews from Cora Ciechanowicz, Mareile Drechsler, Ruth Hill, Oscar Ishizawa, Barry Maher, Catherine Porter, Richard Poulter, Wolter Soer, and Charles Stutley. The team has made every attempt to verify the contents presented, but the information should be interpreted with due consideration to its limitations. The Disaster Risk Financing and Insurance Program—a joint initiative of The World Bank Group’s Finance and Markets Global Practice and the Global Facility for Disaster Reduction and Recovery (GFDRR)—and The World Bank Group’s Poverty and Equity Global Practice are grateful for the financial support received from GFDRR and the U.K. Department for International Development’s Humanitarian Innovation and Evidence Programme. EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 01 Table of Contents Acknowledgements 05 Overview 09 Country V Case Study 15 Country W Case Study 21 Country X Case Study 27 Country Y Case Study 33 Country Z Case Study 39 Guidance Note 43 Country V Annexes 52 Country W Annexes 60 Country X Annexes 68 Country Y Annexes 73 Country Z Annexes 83 Glossary 02 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE List of Tables 9 Table V1.1 – Strategies Considered 10 Table V2.1 – Assumptions Summary - Base Parameters and Sensitivity Analysis 15 Table W1.1 – Strategies Considered 16 Table W2.1 – Assumptions Summary, Base Parameters and Sensitivity Analysis 21 Table X1.1 – Strategies Considered 22 Table X2.1 – Assumptions Summary, Base Parameters and Sensitivity Analysis 28 Table Y1.1 – Strategies Considered 28 Table Y2.1 – Key Assumptions Summary, Base Parameters and Sensitivity Analysis 31 Table Y4.2 – Sensitivity Analysis: Cheapest and Most Expensive Strategies by Return Period 33 Table Z1.1 – Strategies Considered 34 Table Z2.1 – Assumptions Summary, Base Parameters and Sensitivity Analysis 71 Table AY2.2 – Diagnostics of Insurance Pricing Assumptions, Base Case 72 Table AY3.1 – Diagnostics of Insurance Pricing Assumptions, Sensitivities 72 Table AY3.2 – Assumptions with Sensitivity Analysis Not Considered EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 03 List of Figures 11 Figure V3.1 – Relative Cost Saving of Strategy B and C Compared to A 11 Figure V3.2 – Cost of Finance Strategies, Base Case Assumptions 17 Figure W3.1 – Relative Cost Saving of Strategy B and C compared to A 17 Figure W3.2 – Cost of Finance Strategies, Base Case Assumptions 23 Figure X3.1 – Relative Cost Saving of Strategy B and C Compared to A 23 Figure X3.2 – Cost of Finance Strategies, Base Case Assumptions 29 Figure Y3.1 – Costs of Risk Transfer Strategies, Base Case Scenario Assumptions 30 Figure Y4.1 – Cost of Risk Transfer Strategies, Including Sensitivities 35 Figure Z3.1 – Relative Cost Saving of Finance Strategies, Base Case Scenario, Average Cost 36 Figure Z3.2 – Relative Cost Saving of Finance Strategies, 1 in 10 Year Return Period Loss 36 Figure Z3.3 – Relative Cost Saving of Finance Strategies, 1 in 30 Year Return Period Loss 37 Figure Z3.4 – Cost of Finance Strategies, Base Case Assumptions 43 Figure AV1.1 – Cumulative Distribution Function of the Poverty Cost Due to Drought 45 Figure AV3.1 – Marginal Cost as a Multiple of Loss, Base Case Assumptions 46 Figure AV3.2 – Marginal Cost as a Multiple of Loss, Sensitivity to the Spread on the Reserve Fund and Insurance Pricing Multiple 47 Figure AV3.3 – Marginal Cost as a Multiple of Loss – Sensitivity to the Post-Disaster Debt Delay Factor and the Budget Reallocation Hurdle Rate 48 Figure AV4.1 – Relative Cost Saving of Strategies under Increased Reserve Fund 48 Figure AV4.2 – Total Cost of Increased Reserve Fund 49 Figure AV4.3 – Relative Cost Saving of Strategies under Increased Underlying Contingent Liability 50 Figure AV4.4 – Total Cost of Increased Underlying Contingent Liability 51 Figure AV4.5 – Relative Cost Saving of Strategies under Decreased Underlying Contingent Liability 51 Figure AV4.6 – Total Cost of Decreased Underlying Contingent Liability 52 Figure AW1.1 – Cumulative Distribution Function of the Poverty Cost Due to Flood 54 Figure AW3.1 – Marginal Cost as a Multiple of Loss, Base Case Assumptions 55 Figure AW3.2 – Marginal Cost as a Multiple of Loss, Sensitivity to the Spread on the Reserve Fund and Contingent Credit 56 Figure AW3.3 – Marginal Cost as a Multiple of Loss – Sensitivity to the Post-Disaster Debt Delay Factor and the Insurance Multiple 57 Figure AW4.1 – Relative Cost Saving of Reduced Insurance Layer 04 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 57 Figure AW4.2 – Total Cost of Reduced Insurance Layer 58 Figure AW4.3 – Relative Cost Saving of Increasing Non-Insurance Layers 58 Figure AW4.4 – Total Cost of Increasing Non-Insurance Layers 60 Figure AX1.1 – Cumulative Distribution Function of the Yield Loss Due to All Perils 62 Figure AX3.1 – Marginal Cost as a Multiple of Loss, Base Case Assumptions 63 Figure AX3.2 – Marginal Cost as a Multiple of Loss, Sensitivity to the Spread on the Reserve Fund and budget Reallocation Hurdle Rate 64 Figure AX3.3 – Marginal Cost as a Multiple of Loss, Sensitivity to the Post-Disaster Debt Delay Factor and the Insurance Multiple 65 Figure AX4.1 – Relative Cost Saving of Reduced Reserve Fund 65 Figure AX4.2 – Total Cost of Reduced Reserve Fund 67 Figure AX4.3 – Relative Cost Saving of Increased Reserve Fund 67 Figure AX4.4 – Total Cost of Increased Reserve Fund 68 Figure AY1.1 – Cumulative Distribution Function for Undiversified Total Payouts/Costs 69 Figure AY1.2 – Cumulative Distribution Functions for Pooled Cover (by Peril and in Aggregate) 73 Figure AZ1.1 – Cumulative Distribution Function of the Public Losses 76 Figure AZ3.1 – Marginal Cost as a Multiple of Loss, Base Case Assumptions 78 Figure AZ3.2 – Marginal Cost as a Multiple of Loss, Sensitivity to the Spread on the Reserve Fund and The Budget Reallocation 78 Figure AZ3.3 – Marginal Cost as a Multiple of Loss, Sensitivity to the Post-Disaster Debt Delay Factor and the Insurance Multiple 79 Figure AZ3.4 – Marginal Cost as a Multiple of Loss, Sensitivity to the Contingent Credit Assumptions 80 Figure AZ4.1 – Relative Cost Saving of Reduced Insurance Layer 80 Figure AZ4.2 – Total Cost of Reduced Insurance Layer 81 Figure AZ4.3 – Relative Cost Saving of Increasing Non-Insurance Layers 81 Figure AZ4.4 – Total Cost of Increasing Non-Insurance Layers   EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 05 Overview The cost of disasters to governments, households, and of budgetary and financial instruments available to businesses is increasing. Population growth, increasing governments and their development partners.2 The concentration of assets, and climate change are increasing framework covers such instruments as: exposure, hazards, and losses. Developing countries • Risk transfer instruments including insurance, typically lack financial protection against the impacts of reinsurance, catastrophe swaps, and catastrophe bonds these disasters and rely on ex-post measures (for example, budget reallocations, donor assistance, tax increases, and • Reserves / ex-ante budget allocations post-disaster loans) to attempt to meet financing needs. • Contingent credit Disaster risk finance is an important component of the disaster risk management and climate change adaptation • Emergency ex-post budget reallocations agenda. It aims to increase the financial resilience of • Ex-post direct credit (post-disaster debt). countries against natural hazards by strengthening public financial management and promoting market-based disaster This framework has been designed for governments and risk finance solutions (such as, sovereign catastrophe risk development partners to identify the most appropriate and transfer solutions for governments or domestic catastrophe financially efficient strategies to fund disaster losses, based risk insurance markets for public and private assets). on their country risk profile and political constraints. It uses the economic notion of opportunity cost to quantify the However, when designing disaster risk finance solutions, costs and benefits of alternative instruments for funding details matter. Catastrophe risk data and information lay disaster-induced losses. the ground for disaster risk finance solutions, but they need to be processed in order to inform financial decision This report complements the more theoretical framework making. Despite an increasing amount of disaster risk paper with a demonstration of how the framework can data made available from historical databases on disaster be applied in practice. Five case studies illustrate a range losses and catastrophe risk models, countries often lack of questions that policy makers might ask, potential the capacity, resources, and experience to properly analyze instruments to be considered, and economic conditions, and this information for informed financial decision making. a Guidance Note presents principles for such analyses. Without such analysis governments do not have the quantitative tools to evaluate: (i) whether the proposed The structure of the report is as follows: the proposed instrument would offer effective financial protection framework is presented, outlining the approach of the against natural disaster and how it would complement their opportunity-cost framework and its limitations. The five existing strategy, if any, and (ii) whether the price of the case studies are introduced and the contingent liability proposed instrument is cost-effective compared to other and finance strategies considered in each are outlined. financial options. Subsequently, the five case studies are presented in five chapters, each standalone with relevant annexes (including To respond to this, the Disaster Risk Finance Impact at the back of the report). Finally, a Guidance Note outlines Analytics Project developed a comprehensive framework how the framework may be applied in a practical manner to for assessing the costs1 and benefits of the full range 1 Where there are references to costs, these refer to the opportunity cost of 2 Clarke, D. J., O. Mahul, R. Poulter, and T.-L. The. 2016. “Evaluating providing the payouts defined in the contingent liability through the various Sovereign Disaster Risk Finance Strategies: A Framework.” Policy Research financing instruments. Working Paper, The World Bank Group, Washington DC. 06 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE another country’s plans for the disaster risk financing of a The currency considered is US$ and all figures have been contingent liability. Lastly, a Glossary is provided. approximately converted to US$ at average 2015 exchange rates. The purpose of the entire report is to illustrate how to apply the framework to a country-specific question. All formulae and calculations applied in these case studies follow those in the technical framework paper.2 It does not aim to make any Limitations of the Analysis generalized conclusion about which finance mechanisms are The analysis makes multiple assumptions on disaster risk, cheapest or how disaster risk finance should be structured. economic environment, and risk transfer instruments, and focuses solely on a finance structure assuming perfect knowledge of a contingent liability and a mechanism to Introduction to Case Studies measure this contingent liability. The analysis is based on the framework presented in Clarke et al. (2016) and is also In order to demonstrate this framework in a practical subject to the limitations of the framework.3 manner, this report presents five sample country case studies as in the table below. The case studies are based on The analysis is based on information from various sources real countries that are exposed to the perils described, but including World Bank country specialists and economic the countries have been anonymized. The finance strategies information available online. Generally speaking, this considered were selected to reflect questions that were information was of a high quality and broadly sufficient being asked in the country at the time of writing. for the present purposes. Information received was both quantitative (for example, modelled distribution of losses Country Contingent Liability Considered Disaster Risk Finance Instruments Considered Ex-ante Ex-ante Ex-ante Ex-post Ex-post debt reserve contingent risk transfer budget (post- (reserve credit (insurance) reallocation disaster debt) fund) (contingent (budget credit) reallocations) Country V Country-wide response costs due to drought     Country W Country-wide response costs due     to flood Country X Insured losses of two main crops in several areas due to multiple     perils Country Y Insurance program covering public emergency losses in multiple regions of a country  due to earthquake and tropical cyclone events Country Z Public losses (emergency and reconstruction) due to tropical      cyclone events 3 Clarke, D. J., O. Mahul, R. Poulter, and T.-L. Teh. 2016. "Evaluating Sovereign Disaster Risk Finance Strategies: A Framework." Policy Research Working Paper, The World Bank Group, Washington DC. EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 07 from a particular peril) and qualitative (such as, description of the potential insurance coverage that might be available in the country). Where possible and relevant, sensitivity analyzes on the assumptions resulting from this information have been performed. While the analysis provides a sufficient basis for comparing the opportunity costs of financing instruments, its use has limitations, including: 1. Dependence on assumptions: Each case study involves multiple assumptions relating to the disaster risk faced, the economic environment, and the risk transfer instruments available. 2. Limited to financial structure: The analysis focuses only on evaluating the opportunity cost of alternative disaster risk finance strategies to finance a well-defined contingent liability. The analysis does not consider whether or not an investment should be made in the first place (that is, there may be wider political considerations such that a country is content to avoid planning and instead rely on aid from donors following any disaster; this is not considered in this report). 3. Financial considerations only: The focus is on the monetary comparisons only and does not consider other considerations that are more difficult to quantify, such as the degree to which the instrument supports or requires strong public financial management (for example, if a country holds a sizable reserve fund to cover the most extreme potential disasters, it may be at risk of being fully spent on a small disaster due to political considerations). 4. Source of finance: There is no discrimination on the source of the finance as this might come from the regional government, national government, or development partners. Only the total overall opportunity cost is considered. 08 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 09 Country V Case Study Following that, the results in the base case scenario 0. Country V – Introduction (Section 3) and sensitivity scenario (Section 4) are 0.1. Country V is a country in Africa vulnerable to drought. presented. Supporting diagrams and comments are The contingent liability considered is defined as included for the underlying contingent liability (Annex follows: V1), the base case assumptions (Annex V2), and the sensitivity analysis (Annexes V3 and V4). • Peril: Drought • Country area: Whole country 1. Country V – Risk • Contingent liability: The costs associated with supporting vulnerable households in districts affected Finance Strategies by drought. 1.1. The analysis for Country V looks at the cost of 0.2. The focus of the Country V case study is to consider the alternative finance strategies. relative cost saving of different risk finance strategies 1.2. All of the finance strategies considered are assumed to to cover government expenditures to support drought- sit on top of a reserve fund that is established to meet affected households. The contingent liability being approximately the 1 in 1.3 year contingent liability4 (a considered for Country V arises from the financial costs loss equal to US$50m). All strategies also assume that of supporting the population that is estimated to have if the additional measure being considered is exhausted fallen below the poverty line as a result of drought. then post-disaster debt will be issued by Country V. 0.3. This chapter is structured with results presented in The source of the funding has not been considered the main body for three different strategies. First and the conclusions could apply to any combination of the chapter sets out the risk finance strategies under government or donor funding. consideration (Section 1) and the base assumptions 1.3. Table V1.1 outlines the three finance strategies and approach used to assess the strategies (Section 2). considered for Country V. Table V1.1 – Strategies Considered Layer Strategy A Strategy B Strategy C First Reserve fund Reserve fund Reserve fund  Post-disaster debt Insurance Budget reallocations Post-disaster debt Post-disaster debt Last 4 A 1 in 1.3 year financing cost refers to the cost to finance a loss with a return period of 1.3 years, equivalent to a 77 percent probability of occurrence. See Glossary for further details. 10 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 2. Country V – Approach Economic and risk transfer assumptions and Assumptions 2.1. Key assumptions, base parameters, and sensitivity analysis performed are summarized in Table V2.1 below. Natural hazard assumptions 2.2. Further details on the sources of the base assumptions, • A Pareto distribution has been fitted to the number as well as other parameters not material for sensitivity of people falling below the poverty line as a result analysis, are outlined in Annex V2. of drought. • It is assumed that part of the population – those falling below the poverty line even in years of adequate rainfall 3. Country V – Base Case – is covered by an existing social protection program. Scenario Results The contingent liability considers the costs of transitory poverty due to drought only. 3.1. This section outlines the total costs for the three strategies considered. Costs are shown at different • It is assumed that supporting an affected individual costs return periods to highlight which strategies are US$45 per person. cheapest at covering the average loss, loss events of a lower magnitude, and more extreme loss events. For the • From the fitted Pareto distribution, 5,000 drought events Country V case study, the cost of the three strategies have been simulated. over the following return periods are considered: • The simulated loss distribution is presented in Annex V1. • On average • 1 in 5 year return period • 1 in 30 year return period. Table V2.1 – Assumptions Summary - Base Parameters and Sensitivity Analysis Assumption Base Parameter Sensitivity Analysis Reference Amount of reserve fund US$50m Increase to US$132m (which is the Figure AV4.1 – average expenditure) Figure AV4.2 Spread between interest rate 3% Increase the spread from 3% to 5% Figure AV3.2 & investment return (interest rate = 6.625%; investment return = 3.625%) Reduce the spread from 3% to 1% Maximum insurance 1 in 30 year (US$433m) Not considered Insurance pricing multiple 1.35 Increase the insurance pricing Figure AV3.2 multiple from 1.35 to 2 Maximum amount of budget US$100m Not considered reallocation Budget reallocation hurdle 10% Increase to 20% and 40% Figure AV3.3 rate Post-disaster debt delay factor 3 (US$1 now = US$3 post-event) Reduce the delay factor from 3 to 1.5 Figure AV3.3 Contingent liability Pareto distribution for the number Loss distribution increased by 25% Figure AV4.3 – of people falling below the Figure AV4.6 poverty line as a result of drought Loss distribution reduced by 25% Per person cost US$45 Not considered EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 11 3.2. Figure V3.1 presents the relative cost saving of 3.4. While Figure V3.1 compares the relative cost saving of Strategies B and C compared to Strategy A, under the the strategies at different return periods, it does not base assumptions on average and at the 1 in 5 and 1 in allow a direct comparison of the magnitude of the costs. 30 year return periods. Figure 3.2 shows the cost in monetary terms of the different strategies at the different return periods. 3.3. For example, on average across the 5,000 simulations, Strategy B is 43 percent cheaper than Strategy A. Figure V3.1 – Relative Cost Saving of Strategy B and C Compared to A 100% 90% 87% 80% Percentage cost decrease (relative to Strategy A) 70% 66% 60% 50% 43% 43% 40% 31% 30% 20% 16% 10% 0% B C B C B C Average 1 in 5 year return period of loss 1 in 30 year return period of loss Source: Clarke, Cooney, Edwards, and Jinks (2016). Figure V3.2 – Cost of Finance Strategies, Base Case Assumptions 1,400 1,200 Total cost (US$m) 1,000 800 600 400 200 0 A B C A B C A B C Average 1 in 5 year return period of loss 1 in 30 year return period of loss Reserve Fund Insurance Budget reallocation Post-disaster debt Source: Clarke, Cooney, Edwards, and Jinks (2016). Return period of loss 12 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 3.5. The main conclusions from the base case scenario as Sensitivity Results: Varying the Economic and demonstrated in Figures V3.1 and V3.2 are: Financial Assumptions • On average, Strategy B is the cheapest; insurance 4.2. A marginal cost analysis for each finance instrument is is more cost-effective than post-disaster debt due used to demonstrate their features and benefits over to the assumption of an insurance pricing multiple varying return periods. The marginal cost analysis in of 1.35 compared to a delay factor of 3.0 on post- Annex V3 demonstrates the intuitive notion that as disaster debt. the economic cost of a finance source increases, the attractiveness of that source decreases, namely: • On average, Strategy C is only marginally more expensive than Strategy B. This is because although • Reserve funds are marginally the cheapest finance the assumed budget reallocation hurdle rate of 10 instrument up to approximately the 1 in 2.1 year percent is lower than the assumed insurance pricing return period. multiple of 1.35, this is more than offset by the fact that budget reallocation is exhausted (at US$100m) • After the 1 in 2.1 year return period, budget at a lower level than insurance (at US$433m) and reallocation becomes the cheapest instrument. hence more expensive post-disaster debt covers However, the marginal cost analysis ignores that more of the losses. there might be a limit on the extent to which government budgets can be reallocated. • Note that the costs at the 1 in 5 year period are higher than the average costs for all strategies. 4.3. The results indicated by the marginal costs analysis This is because the average loss under the assumed are dependent on the financial and other assumptions distribution is smaller than the 1 in 5 year loss. (See selected. If these assumptions are varied, the outcomes Annex V1 for the assumed distribution of losses.) can be materially different. Sensitivity to economic parameters for each of these finance instruments is also • At higher return periods, the costs of Strategy B demonstrated in Annex V3. The results vary intuitively are significantly lower than the costs of the other as the economic parameters are adjusted and the strategies as losses are passed onto the insurer. following can be noted: • Strategy A always has the greatest cost due to the • Increasing the assumed budget reallocation hurdle relatively higher post-disaster delay factor costs rate reduces the cost benefit of budget reallocation. compared to other finance instruments. • Similarly, increasing the insurance pricing multiple decreases the cost benefit gained from insurance. 4. Country V – Sensitivity Results • Adjusting the delay factor downward makes post- disaster debt more attractive. 4.1. The Country V case study considers sensitivity analysis to: • Increasing the spread between the investment and borrowing rates increases the marginal cost of the • The economic and financial assumptions used to reserves as it increases the cost of holding reserve derive the costs of the strategies funds that may not be called on. • The maximum amount of losses covered by the different finance strategies. EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 13 Sensitivity Results: Varying Maximum Funding 5. Country V – Concluding Remarks by Finance Instrument 5.1. The most cost-effective strategy will depend on the 4.4. The results shown in the base case scenario are risk tolerance of policy makers. The analysis shows that dependent on the amount of funding assumed to when considering drought events, losses that are of a be available by each finance instrument and the lower impact and occur more frequently are likely to be assumed loss distribution. Sensitivity to the size of the most cost-effectively financed by holding a reserve fund reserve fund layer and underlying loss distribution is and reallocating from existing budgets. demonstrated through examination of the total cost analysis. The results vary intuitively with the following 5.2. Given the likely limitations on the amount of the key results (see Annex V4 for details): reserve fund and the budget reallocation that will be available, insurance is a cost-effective alternative. • Increasing the size of the reserve fund decreases Insurance may result in an overall cheaper strategy as the costs of all strategies as more losses are met by although it is marginally more expensive at lower return the reserve fund, which is the most cost-effective periods, it can likely cover a greater layer of loss before strategy at lower return periods. the most expensive post-disaster debt finance kicks in. • Increasing the assumed losses increases the costs of 5.3. Additionally, strategies involving insurance are likely to all strategies. It also reduces the cost-effectiveness be attractive at the higher return periods when losses of the strategies if the size of the layers are are ceded to the insurer. unchanged. • Decreasing the assumed losses reduces the costs of all strategies. It also increases the cost-effectiveness of Strategies A and C as more losses are covered by the reserve fund. 14 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 15 Country W Case Study 0. Country W – Introduction 1. Country W – Risk 0.1. Country W is a country in Africa vulnerable to flood. Finance Strategies The contingent liability considered is defined as 1.1. The analysis for Country W looks at the cost of follows: alternative finance strategies. • Perils: Flood 1.2. All of the finance strategies considered are assumed to • Country area: Majority of the regions in the country sit on top of a reserve fund that is established to meet approximately the 1 in 2.3 year contingent liability (a • Contingent liability: Planned Government loss equal to US$100m). All strategies assume that if social protection expenditures to support flood- the additional finacial instrument being considered affected households. is exhausted then post-disaster debt will be issued by 0.2. The focus of the Country W case study is to consider Country W. The source of the funding has not been the relative cost saving of different risk finance considered and the conclusions could apply to any strategies to cover government expenditures to support combination of government or donor funding. flood-affected households. The contingent liability 1.3. Table W1.1 outlines the three finance strategies being considered for Country W arises from the considered for Country W. financial costs of social protection transfers to flood- affected households. 0.3. This chapter is structured with results presented in the 2. Country W – Approach and main body for three different strategies. First the report Assumptions sets out the risk finance strategies under consideration (Section 1) and the base assumptions and approach Natural hazard assumptions used to assess the strategies (Section 2). Following that, the results in the base case scenario (Section 3) • Based on over 30 years of historic data of the number of and sensitivity scenario (Section 4) are presented. people in poverty due to flood. Supporting diagrams and comments are included for • Approximately 25 percent of historical years showed no- the underlying contingent liability (Annex W1), the one affected by flood. A 25 percent probability of nobody base case assumptions (Annex W2) and the sensitivity being affected by flood is therefore assumed. analysis (Annexes W3 and W4). Table W1.1 – Strategies Considered Layer Strategy A Strategy B Strategy C First Reserve fund Reserve fund Reserve fund  Post-disaster debt Insurance Contingent credit Post-disaster debt Post-disaster debt Last 16 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE • The remaining 75 percent of historical years have been 2.2. Further details on the sources of the base assumptions, fitted to an exponential distribution with mean of 1.8m as well as other parameters not material for sensitivity people affected (that is, when there is a flood, on average analysis, are outlined in Annex W2. 1.8m people are affected with flood events following an exponential distribution). • Combining the years in which people are affected and the 3. Country W – Base Case years in which no-one is affected, the total mean number Scenario Results of people in poverty is 1.35m. Monetary losses are derived by multiplying the assumed number of people affected by 3.1. This section outlines the total costs for the three a per person cost of US$100. strategies considered. Costs are shown at different return periods, to highlight which strategies are • The fit to the data is demonstrated in Annex W1. cheapest at covering the average loss, loss events of a lower magnitude, and more extreme loss events. For the Economic and risk transfer assumptions Country W case study, the cost of the three strategies 2.1. Key assumptions, base parameters, and sensitivity over the following return periods are considered: analysis performed are summarized in Table W2.1. Table W2.1 – Assumptions Summary, Base Parameters and Sensitivity Analysis Assumption Base Parameter Sensitivity Analysis Reference Amount of reserve US$100m Increase to US$150m Figure AW4.3 available – AW4.4 Spread between interest 10% Increase the spread from 10% to 15% Figure AW3.2 rate & investment return (interest rate = 13%; investment return = 3%) Decrease the spread from 10% to 5% Amount of contingent US$100m Increase to US$150m Figure AW4.3 credit available – AW4.4 Contingent credit interest 2.5% Increase to 5% Figure AW3.2 rate Contingent credit facility 0.5% of maximum loan Not considered arrangement fee amount Maximum insurance 1 in 30 Not considered (US$559m) Proportion of losses 100% Decrease to 50% (with remainder covered by Figure AW4.1 ceded to insurance post-disaster debt) – AW4.2 Insurance pricing 1.5 Increase the insurance pricing multiple from Figure AW3.3 multiple 1.5 to 2 Post-disaster debt delay 3 (US$1 now = US$3 post- Reduce the delay factor from 3 to 1.4 Figure AW3.3 factor event) Contingent liability Exponential distribution Not considered for the number of people affected by flood Per person cost US$100 Not considered EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 17 • On average 3.3. While Figure W3.1 compares the relative cost saving of the strategies at different return periods, it does not • 1 in 5 year return period allow a direct comparison of the magnitude of the costs. • 1 in 30 year return period. Figure W3.2 shows the cost, in monetary terms of the different strategies at the different return periods. 3.2. Figure W3.1 presents the relative cost saving of Strategies B and C compared to Strategy A, under the 3.4. The main conclusions from the base case scenario as base assumptions on average and at the 1 in 5 and 1 in demonstrated in Figures W3.1 and W3.2 are: 30 year return periods. Figure W3.1 – Relative Cost Saving of Strategy B and C compared to A 100% 90% 85% 80% Percentage cost decrease (relative to Strategy A) 70% 59% 60% 50% 40% 40% 36% 30% 23% 20% 14% 10% 0% B C B C B C Average 1 in 5 year return period of loss 1 in 30 year return period of loss Source: Clarke, Cooney, Edwards, and Jinks (2016). Figure W3.2 – Cost of Finance Strategies, Base Case Assumptions 1,600 1,400 1,200 Total cost (US$m) 1,000 800 600 400 200 0 A B C A B C A B C Average 1 in 5 year return period of loss 1 in 30 year return period of loss Reserve Fund Contingent Credit Insurance Post-disaster debt Source: Clarke, Cooney, Edwards, and Jinks (2016). 18 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE • On average, Strategy B is the cheapest; insurance is Sensitivity Results: Varying the Economic and more cost-effective than post-disaster debt due to Financial Assumptions the assumption of an insurance pricing multiple of 1.5 compared to a delay factor of 3 on post-disaster 4.2. A marginal cost analysis for each finance instrument is debt. used to demonstrate their features and benefits over varying return periods. The marginal cost analysis in • Strategy C, although including contingent credit Annex W3 demonstrates the intuitive notion that as financing which at lower return periods is more the economic cost of a finance source increases, the cost-effective than insurance, is not cheaper than attractiveness of that source decreases, namely: Strategy B because contingent credit covers only a relatively small amount of loss. The remainder Reserves are marginally the cheapest finance is financed by post-disaster debt, which drives the instrument (though contingent credit is only very overall cost of Strategy C. marginally more expensive) up to approximately the 1 in 7 year return period, after which insurance becomes • Note that the costs at the 1 in 5 year period are the cheapest instrument. higher than the average costs for all strategies. This is because the average loss under the assumed 4.3. The results indicated by the marginal costs analysis distribution is smaller than the 1 in 5 year loss (see are dependent on the financial and other assumptions Annex W1 for the assumed distribution of losses). selected. If these assumptions are varied the outcomes can be materially different. Sensitivity to economic • At higher return periods, the costs of Strategy B parameters for each of these finance instruments is also are significantly lower than the costs of the other demonstrated in Annex W3.The results vary intuitively strategies as finance costs are passed onto the as the economic parameters are adjusted and the insurer. following can be noted: • Strategy A always has the greatest cost due to the • Increasing the insurance pricing multiple decreases relatively higher post-disaster delay factor costs the cost benefit gained from insurance. compared to other finance instruments. • Adjusting the post-disaster debt delay factor downward makes post-disaster debt more attractive. 4. Country W – Sensitivity Results • Increasing the spread between the investment and borrowing rates increases the marginal cost of the 4.1. The Country W case study considers sensitivity reserves as it increases the cost of holding reserve analysis to: funds which may not be called on. • The economic and financial assumptions used to • Similarly, increasing the interest rate charged on derive the costs of the strategies contingent credit reduces the cost benefit of the • The maximum amount of losses covered by the contingent credit. different finance strategies. EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 19 Sensitivity Results: Varying Maximum Funding 5. Country W – Concluding Remarks by Finance Instrument 5.1. The most cost-effective strategy will depend on the 4.4. The results shown in the base case scenario are risk tolerance of policy makers. The analysis shows dependent on the amount of funding assumed to be that when considering flood events, losses that are of a available by each finance instrument. Sensitivity to the lower impact and occur more frequently are likely to be size of the layers is demonstrated through examination most cost-effectively financed by holding reserves and of the total cost analysis. The results (see Annex W4 contingent credit. for details) vary intuitively as the amounts available from each finance instruments are adjusted, with the 5.2. Given the likely limitations on the amount of reserves following key results: and contingent credit that will be available, insurance is a cost-effective alternative. Insurance may result in • Decreasing the percentage of loss covered by an overall cheaper strategy as although it is marginally insurance demonstrates that on average Strategy C, more expensive at lower return periods, it is assumed to which includes contingent credit, is the cheapest. cover a greater layer of loss before the most expensive This is due to the fact that the proportion in post-disaster debt finance kicks in. Strategy B not ceded to insurance is covered by the more costly post-disaster debt. 5.3. Additionally, strategies involving insurance are likely to be attractive at the higher return periods when losses • Increasing the amount of financing available from are ceded to the insurer. reserves and contingent credit reduces the cost savings of Strategies B and C (relative to Strategy A) because more loses are met by reserves and contingent credit which are both cheaper than post- disaster debt. 20 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 21 Country X Case Study consideration (Section 1) and the base assumptions 0. Country X – Introduction and approach used to assess the strategies (Section 2). 0.1. Country X is a country in Asia vulnerable to flood, Following that, the results in the base case scenario drought, and other perils. The contingent liability (Section 3) and sensitivity scenario (Section 4) are considered is defined as follows: presented. Supporting diagrams and comments are included for the underlying contingent liability (Annex • Perils: All natural perils affecting maize crops X1), the base case assumptions (Annex X2) and the (flood, drought, tropical cyclone, pests) sensitivity analysis (Annexes X3 and X4). • Country area: Three regions of the country (covering less than 5 percent of the country’s population) that are vulnerable to several perils and 1. Country X – Risk rely heavily on the yield from maize produced in Finance Strategies the regions 1.1. The analysis for Country X looks at the cost of • Contingent liability: Insured losses (in US$) due to alternative finance strategies. a reduction in yield from crop failure for two maize varieties. 1.2. All of the finance strategies considered are assumed to sit on top of a reserve fund that is established to meet 0.2. The focus of the Country X case study is to consider approximately the 1 in 2.5 year contingent liability (a the relative cost saving of different risk finance loss equal to US$20m). All strategies also assume that strategies to cover the insured losses from publicly- if the additional measure being considered is exhausted supported maize insurance policies. The contingent then post-disaster debt will be issued by Country X. liability being considered for Country X arises from the The source of the funding has not been considered money that would be required if crop losses triggered and the conclusions could apply to any combination of insurance payouts. government or donor funding. 0.3. This chapter is structured with results presented in 1.3. Table X1.1 outlines the three finance strategies the main body for three different strategies. First considered for Country X. the chapter sets out the risk finance strategies under Table X1.1 – Strategies Considered Layer Strategy A Strategy B Strategy C First Reserve fund Reserve fund Reserve fund  Post-disaster debt Insurance Budget reallocations Post-disaster debt Post-disaster debt Last 22 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 2. Country X – Approach and 3. Country X – Base Case Assumptions Scenario Results Natural hazard assumptions 3.1. This section outlines the total costs for the three strategies considered. Costs are shown at different return periods, • Based on a third party model, which simulates the to highlight which strategies are cheapest at covering the reduction in maize yields caused by all perils. average loss, loss events of a lower magnitude, and more extreme loss events. For the Country X case study, the cost • Yields are projected in the local currency for two types of of the three strategies outlined above over the following maize in each of the three regions considered. return periods are considered: • The distribution is based on 5,000 simulations of yield • On average loss. • 1 in 5 year return period • The corresponding yield loss cost is converted to US$ using average recent exchange rates. • 1 in 30 year return period. • The simulated loss distribution is demonstrated in Annex 3.2. Figure X3.1 presents the relative cost savings of X1. Strategies B and C compared to Strategy A, under the base assumptions. Economic and risk transfer assumptions 3.3. While Figure X3.1 compares the relative cost saving of 2.1. Key assumptions, base parameters, and sensitivity the strategies at different return periods, it does not analysis performed are summarized in Table X2.1 below: allow a direct comparison of the magnitude of the costs. 2.2. Further details on the sources of the base assumptions, Figure X3.2 shows the cost, in monetary terms of the as well as other parameters not material for sensitivity different strategies at the different return periods. analysis, are outlined in Annex X2. Table X2.1 – Assumptions Summary, Base Parameters and Sensitivity Analysis Assumption Base Parameter Sensitivity Analysis Reference Amount of reserve US$20m Decrease to US$10m Figure AX4.1 – available Increase to US$30m Figure AX4.4 Spread between interest 2% Increase the spread from 2% to 4% Figure AX3.2 rate & investment return (interest rate = 5%; investment return = 3%) Maximum insurance 1 in 30 Not considered (US$52.4m) Insurance pricing multiple 1.35 Increase the insurance pricing multiple from 1.35 to 2 Figure AX3.3 Amount of budget US$20m Not considered reallocation Budget reallocation 20% Decrease to 10% Figure AX3.2 hurdle rate Increase to 40% Post-disaster debt 3 (US$1 now = US$3 Increase the delay factor from 3 to 5 Figure AX3.3 delay factor post-event) Reduce the delay factor from 3 to 1.5 Contingent liability Third party model of Not considered reduction in maize yields EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 23 Figure X3 .1 – Relative Cost Saving of Strategy B and C Compared to A 100% 90% 80% 77% Percentage cost decrease (relative to Strategy A) 70% 60% 50% 46% 40% 37% 32% 30% 27% 26% 20% 10% 0% B C B C B C Average 1 in 5 year return period of loss 1 in 30 year return period of loss Source: Clarke, Cooney, Edwards, and Jinks (2016). Figure X3.2 – Cost of Finance Strategies, Base Case Assumptions 140 120 Total cost (US$m) 100 80 60 40 20 0 A B C A B C A B C Average 1 in 5 year return period of loss 1 in 30 year return period of loss Reserve Fund Insurance Budget reallocation Post-disaster debt Source: Clarke, Cooney, Edwards, and Jinks (2016). 24 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 3.4. The main conclusions from the base case scenario as Sensitivity Results: Varying the Economic and demonstrated in Figures X3.1 and X3.2 are: Financial Assumptions On average, Strategy B is the cheapest; insurance is • 4.2. A marginal cost analysis for each finance instrument is more cost-effective than post-disaster debt due to the used to demonstrate their features and benefits over assumption of an insurance pricing multiple of 1.35 varying return periods. The marginal cost analysis in compared to a delay factor of 3.0 on post-disaster debt. Annex X3 demonstrates the intuitive notion that as the economic cost of a finance source increases, the • On average, Strategy C is only marginally more attractiveness of that source decreases, namely: expensive than Strategy B. This is because although the assumed hurdle rate of 20 percent is lower than • Reserves are marginally the cheapest finance the assumed insurance pricing multiple of 1.35, this is instrument up to approximately the 1 in 8.5 year more than offset by the fact that budget reallocation return period. is exhausted (at US$40m) at a lower level than insurance (at US$52.4m) and hence more expensive • After the 1 in 8.5 year return period, budget post-disaster debt covers more of the losses. reallocation becomes the cheapest instrument. However, the marginal cost analysis ignores that • Note that the costs at the 1 in 5 year period are there might be a limit on the extent to which higher than the average costs for all strategies. government budgets can be reallocated. This is because the average loss under the assumed distribution is smaller than the 1 in 5 year loss (see 4.3. The results indicated by the marginal costs analysis Annex X1 for the assumed distribution of losses). are dependent on the financial and other assumptions selected. If these assumptions are varied, the outcomes • At higher return periods, the costs of Strategy B can be materially different. Sensitivity to economic are significantly lower than the costs of the other parameters for each of these finance instruments is also strategies as finance costs are passed onto the insurer. demonstrated in Annex X3. The results vary intuitively as the economic parameters are adjusted and the • Strategy A always has the greatest cost due to the following can be noted: relatively higher post-disaster delay factor costs compared to other finance instruments. • Increasing the assumed hurdle rate for budget reallocation reduces the cost benefit of budget reallocation. 4. Country X – Sensitivity Results • Similarly, increasing the insurance pricing multiple 4.1. The Country X case study considers sensitivity decreases the cost benefit gained from insurance. analysis to: • Adjusting the delay factor downward makes post- • The economic and financial assumptions used to disaster debt more attractive. derive the costs of the strategies • Increasing the spread between the investment and • The maximum amount of losses covered by the borrowing rates increases the marginal cost of the different finance strategies. reserves as it increases the cost of holding reserve funds which may not be called on. EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 25 Sensitivity Results: Varying Maximum Funding by Finance Instrument 4.4. The results shown in the base case scenario are dependent on the amount of funding assumed to be available by each finance instrument. Sensitivity to the size of the reserve layer is demonstrated through examination of the total cost analysis. The results (see Annex X4 for details) vary intuitively as the reserve is adjusted, with the following key results: • Decreasing the size of the reserve fund increases the costs of all strategies as fewer losses are met by the reserves which is the most cost-effective strategy at lower return periods. • Increasing the size of the reserve fund decreases the costs of all strategies as more losses are met by the reserves, and is the most cost-effective strategy at lower return periods. If the reserve is increased to US$30m then Strategy A becomes the cheapest strategy at lower return periods. 5. Country X – Concluding Remarks 5.1. The most cost-effective strategy will depend on the risk tolerance of policy makers. The analysis shows that when considering maize losses due to multiple perils, losses which are of a lower impact and occur more frequently are likely to be most cost-effectively financed by holding reserves. 5.2. Budget reallocation is assumed to have the lowest marginal cost at the higher loss events. However, there may be a limit on the extent to which government budgets can be reallocated. As a result, strategies involving insurance are likely to be attractive, particularly at the higher return periods when losses are ceded to the insurer. 26 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 27 Country Y Case Study function of wind speed (tropical cyclone coverage) and 0. Country Y – Introduction ground acceleration (earthquake coverage). The model 0.1. Country Y is a country with a large diversified economy has been designed to try to proxy emergency losses and has regions that have very high recurrent risk of incurred by the government in the local regions. disasters from both earthquakes and tropical cyclones. Insurance payouts 0.2. Thirteen regions in Country Y are assumed to have • The insurance contract has a two-step payout selected parametric insurance coverage for earthquake function with defined partial and full payouts. and tropical cyclone risk, with claim payments based on modelled loss, as determined by a pre-agreed • The attachment point (trigger point) for partial catastrophe risk model. payouts is the 1 in 10 year emergency loss. Partial payouts are assumed to be US$16m across 0.3. The focus of the Country Y case study is to evaluate the tropical cyclone and earthquake (allocated either costs of potential disaster risk finance structures that US$8m/$8m if the risk of losses from each peril is could provide the desired insurance coverage, where considered roughly equal or US$12m/$4m if the regions either act independently or work together in region is more vulnerable to tropical cyclone). different ways. • The attachment point for full payouts is the 1 in 30 0.4. This case study is structured with results presented in year emergency loss. Full payouts are assumed to the main body for two main scenarios – the base case be US$40m across tropical cyclone and earthquake scenario and the sensitivity scenario. The case study is (allocated either US$20m/$20m or US$30m/$10m structured as follows. First the risk finance strategies under the same rationale as the partial payouts. (Section 1) and relevant assumptions (Section 2) are outlined. Then the results in the base case scenario • More than 1 partial payout can be made in a year (Section 3) and sensitivity scenario (Section 4) are subject to a maximum annual payout equal to the presented. Supporting diagrams and comments are full payout. included for the underlying contingent liability (Annex Y1), the base case assumptions (Annex Y2) and the 1.2. The contingent liability considered in the opportunity sensitivity analysis (Annex Y3). cost analysis are the cumulative insurance payouts (or costs) for all individual insurance policies (for the 13 regions) as defined above. 1. Country Y – Risk 1.3. Three alternative insurance placement arrangements Finance Strategies with different pooling mechanisms were considered as outlined in Table Y1.1. 1.1. The analysis for Country Y looks at the cost of financing regional insurance policies through alternative insurance placement arrangements (see Table Y1.1). The underlying insurance contracts are parametric in nature with insurance premiums and payouts defined through a catastrophe risk model as a 28 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE Table Y1.1 – Strategies Considered Insurance Strategy A Insurance Strategy B Insurance Strategy C Individual insurance Regions jointly approach the Regional Insurance Facility contracts for each region. reinsurance market with a portfolio of region-specific Regions establish a catastrophe risk insurance facility, acting insurance policies. as a joint reserve mechanism, where smaller payouts are retained through reserves and excess losses are transferred to the reinsurance market. Retention level (smaller losses) Up to first 1 in 10 year aggregate loss of the portfolio Reinsurance (excess losses) All losses beyond the 1 in 10 year aggregate loss of the portfolio 2.2. The base case scenario assumptions and sensitivity 2. Country Y – Approach and analysis performed on these are outlined below in Table Assumptions 2.1, with supporting detail in Annex Y2. All sensitivity analyses are presented in section 4 with supporting Natural hazard assumptions detail in Annex Y3. 2.1. The analysis is based on 10,000 simulated years of emergency losses caused by tropical cyclone and earthquake events across 13 regions, many of which years have multiple events. On average, there are a total of 3.4 events per year per region. The average tropical cyclone impacts 3.8 regions and the average earthquake impacts 2.1 regions. Table Y2.1 – Assumptions Summary, Base Parameters and Sensitivity Analysis Assumption Base Parameter Sensitivity Analysis Strategy A pricing multiple 1.64 N/A Strategy B pricing multiple 1.47 (= 90% * 1.64) where there 1.31 (= 80% * 1.64) where there is a 20% is a 10% diversification benefit diversification benefit compared to compared to Strategy A Strategy A Strategy C Pricing multiple (paid for excess 2.0 Decrease to 1.47 for comparison against losses above the first 1 in 10 year event in a Strategy B year for Strategy C) Spread between interest rate & investment 0% Increase the spread from 0% to 5% return (interest rate = 4%; investment return = 4%) EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 29 • On average, the cost of Strategy C is lower than 3. Country Y – Base Case Strategy A and B. This is because on average, it is Scenario Results cheaper to finance the cost of the relevant payouts through a reserve fund (with no charge applied) 3.1. Figure Y3.1 presents the costs of the three risk transfer than to pay a pricing premium (through a pricing strategies at various return periods in the base case multiple) for insurance placement. scenario assumptions. • For greater payouts at the 1 in 5 year return and 3.2. The cost of Strategy B is always lower than Strategy A, beyond, the cost of Strategy C becomes higher than due to the diversification benefit in Strategy B. Strategy Strategy A and B, since the payouts retained increase A and B have all underlying assumptions identical and have to be financed by the reserve funds. except Strategy B has a diversification benefit of 10 percent (decreasing the cost) and a market fee of 2.5 • Beyond the 1 in 10 year return period, Strategy C percent (increasing the cost). The result is a constant cost levels off because only up to the 1 in 10 year net decrease at all return periods in the cost of Strategy payout is retained in the reserve fund, as defined in B compared to Strategy A. the mechanism for Strategy C. 3.3. The cost of Strategy C is driven by the cost of risk retention. In the base case scenario, there is no foregone investment return on reserve funds held since 4. Country Y – Sensitivity Results the investment return is assumed to be equal to the 4.1. Figure Y4.1 presents the costs of the three risk transfer discount rate, and the cost of financing the retained strategies at various return periods in the base case payouts is equal to the retained payouts themselves at scenario, as well as the following sensitivity scenarios: all return periods: Figure Y3.1 – Costs of Risk Transfer Strategies, Base Case Scenario Assumptions 120 Strategy A 100 Strategy B 80 Strategy C - risk retention 60 Strategy C - 40 reinsurance (premium) 20 0 Average 1 in 3 1 in 5 1 in 10 1 in 50 Source: Clarke, Cooney, Edwards, and Jinks (2016). 30 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE • Increasing the Strategy B diversification benefit 4.4. For payouts at the 1 in 3 year return period, the results from 10 percent to 20 percent are dependent on the sensitivities: • Reducing the Strategy C pricing multiple from 2.0 to • Strategy C is again the cheapest if the spread 1.47 between investment return and discount rate is zero, but Strategy B with a greater diversification • Increasing the spread (between the interest rate and benefit is only marginally more expensive. investment return) from 0 percent to 5 percent for Strategy C retained risk. • If Strategy C is considered with a greater spread (of 5 percent), then it becomes the most expensive, with 4.2. Annex Y3 outlines the rationale for selecting these a greater cost than Strategy A and B. sensitivities and presents the resulting diagnostics (pricing multiples and risk volatility factors) for each 4.5. For higher payouts at or greater than the 1 in 5 year strategy as a comparison. return period, Strategy B with a greater diversification benefit has a significantly cheaper cost than any other 4.3. On average, Strategy C is the cheapest strategy if the strategy. A summary of the cheapest, second cheapest, spread between the investment return and discount rate and most expensive strategies is presented in Table Y4.2. is kept minimal. This is consistent with the conclusions in the base case scenario, where on average it is cheaper to finance the cost of the relevant payouts through a reserve fund (with no charge applied) than to pay a pricing premium (through a pricing multiple) for insurance placement. However, when a spread is introduced such that there is a charge on the reserves held, Strategy C becomes more expensive than Strategy B. Figure Y4.1 – Cost of Risk Transfer Strategies, Including Sensitivities 120 Strategy A 100 Strategy B Strategy B w/ greater diversi ication 80 Strategy C w/ greater spread 60 Strategy C - risk retention 40 Strategy C - reinsurance (premium) 20 0 Strategy C w/ lower pricing multiple Average 1 in 3 1 in 5 1 in 10 1 in 50 Source: Clarke, Cooney, Edwards, and Jinks (2016). EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 31 Table Y4.2 – Sensitivity Analysis: Cheapest and Most Expensive Strategies by Return Period Average 1 in 3 1 in 5 and greater Strategy A Most expensive Strategy B Second cheapest Strategy B w/ greater diversification Only marginally more Cheapest expensive than Strategy C Strategy C Second cheapest Second cheapest Overall Strategy C is more Strategy C w/ lower pricing multiple Cheapest Cheapest expensive than Strategy A and B beyond the 1 in 5 year return period, Strategy C w/ greater spread Most expensive under all sensitivities considered Source: Clarke, Cooney, Edwards, and Jinks (2016). 5. Country Y – Concluding Remarks 5.1. Strategy C, which includes a portion of risk retention, is cheapest on average due to the low or non-existent cost charge on the reserves required to fund the retained level of payout (compared to the pricing premium charge of placing insurance coverage). 5.2. The greater the diversification benefit that can be achieved in Strategy B and the greater the charge (spread) on the reserves held for Strategy C, the lower the payouts at which Strategy B will become the most cost-effective strategy. This likely happens at some point between payouts at the 1 in 3 year and the 1 in 5 year return period. 5.3. The most cost-effective strategy will depend on the risk tolerance of policy makers. If the focus is on losses at lower return periods, or a long-term average cost, retaining a layer of payouts as in Strategy C may be the optimal choice. For increasingly greater payouts and when considering catastrophic tail risk, Strategy B is likely the most cost-effective strategy beyond the 1 in 5 year payout. 32 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 33 Country Z Case Study used to assess the strategies (Section 2). Following 0. Country Z – Introduction that, the results in the base case scenario (Section 3) • Country Z is a small island developing state, with the and sensitivity scenario (Section 4) are presented. entire country vulnerable to the damage caused by Supporting diagrams and comments are included for tropical cyclones. the underlying contingent liability (Annex Z1), the base case assumptions (Annex Z2) and the sensitivity analysis • The focus of the Country Z case study is to consider the (Annexes Z3 and Z4). relative cost saving of different risk finance strategies to cover the losses caused by tropical cyclones. The contingent liability being considered for Country Z is the 1. Country Z – Risk required public expenditure to finance reconstruction of public capital infrastructure destroyed or damaged due to Finance Strategies tropical cyclones. • The analysis for Country Z looks at the cost of alternative • Since the primary focus of the analysis is in assessing the finance strategies. relative costs and benefits of the finance strategies, this • All of the finance strategies considered are assumed to case study assumes that government finance strategies sit on top of a reserve fund that is established to meet are exhausted at the 1 in 50 year return period. Beyond approximately the 1 in 6 year contingent liability (a loss this point, it is assumed that donor support would be equal to roughly 0.2 percent of GDP or US$25m). All provided, and rather than model this cost that would be strategies also assume that if the additional measure the same in all strategies, the contingent liability losses being considered is exhausted then post-disaster debt will are capped at the 1 in 50 year return period. be issued by Country Z. • This chapter is structured with results presented in the • The alternative strategies and finance instruments main body for four different strategies. First the report considered for Country Z analysis are summarized in sets out the risk finance strategies under consideration Table 2.1 below. (Section 1) and the base assumptions and approach Table Z1.1 – Strategies Considered Layer Strategy A Strategy B Strategy C Strategy D First Reserve fund Reserve fund Reserve fund Reserve fund ↓ Post-disaster debt Insurance Budget reallocations Contingent credit Post-disaster debt Post-disaster debt Post-disaster debt Last 34 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE • Public capital losses have been capped at the 1 in 50 year 2. Country Z – Approach and return period (approximately US$300m or 2.5 percent of Assumptions GDP). Losses beyond this magnitude are assumed to be financed by donor support in any finance strategy – the Natural hazard assumptions cost of this donor support would be consistent for all • The analysis is based on 10,000 simulated years of losses strategies and is excluded from this analysis. caused by tropical cyclone events across the entire Economic and risk transfer assumptions country. These simulated losses were extrapolated from an extract of return period losses from a third-party 2.1. Key assumptions, base parameters, and sensitivity catastrophe modelling report. Annex Z1 includes further analysis performed are summarized in Table Z2.1: detail on the underlying distribution of losses. 2.2. Further details on the sources of the base assumptions, • Since our analysis is only interested in public capital as well as other parameters not material for sensitivity losses, it is assumed that 30 percent of the losses are analysis, are outlined in Annex Z2. public capital losses, in line with the proportion of exposure assumed to be public capital in the underlying catastrophe model. Table Z2.1 – Assumptions Summary, Base Parameters and Sensitivity Analysis Assumption Base Parameter Sensitivity Analysis Reference of Where Results Are Presented Reserve fund US$25m Double the maximum to US$50m Figure AZ4.3 – maximum Figure AZ4.4 Spread between 3% Increase in the spread from 3% to 5% Figure AZ3.2 interest rate & (interest rate = 6.75%; Decrease in the spread from 3% to 1% investment return investment return = 3.75%) Contingent credit US$30m Double the maximum to US$60m Figure AZ4.3 – maximum Figure AZ4.4 Contingent credit 2.5% interest on used funds, 0.5% Consider reduced interest (1%) Figure AZ3.4 arrangements arrangement fee Insurance 1 in 30 year loss 1 in 15 year loss Figure AZ4.1 – maximum limit Figure AZ4.2 Risk volatility 25% (broadly equivalent to an Decrease to 12.5% (multiple of 1.4) and Figure AZ3.3 loading insurance pricing multiple of 1.85) increase to 45% (multiple of 2.5) Amount of budget US$100m Double the maximum to US$200m Figure AZ4.3 – reallocation Figure AZ4.4 Budget 37% Decrease to 10% and increase to 50% Figure AZ3.2 reallocation hurdle rate Post-disaster debt 18.4%, based on underlying Increase to 38% (equivalent to a post- Figure AZ3.3 delay factor assumptions outlined in Annex Z2 disaster borrowing rate of 8%, rather than 6.75% ex ante rate) Contingent liability Third party model of losses caused Not considered by tropical cyclone events EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 35 3.2. Figures Z3.1, Z3.2, and Z3.3 show the cost savings of 3. Country Z – Base Case Strategies B, C, and D relative to Strategy A. In other Scenario Results words, they show the relative cost saving or cost from having a finance instrument that sits between the 3.1. This section outlines the total costs for the four reserve fund and Country Z’s post-disaster debt. strategies considered. Costs are shown at different return periods, to highlight which strategies are 3.3. Figure Z3.1 presents the relative cost savings of cheapest at covering the average loss, loss events of a Strategies B, C, and D on average, under the base lower magnitude, and more extreme loss events. For assumptions. the Country Z case study, the cost of the four strategies outlined above over the following return periods are considered: • On average • 1 in 10 year return period • 1 in 30 year return period. Figure Z3 .1 – Relative Cost Saving of Finance Strategies, Base Case Scenario, Average Cost 50% • The average cost of Strategy B (insurance) is around 30 Percentage cost decrease (increase) relative to Strategy A percent higher than the average cost of Strategy A. This is 40% because the insurance premium payable covers for higher 30% loss scenarios. 20% • The average cost of Strategy C (budget reallocation) is around 3 percent higher than the average cost of Strategy 10% A. This is because the hurdle rate is higher than the -29% -3% 1% 0% assumed cost of post-disaster debt. -10% • The average cost of Strategy D (contingent credit) is around 1 percent lower than the average cost of Strategy -20% A. This is because the contingent credit interest rate is -30% lower than the government borrowing rate. -40% -50% B C D Average Source: Clarke, Cooney, Edwards, and Jinks (2016). 36 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE Figure Z3 .2 – Relative Cost Saving of Finance Strategies, 1 in 10 Year Return Period Loss 50% 3.4. Figures Z3.2 and Z3.3 demonstrate the same analysis at Percentage cost decrease (increase) relative to Strategy A the 1 in 10 and 1 in 30 return periods. 40% • At the 1 in 10 return period, Strategies B, C, and D do 30% not require post-disaster debt to be issued because 20% the finance instrument are sufficient to meet the losses. 10% 6% 1% -4% • Strategy B starts to appear cheaper (relative to 0% Strategy A) as the size of the premium relative to the -10% size of the loss reduces. -20% • The cost of Strategy C (with budget reallocation) continues to be the higher than Strategy A because -30% of the high hurdle rate. -40% • The cost of Strategy D (with contingent credit) -50% is the cheapest because of the relatively low B C D contingent credit interest rate. 1 in 10 year return period of loss Source: Clarke, Cooney, Edwards, and Jinks (2016). Figure Z3 .3 – Relative Cost Saving of Finance Strategies, 1 in 30 Year Return Period Loss 90% • For greater losses at higher return periods, Strategy B is Percentage cost decrease (increase) relative to Strategy A 81% 80% significantly (at the 1 in 30 year, 81 percent) cheaper than 70% other strategies because a significant proportion of the 60% large losses are ceded to the insurer. 50% • Strategy C (with budget reallocation) has the highest cost 40% because of the high hurdle rate. 30% • The cost of Strategy D (with contingent credit) is slightly 20% lower than the costs of Strategies A and C because of the 10% 2% relatively low contingent credit interest rate. -4% 0% -10% -20% -30% -40% -50% B C D 1 in 30 year return period of loss Source: Clarke, Cooney, Edwards, and Jinks (2016). EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 37 Figure Z3.4 – Cost of Finance Strategies, Base Case Assumptions 300 250 Total cost (US$m) 200 150 100 50 0 A B C D A B C D A B C D Average 1 in 10 year return period of loss 1 in 30 year return period of loss Reserve Fund Contingent Credit Insurance Budget reallocation Post-disaster debt Source: Clarke, Cooney, Edwards, and Jinks (2016). 3.5. While Figures Z3.1, Z3.2, and Z3.3 compare the relative 4. Country Z – Sensitivity Results cost saving of the strategies at different return periods, it does not allow a direct comparison of the magnitude 4.1. Country Z case study considers sensitivity analysis to: of the costs. Figure Z3.4 shows the cost, in monetary • The economic and financial assumptions used to terms of the different strategies at the different return derive the costs of the strategies periods. • The maximum amount of losses covered by the 3.6. The main conclusions from the base case scenario are: different finance strategies. • The costs of Strategy B (insurance) are highest at lower return periods because the insurance Sensitivity Results: Varying the Economic and premium exceeds the average loss (which is roughly Financial Assumptions at the 1 in 7 year return period). 4.2. A marginal cost analysis for each finance instrument is • At higher return periods, the costs of Strategy B used to demonstrate their features and benefits over are significantly lower than the costs of the other varying return periods. The marginal cost analysis in strategies as losses are passed onto the insurer. Annex Z3 demonstrates the intuitive notion that as the economic cost of a finance source increases, the • Strategy C always has the greatest cost due to the attractiveness of that source decreases, namely: relatively higher budget reallocation costs compared to other finance instruments. • Reserves are marginally the cheapest finance instrument up to approximately the 1 in 7.6 year • At the return periods shown, the cost of Strategy D return period, after which post-disaster debt is lower than the cost of Strategies A and C because becomes the cheapest instrument. the assumed interest rate of contingent credit is much lower than the costs associated with budget 4.3. The results indicated by the marginal costs analysis reallocation or post-disaster debt issuance. are dependent on the financial and other assumptions 38 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE selected. If these assumptions are varied the outcomes 5. Country Z – can be materially different. Sensitivity to economic parameters for each of these finance instruments is also Concluding Remarks demonstrated in Annex Z3. The results vary intuitively 5.1. The analysis shows that when considering tropical as the economic parameters are adjusted and the cyclone events, losses which are of a lower impact following can be noted: and occur more frequently are likely to be most cost- • Increasing the insurance risk volatility loading effectively financed by contingent credit. However, decreases the cost benefit gained from insurance. there is unlikely to be sufficient contingent credit available to provide cover for larger losses and hence • Increasing the delay factor makes post-disaster debt post-disaster debt is likely to be required. less attractive. 5.2. Post-disaster debt is assumed to have the lowest • Increasing the spread between the investment and marginal cost at the higher loss events. However, borrowing rates increases the marginal cost of the strategies with insurance attaching at a lower return reserves as it increases the cost of holding reserve period had a much lower total cost – reflecting the fact funds which may not be called on. that using insurance results in losses being ceded to the • Similarly, increasing the interest charged on insurer. contingent credit reduces the cost benefit of the 5.3. The most cost-effective strategy will depend on the contingent credit. risk tolerance of policy makers and realistic amounts • Decreasing the budget reallocation hurdle rate available from each financial instrument. In practice, increases the cost-effectiveness of the budget the government may wish to combine insurance with reallocation layer. another instrument such that only a percentage of the layer is ceded out for reinsurance, and the rest is Sensitivity Results: Varying Maximum Funding financed through other instruments. The impact of only by Finance Instrument ceding a percentage of the layer would be similar to that of reducing the insurance exhaustion point. 4.4. The results shown in the base case scenario are dependent on the amount of funding assumed to be available by each financial instrument. Sensitivity to the size of the layers is demonstrated through examination of the total cost analysis. The results (see Annex Z4 for details) vary intuitively as the amounts available from each financial instrument are adjusted, with the following key results: • Increasing the amount of financing available from reserve and budget instruments reduces the cost at higher return periods because fewer finance costs are met by budget reallocation and post-disaster debt, which are typically more expensive. • Decreasing the exhaustion point (maximum loss covered) of insurance demonstrates that at higher return periods, post-disaster debt is now required, hence increasing the total cost. EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 39 Guidance Note The purpose of this Guidance Note is to give guidance • Contingent credit on the steps that should normally be taken to conduct • Emergency ex-post budget reallocations an evaluation of alternative of sovereign disaster risk finance strategies. This note should be read in conjunction • Ex-post direct credit (borrowing/ post-disaster debt) with the formulae and descriptions in the World Bank Policy Research Working Paper, “Evaluating Sovereign Define which instruments will act to finance the contingent Disaster Risk Finance Strategies: A Framework,” by D.J. liability, in which order, and to what extent. Clarke, O. Mahul, R. Poulter, and T.-L. Teh (hereafter, the • The minimum and maximum point at which each Framework Paper). instrument will finance the liability, as well as the total maximum funding available from each instrument should be defined. 1. Define Contingent Liability • The source of the financing may be from national or Define the expenditures (or losses) that would be financed subnational government, or from development partners. by government and/or development partners in the Any application of the framework should include a aftermath of potential future natural disasters (for example, suitable caveat about how much reliance can be placed tropical cyclones, earthquakes, floods, droughts). on the results by a government if the funding sources The underlying expenditures considered should have a clear is unspecified. element of uncertainty and a way to probabilistically model • One of the instruments will require an assumption that it this uncertainty through a set of simulated expenditures. is unlimited so that the entire contingent liability can be Typically expenditures are simulated over a 12 month fully financed. This is usually assumed to be post-disaster period, to coincide with agricultural or tropical cyclone debt. seasons, or the annual budgeting period of government. This data on simulated expenditures might come from a Each combination of one or more instruments that in natural catastrophe model, from a distribution fitted to aggregate can precisely finance the entire contingent historic loss data, or from other sources. The contingent liability is then considered a strategy. Typically comparing liability being considered for financing could be a truncation three to four overall strategies yields the most insight or a layer of the underlying expenditures (losses). without introducing too many considerations or assumptions. 2. Define Finance Strategies 3. Set Base Assumptions and Layers Assumptions about the economic and Select potential financial instruments to be considered and commercial environment in which combination, such as: • Interest rates (that is, borrowing rates) should normally • Risk transfer instruments including insurance, be taken to be consistent with market-implied interest reinsurance, catastrophe swaps, and catastrophe bonds rates for sovereign debt, consistent with the currency • Reserves / ex-ante budget allocations 40 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE used for analysis (that is, for analysis in US$, Eurobond 4. Calculate Results under debt rates issued in US$ should be used). Base Assumptions • The discount rate used to discount costs incurred in the future into present day terms should normally be chosen to equal the marginal interest rate on pre-disaster Calculate the opportunity cost for each strategy for each sovereign debt. simulation of the contingent liability: • The investment return on undisbursed contingency funds • Refer to the Framework Paper for formulae to calculate or budgets should normally be chosen to be consistent the opportunity cost of each financial instrument with the asset classes the funds or budget lines are depending on the quantum of the layer financed by the invested in. This is expected to be lower than the market- instrument. These formulae may be adjusted where implied interest rate. appropriate, for example, to allow for a different rule of thumb for pricing risk transfer instruments. • The hurdle rate of return for projects that would have funding cut in the case of budget reallocations can be • Demonstrating the savings of certain alternative taken from any government rules on the social rate of strategies compared to a base strategy is a helpful way to return required on projects, or other economic studies present results. of the internal rate of return of public expenditure. • This will typically be for 10,000 or more simulated The hurdle rate may vary for different tranches of annual expenditures; however, 5,000 simulations is likely reallocations (that is, the first few US$m of reallocations sufficient to consider lower return periods. might be subject to a lower hurdle rate than the next few US$m). For simplicity, it is usually best to set one hurdle Present the resulting opportunity cost results at rate and assume a limit on the maximum amount of return periods that are relevant for or requested by the budget reallocation available that might be subject to this stakeholders of the analysis. hurdle rate. • For example, for catastrophic natural disasters • Where possible, ex-post borrowing rates and delay factors (tropical cyclone, earthquake), at the mean, 1 in 10 should be taken from economic studies. and 1 in 50 year results may be relevant. • Rules of thumb for pricing risk transfer instruments • For disasters such as flood or drought, at least the should be designed to approximate market pricing as mean, 1 in 5 and 1 in 30 year results may be relevant. closely as possible. In some circumstances it may be appropriate to make different assumptions depending on the source of funds, for example, if some parts of government or some development partners are able to offer budget reallocations at lower opportunity cost than others. However, typically it may be reasonable to set assumptions that are neutral to the source of the funding – that is, such that they could apply to funding from the government or from external development partners. EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 41 5. Consider Relevant Sensitivities 6. Conclude on Risk and Re-Calculate Results Finance Implications Sensitivities involve considering alternative parameters A combination of base result and sensitivity analysis for the layers, economic assumptions, or risk should demonstrate: transfer assumptions. • Which strategies tend to have the lowest opportunity • Sensitivities may be driven by the uncertainty of certain costs on average and at various return periods parameters (for example, discount rate) or by the • Which assumptions and parameters have the greatest political landscape of the country (such as, available impact on the results. emergency budget reallocation may be very limited, but it is insightful to consider what significantly increasing this Reporting should summarise the conclusions, and also might do to the risk finance strategies). consider any limitations of the analysis or any additional implicit assumptions that have been made. • Economic assumption sensitivities can be succinctly presented through the use of marginal opportunity The most cost-effective strategy will depend on the cost charts. assumptions, the risk tolerance of policy makers, and potentially other considerations. Any conclusions and Re-calculate the results as in (4) and consider how the results also need to be interpreted in the context of the assumptions changes impact which strategies are the most objectives of the stakeholders of the analysis. cost-effective at various return periods. 42 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 43 Country V Annexes Annex V1 – Contingent Liability Figure AV1.1 demonstrates the cumulative distribution function of the costs associated with supporting food insecure households in districts across the country affected by drought. This cumulative distribution function of the contingent liability demonstrates a long tail of extreme potential losses. The sensitivity of the assumed loss distribution is considered further in Annex V4 and the alternative loss distributions considered are also shown in Figure V1.1. Figure AV1.1 – Cumulative Distribution Function of the Poverty Cost Due to Drought 3000 2500 2000 Loss (US$m) 1500 1000 500 Baseline Sensitivity: Increased Contingent Liability 0 Sensitivity: Decreased Contingent Liability 0% 20% 40% 60% 80% 100% Cumulative Probability Source: Clarke, Cooney, Edwards, and Jinks (2016). Annex V2 – Assumptions Reserve fund assumptions (all strategies) Under all strategies, initial losses are retained through a reserve fund. The base case assumes that the reserve fund is assumed to be equal to US$50m, which is equal to a 1 in 1.3 year event. The cost of reserve funds reflects the assumption that Country V has to borrow to fund the reserves and has to pay interest on the amount borrowed. While this is offset by the investment returns achieved on the reserves, the investment returns are typically assumed to be lower than the borrowing rate. The economic assumptions required for calculating the cost of reserve fund are therefore: 44 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE • Discount rate used to discount costs incurred in the future into present day terms • Interest rate on amounts that are borrowed to fund reserve fund • Investment return earned on reserve funds not used to finance costs. The interest rate charged on amounts borrowed to fund the reserve fund is assumed to be 6.625 percent. The reserve fund is assumed to be invested in low risk assets, hence it is assumed that the investment return earned is equal to the borrowing rate, minus a spread of 3 percent. For simplicity, it is assumed that the discount rate is the same as the borrowing rate – varying this assumption does not have a material effect on any conclusions drawn in this case study. Post-disaster debt assumptions (all strategies) Delay factor for post-disaster debt response: This is the impact on benefit costs due to a delay in providing response (for example, due to reliance on slow finance instruments such as post-disaster debt). Currently this is assumed to be equivalent to a factor of 3, such that US$1 early (immediate financing of drought losses) is equivalent to US$3 late (post-disaster debt- financed), based on a review of literature on this topic for this country. Insurance assumptions (Strategy B) Strategy B assumes that insurance will start to payout once the reserve fund has been exhausted. The base case insurance contract structure is defined as follows: • Insurance Coverage: The attachment point is 1 in 1.3 year losses when the reserve fund is exhausted. The insurance layer is assumed to cover losses up to the 1 in 30 year event (equivalent to US$433.4m). • Insurance Premium: The annual premium payable is US$105m for drought cover. The assumed premium was set using a pricing multiple of 1.35, which is representative of the drought peril insured at the time of writing this paper. Fees and expenses associated with insurance mechanisms are assumed to be included within the premium. Budget reallocation assumptions (Strategy C) Strategy C assumes that once the reserve fund has been exhausted, Country V will reallocate existing budgets to fund the finance costs. The base case assumes that Country V is able to reallocate budgets equal to US$100m, such that, together with the reserve fund, the maximum budget available to finance costs is US$150m (equivalent to a 1 in 3.6 year event). It is assumed that the cost of reallocating budgets is a hurdle rate of 10 percent. Annex V3 – Sensitivity Analysis: Economic and Financial Assumptions Marginal cost – base case scenario Figure AV3.1 compares the marginal cost (as a multiple of expected loss in layer) for the various finance sources under the base case assumptions. The marginal cost represents the additional cost of each risk finance instrument per unit of annual average loss in layer, for a specific return period. EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 45 Figure AV3.1 – Marginal Cost as a Multiple of Loss, Base Case Assumptions 3.5 per $1 of annual average scale up expenditure Annual average economic cost of nancing, 3.0 2.5 2.0 1.5 1.0 Post Disaster Debt - Delay actor o 3 Insurance multiple o 1.35 0.5 Budget reallocation - 10% hurdle rate Reserve Fund - 3% spread 0.0 0 5 10 15 20 25 30 35 40 45 50 Return period of scale up expenditure Source: Clarke, Cooney, Edwards, and Jinks (2016). • The reserve fund has a marginal cost increasing in the return period due to the difference between the cost of borrowing funds (the interest rate) and the investment return earned on unspent reserves, which is lower. At losses at higher return periods, the reserve fund is less likely to be called on and therefore more likely to incur a cost of holding funds. • Post-disaster debt has a cost of exactly 3 times the loss at all return periods by definition of the delay factor of 3. It is assumed that US$1 of aid provided early costs US$3 when the response is provided late. • Insurance has a cost of 1.35, reflecting the constant assumed 1.35 insurance pricing multiple. • Budget reallocation has a constant marginal cost of 1.03 under the base case scenario, representing the spread between the hurdle rate (10 percent) and the discount rate (6.625 percent). The marginal cost does not reflect the limitations and budgetary constraints of various finance sources – most notably funds available through some instruments are cost-effective but very limited. The graph implies that theoretically, budget reallocation is most cost-effective for high finance cost return periods. However, this ignores the fact that there might be a limit on the extent to which government budgets can be reallocated. Where the different lines of marginal cost intersect is where one finance strategy becomes marginally more cost-effective than another: • Reserve funds are the cheapest finance instrument up the 1 in 2.1 year return period. • For losses greater than the 1 in 2.1 year loss, budget reallocation is always marginally the cheapest finance instrument. • Reserve funds remain the second cheapest between the 1 in 2.1 year and the 1 in 13.4 year loss, after that insurance is the second cheapest. 46 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE Marginal cost - sensitivities Figures AV3.2 and AV3.3 consider the impact on the marginal cost of adjusting the following economic and financial assumptions: Figure AV3.2 – Marginal Cost as a Multiple of Loss, Sensitivity to the Spread on the Reserve Fund and Insurance Pricing Multiple 3.5 per $1 of annual average scale up expenditure Annual average economic cost of nancing, 3.0 2.5 2.0 Post Disaster Debt - Delay actor o 3 1.5 Insurance multiple o 1.35 Insurance multiple o 2.0 1.0 Reserve Fund - 3% spread Reserve Fund - 5% spread 0.5 Reserve Fund - 1% spread Budget reallocation - 10% hurdle rate 0.0 0 5 10 15 20 25 30 35 40 45 50 Return period of scale up expenditure Source: Clarke, Cooney, Edwards, and Jinks (2016). • Increasing the spread between the interest rate and investment return of the reserve fund increases the slope of the marginal cost line, such that the reserve fund becomes less cost-effective. • Similarly, increasing the insurance pricing multiple increases the point at which insurance becomes marginally the least cost-effective strategy compared to reserve fund. EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 47 Figure AV3.3 – Marginal Cost as a Multiple of Loss – Sensitivity to the Post-Disaster Debt Delay Factor and the Budget Reallocation Hurdle Rate 3.5 per $1 of annual average scale up expenditure Annual average economic cost of nancing, 3.0 2.5 2.0 Insurance multiple o 1.35 1.5 Post Disaster Debt - Delay actor o 3 Post Disaster Debt - Delay actor o 1.5 1.0 Budget reallocation - 10% hurdle rate Budget reallocation - 20% hurdle rate 0.5 Budget reallocation - 40% hurdle rate Reserve Fund - 3% spread 0.0 0 5 10 15 20 25 30 35 40 45 50 Return period of scale up expenditure Source: Clarke, Cooney, Edwards, and Jinks (2016). • Reducing the post-disaster finance delay factor shifts down the horizontal line showing the post-disaster finance cost, such that it is significantly cheaper. • Increasing the budget reallocation hurdle rate reduces the cost-effectiveness of budget reallocation and increases the period over which contingency funds are the most cost-effective strategy. Annex V4 – Sensitivity Analysis: Varying Maximum Funding by Finance Instrument Increased reserve fund coverage Figures AV4.1 and AV4.2 show the cost of the three strategies over different return periods, assuming that the reserve fund is increased to US$132.1m (the average loss). For the alternative finance strategies considered: • For Strategy B, it is assumed that insurance still attaches after the reserve fund and is assumed to cover losses up to the 1 in 30 year event. • For Strategy C, it is assumed that the government is still able to reallocate budgets equal to US$100m, such that, together with the reserve fund, the maximum budget available to finance losses is US$232.1m (equivalent to a 1 in 7.4 year event). 48 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE Figure AV4 .1 – Relative Cost Saving of Strategies under Increased Reserve Fund 100% 90% 83% 80% Percentage cost decrease (relative to Strategy A) 70% 60% 50% 40% 38% 36% 30% 27% 20% 19% 19% 10% 0% B C B C B C Average 1 in 5 year return period of loss 1 in 30 year return period of loss Source: Clarke, Cooney, Edwards, and Jinks (2016). Figure AV4.2 – Total Cost of Increased Reserve Fund 1,200 1,000 Total cost (US$m) 800 600 400 200 0 A B C A B C A B C Average 1 in 5 year return period of loss 1 in 30 year return period of loss Reserve Fund Insurance Budget reallocation Post-disaster debt Source: Clarke, Cooney, Edwards, and Jinks (2016). • Increasing the reserve fund decreases the average costs for all three strategies as there are more losses met from the reserve fund, which is the most cost-effective strategy. • Strategy B is still the cheapest, both on average and at the return periods considered. Increasing the reserve fund decreases the cost savings of Strategy B relative to Strategy A as there are additional losses covered by the reserve fund in both strategies; hence the costs under both strategies are closer. • Strategy C is still cheaper than Strategy A, but the relative savings at the higher return periods are increased. This is because there is the same absolute cost saving (in US$ terms) between Strategies A and C. EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 49 Increased underlying contingent liability Figures AV4.3 and AV4.4 show the cost of the three strategies over different return periods, assuming that contingent losses are 25 percent higher. For the alternative finance strategies considered: • In all strategies it is assumed that the level of reserve fund is unchanged at US$50m (note that this is exhausted in all simulations as the minimum loss is US$128m). • Strategy B assumes that insurance still attaches after the reserve fund and is assumed to cover finance costs up to the higher 1 in 30 year event (which is now US$634m). • Strategy C assumes that the government is still able to reallocate budgets equal to US$100m, such that, together with the reserve fund, the maximum budget available to finance costs is US$150m (equivalent to a 1 in 1.2 year event). Figure AV4 .3 – Relative Cost Saving of Strategies under Increased Underlying Contingent Liability 100% 90% 82% 80% Percentage cost decrease (relative to Strategy A) 70% 64% 60% 49% 50% 40% 30% 29% 23% 20% 11% 10% 0% B C B C B C Average 1 in 5 year return period of loss 1 in 30 year return period of loss Source: Clarke, Cooney, Edwards, and Jinks (2016). 50 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE Figure AV4.4 – Total Cost of Increased Underlying Contingent Liability 2,000 1,800 1,600 Total cost (US$m) 1,400 1,200 1,000 800 600 400 200 0 A B C A B C A B C Average 1 in 5 year return period of loss 1 in 30 year return period of loss Reserve Fund Insurance Budget reallocation Post-disaster debt Source: Clarke, Cooney, Edwards, and Jinks (2016). • Increasing the contingent liabilities increases the average costs for all strategies and the costs at all return periods considered. • The cost savings of Strategy C relative to Strategy A is reduced, particularly at higher return periods because the size of the layers is unchanged and hence more losses are covered by post-disaster debt. Decreased underlying contingent liability Figures AV4.5 and AV4.6 show the cost of the three strategies over different return periods, assuming that contingent losses are 25 percent lower. For the alternative finance strategies considered: • In all strategies it is assumed that the size of the reserve fund is unchanged at US$50m (equivalent to a 1 in 5.2 year event). • Strategy B assumes that insurance still attaches after the reserve fund and is assumed to cover finance costs up to the lower 1 in 30 year event (which is now US$233m). • Strategy C assumes that the government is still able to reallocate budgets equal to US$100m, such that, together with the reserve fund, the maximum budget available to finance costs is US$150m (equivalent to a 1 in 14.5 year event). EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 51 Figure AV4 .5 – Relative Cost Saving of Strategies under Decreased Underlying Contingent Liability 100% 88% 80% Percentage cost decrease (relative to Strategy A) 60% 40% 34% 33% 30% 20% -46% 0% 0% -20% -40% -60% B C B C B C Average 1 in 5 year return period of loss 1 in 30 year return period of loss Source: Clarke, Cooney, Edwards, and Jinks (2016). Figure AV4.6 – Total Cost of Decreased Underlying Contingent Liability 700 600 500 Total cost (US$m) 400 300 200 100 0 A B C A B C A B C Average 1 in 5 year return period of loss 1 in 30 year return period of loss Reserve Fund Insurance Budget reallocation Post-disaster debt Source: Clarke, Cooney, Edwards, and Jinks (2016). • Decreasing the contingent liabilities decreases the average costs for all strategies at all return periods considered. • Strategy B is still the most cost-effective strategy on average and at higher return periods. • At lower return periods, Strategy B is more expensive than Strategy A. This is because at these low return periods, losses are met from the reserve fund. However the insurance premium is still payable. • The cost savings of Strategy C relative to Strategy A is reduced at lower return periods and on average. This is because at these low return periods, losses are met from the reserve fund and hence the costs are identical under Strategies A and C. At higher return periods, the cost savings of Strategy C is more pronounced as a higher share of the loss is met from budget reallocation. 52 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE Country W Annexes Annex W1 – Contingent Liability Figure AW1.1 demonstrates the cumulative distribution function of the public capital losses relating to the cost of poverty due to flood. This cumulative distribution function of the contingent liability demonstrates a long tail of extreme potential losses. Both historical data and the fitted distribution assume a US$100 per person cost. Figure AW1.1 – Cumulative Distribution Function of the Poverty Cost Due to Flood 1,600 1,400 1,200 1,000 USD Millions 800 600 400 200 Fitted distribution 0 Historic data 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Source: Clarke, Cooney, Edwards, and Jinks (2016). Annex W2 – Assumptions Reserve fund assumptions (all strategies) Under all strategies, initial intial losses are retained through a reserve fund. The base case assumes that the reserve fund is assumed to be equal to US$100m, which is equal to a 1 in 2.3 year event. The cost of reserve funds reflects the assumption that Country W has to borrow to fund the reserves and has to pay interest on the amount borrowed. While this is offset by the investment returns achieved on the reserves, the investment returns are typically assumed to be lower than the borrowing rate. The economic assumptions required for calculating the cost of reserve fund are therefore: • Discount rate used to discount costs incurred in the future into present day terms • Interest rate on amounts that are borrowed to fund reserves EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 53 • Investment return earned on reserve not used to fund the losses. The interest rate charged on amounts borrowed to fund the reserves is assumed to be 13 percent. The fund is assumed to be invested in low risks assets, hence it is assumed that the investment return earned is equal to the borrowing rate, minus a spread of 10 percent. For simplicity, it is assumed that the discount rate is the same as the borrowing rate – varying this assumption does not have a material effect on any conclusions drawn in this case study. Post-disaster debt assumptions (all strategies) Delay factor for post-disaster debt response: This is the impact on benefit costs due to a delay in providing response (for example, due to reliance on slow finance instruments such as post-disaster debt). Currently this is assumed to be equivalent to a factor of 3, such that US$1 early (immediate financing of response costs) is equivalent to US$3 late (post-disaster debt- financed). A factor of 3 is assumed in line with recent World Bank research. Insurance assumptions (Strategy B) Strategy B assumes that insurance will start to pay out once the reserve fund has been exhausted. The base case insurance contract structure is defined as follows: • Insurance Coverage: The attachment point is the 1 in 2.3 year losses when the reserve fund is exhausted. The insurance layer is assumed to cover losses up to the 1 in 30 year event. • Insurance Premium: The annual premium payable is US$101.7m for flood cover. The assumed premium was set using a pricing multiple of 1.5, which is representative of the flood perils insured at the time of writing this paper. Fees and expenses associated with insurance mechanisms are assumed to be included within the premium. Contingent credit assumptions (Strategy C) Strategy C assumes that Country W has contingent credit arrangements to provide immediate liquidity in the aftermath of a flood event. It is assumed that Country W can secure contingent credit of up to a maximum of US$100m, set equal to the reserve fund maximum for easier comparison. To derive the opportunity cost of contingent credit, it is assumed that Country W would otherwise have to borrow the amount of the line of contingent credit from the commercial market (at the government’s ex-ante borrowing rate) in order to finance the same portfolio of expenditures. As a result, the opportunity cost of contingent credit depends not only on the assumed contingent credit interest rate but also the spread between the interest rate on amounts borrowed and the contingent credit interest rate. The economic assumptions required for calculating the cost of contingent credit are therefore: • Discount rate used to discount costs incurred in the future into present day terms • Interest rate on amounts that are borrowed (the ex-ante borrowing rate) • The interest rate charged on contingent credit. 54 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE Contingent credit interest rates, such as catastrophe risk deferred drawdown options, are set based on a spread over LIBOR. Based on current US$ LIBOR rates and IBRD lending rates, a contingent credit interest rate of 2.5 percent is assumed. In addition to the contingent credit interest rate, contingent credit arrangements such as catastrophe risk deferred drawdown options charge fees for establishing these lines of credit. For simplicity, it is assumed that there is a single front- end fee of 0.5 percent of the maximum loan amount. Annex W3 – Sensitivity Analysis: Economic and Financial Assumptions Marginal cost – base case scenario Figure AW3.1 compares the marginal cost (as a multiple of expected loss in layer) for the various finance sources under the base case assumptions. The marginal cost represents the additional cost of each risk finance instrument per unit of annual average loss in layer, for a specific return period. Figure AW3.1 – Marginal Cost as a Multiple of Loss, Base Case Assumptions 3.5 per $1 of annual average scale up expenditure Annual average economic cost of nancing, 3.0 2.5 2.0 1.5 1.0 Reserves - 10% spread Post Disaster Financing Delay actor o 3.0 0.5 Contingent Credit - 2.5% interest Insurance pricing multiple o 1.5 0.0 0 5 10 15 20 25 30 35 40 45 50 Return period of loss Source: Clarke, Cooney, Edwards, and Jinks (2016). • The reserve fund has an increasing marginal cost due to the difference between the cost of borrowing funds (the interest rate) and the investment return earned on funds held in reserves, which is lower. At higher return periods, the reserve fund is less likely to be called on and therefore more likely to incur a cost of holding funds. • Contingent credit similarly has an increasing marginal cost due to the difference between the cost of borrowing funds (interest/discount rate) and the investment return earned on the amount of contingent credit unused, which is lower. This spread (10.5 percent being the difference between 13.0 percent and 2.5 percent) is greater than for the reserve fund and so the marginal cost increases more sharply. EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 55 • Post-disaster debt has a cost of exactly 3 times the loss at all return periods by definition of the delay factor of 3. It is assumed that US$1 of aid provided early costs US$3 when the response is provided late. • Insurance has a cost of 1.5, reflecting the constant assumed 1.5 insurance pricing multiple. The marginal cost does not reflect the limitations and budgetary constraints of various finance sources – most notably funds available through some instruments are cost-effective but very limited. The graph implies insurance is most cost-effective at high return periods. Where the different lines of marginal cost intersect is where one finance strategy becomes marginally more cost-effective than another: • Reserves are the cheapest finance instrument up the 1 in 7 year return period. • For losses greater than the 1 in 7 year loss, insurance is always marginally the cheapest financing instrument. • Reserves remain the second cheapest between the 1 in 7 year and the 1 in 24 year loss, after that post-disaster debt is the second cheapest. Marginal cost - sensitivities Figure AW3.2 and AW3.3 consider the impact on the marginal cost of adjusting the following economic and financial assumptions: • Increasing (decreasing) the spread between the interest rate and investment return of the reserve increases (decreases) the slope of the marginal cost line, such that the reserve becomes less (more) cost-effective. • Similarly, increasing the interest earned on contingent credit facilities not used to fund losses reduces the “spread” of this instrument, reducing the slope of this line and making contingent credit more cost-effective. Figure AW3.2 – Marginal Cost as a Multiple of Loss, Sensitivity to the Spread on the Reserve Fund and Contingent Credit 3.5 per $1 of annual average scale up expenditure Annual average economic cost of nancing, 3.0 2.5 2.0 1.5 Insurance pricing multiple o 1.5 Post Disaster Financing Delay actor o 3.0 1.0 Contingent Credit - 2.5% interest Contingent Credit - 5.0% interest 0.5 Reserves - 10% spread Reserves - 5% spread 0.0 Reserves - 15% spread 0 5 10 15 20 25 30 35 40 45 50 Return period of loss Source: Clarke, Cooney, Edwards, and Jinks (2016). 56 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE • Increasing the insurance pricing multiple increases the point at which insurance becomes marginally the least cost- effective strategy compared to reserves and contingent credit financing. • Decreasing the post-disaster finance delay factor shifts down the vertical line showing the post-disaster finance cost, such that it becomes a more cost-effective option – if the delay factor is lower than the insurance pricing multiple, then post- disaster debt becomes the cheapest strategy beyond a certain return period. Figure AW3.3 – Marginal Cost as a Multiple of Loss – Sensitivity to the Post-Disaster Debt Delay Factor and the Insurance Multiple 3.5 per $1 of annual average scale up expenditure Annual average economic cost of nancing, 3.0 2.5 2.0 1.5 Insurance pricing multiple o 1.5 Insurance pricing multiple o 2.0 1.0 Post Disaster Financing Delay actor o 3.0 0.5 Post Disaster Financing Delay actor o 1.4 Contingent Credit - 2.5% interest 0.0 Reserves - 10% spread 0 5 10 15 20 25 30 35 40 45 50 Return period of loss Source: Clarke, Cooney, Edwards, and Jinks (2016). Annex W4 – Sensitivity Analysis: Varying Maximum Funding by Finance Instrument Reduced insurance coverage FIgures AW4.1 and AW4.2 show the cost of the three strategies over different return periods, assuming that the insurance layer covers only 50 percent of the losses between the reserve fund (1 in 2.3 year return period) and the 1 in 30 year return period loss. The remaining 50 percent is assumed to be funded by post-disaster debt. EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 57 Figure AW4 .1 – Relative Cost Saving of Reduced Insurance Layer 45% 43% 40% 40% Percentage cost decrease 35% (relative to Strategy A) 30% 30% 25% 23% 20% 18% 15% 14% 10% 5% 0% B C B C B C Average 1 in 5 year return period of loss 1 in 30 year return period of loss Source: Clarke, Cooney, Edwards, and Jinks (2016). Figure AW4.2 – Total Cost of Reduced Insurance Layer 1,600 1,400 1,200 Total cost (US$m) 1,000 800 600 400 200 0 A B C A B C A B C Average 1 in 5 year return period of loss 1 in 30 year return period of loss Reserve Fund Contingent Credit Insurance Post-disaster debt Source: Clarke, Cooney, Edwards, and Jinks (2016). • On average and at lower return periods, the total cost of Strategy B is now higher compared to Strategy C. This is because fewer losses are covered by insurance and more losses are covered by the more expensive post-disaster debt. On average, however, Strategy B is still cheaper than Strategy A. • Decreasing the insurance layer shows that at higher return periods, post-disaster debt is now required, hence increasing the total cost of Strategy B. While it is still cheaper than the other strategies at the 1 in 30 year return period, the saving is not as great due to the requirement for post-disaster debt. 58 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE Increase layers of non-insurance finance arrangements Figures AW4.3 and AW4.4 demonstrate the cost of the three strategies above over different return periods, assuming that the layers of non-insurance instruments are increased by 50 percent. Figure AW4 .3 – Relative Cost Saving of Increasing Non-Insurance Layers 100% 90% 82% 80% Percentage cost decrease (relative to Strategy A) 70% 60% 50% 43% 40% 40% 31% 30% 25% 23% 20% 10% 0% B C B C B C Average 1 in 5 year return period of loss 1 in 30 year return period of loss Source: Clarke, Cooney, Edwards, and Jinks (2016). Figure AW4.4 – Total Cost of Increasing Non-Insurance Layers 1,400 1,200 Total cost (US$m) 1,000 800 600 400 200 0 A B C A B C A B C Average 1 in 5 year return period of loss 1 in 30 year return period of loss Reserve Fund Contingent Credit Insurance Post-disaster debt Source: Clarke, Cooney, Edwards, and Jinks (2016). EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 59 • In this sensitivity scenario, the reserve covers losses up to the 1 in 3.1 year return period and contingent credit covers losses between the 3.1 year and 7.2 year return period. • Strategy B is still the cheapest on average and at the 1 in 5 and 1 in 30 year return periods, because the layer of losses financed by contingent credit (up to the 7.2 year loss) is still significantly lower than the layer of losses financed by insurance (up to the 30 year loss), with the remainder financed by the more expensive post-disaster debt. • However, compared to the base scenario, the savings offered by Strategy B compared to Strategy A are decreased, because there is not as much post-disaster debt required in Strategy A (which drove up the overall cost in the base scenario). • Similarly, the savings offered by Strategy C compared to Strategy A are decreased compared to the base scenario, due to the lower level of post-disaster debt required. 60 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE Country X Annexes Annex X1 – Contingent Liability Figure AX1.1 demonstrates the cumulative distribution function of poverty losses caused by reduced crop yields that arise from all perils. This cumulative distribution function of the contingent liability demonstrates a long tail of extreme potential losses. Figure AX1.1 – Cumulative Distribution Function of the Yield Loss Due to All Perils 120 100 80 Loss (US$m) 60 40 20 0 0% 20% 40% 60% 80% 100% Cumulative Probability Source: Clarke, Cooney, Edwards, and Jinks (2016). Annex X2 – Assumptions Reserve fund assumptions (all strategies) Under all strategies, initial losses are retained through a reserve fund. The base case assumes that the reserve fund is assumed to be equal to US$20m, which is equal to a 1 in 2.5 year event. The cost of reserve funds reflects the assumption that Country X has to borrow to fund the reserves and has to pay interest on the amount borrowed. While this is offset by the investment returns achieved on the reserves, the investment returns are typically assumed to be lower than the borrowing rate. The economic assumptions required for calculating the cost of reserve fund are therefore: • Discount rate used to discount costs incurred in the future into present day terms • Interest rate on amounts that are borrowed to fund reserves EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 61 • Investment return earned on reserve not used to fund losses. The interest rate charged on amounts borrowed to fund the reserves is assumed to be 5 percent. The fund is assumed to be invested in low risks assets, hence it is assumed that the investment return earned is equal to the borrowing rate, minus a spread of 2 percent. For simplicity, it is assumed that the discount rate is the same as the borrowing rate – varying this assumption does not have a material effect on any conclusions drawn in this case study. Post-disaster debt assumptions (all strategies) Delay factor for post-disaster debt response: This is the impact on costs due to a delay in providing response (for example, due to reliance on slow finance instruments such as post-disaster debt). Currently this is assumed to be equivalent to a factor of 3, such that US$1 early (immediate financing of flood losses) is equivalent to US$3 late (post-disaster debt-financed). A factor of 3 is assumed in line with recent World Bank research. Insurance assumptions (Strategy B) Strategy B assumes that insurance will start to pay out once the reserve fund has been exhausted. The base case insurance contract structure is defined as follows: • Insurance Coverage: The attachment point is 1 in 2.5 year loss when the reserve fund is exhausted. The insurance layer is assumed to cover losses up to the 1 in 30 year event (equivalent to US$52.4m). • Insurance Premium: The annual premium payable is US$6.7m for all perils cover. The assumed premium was set using a pricing multiple of 1.35, which is representative of the perils insured at the time of writing this paper. Fees and expenses associated with insurance mechanisms are assumed to be included within the premium. Budget reallocation assumptions (Strategy C) Strategy C assumes that once the reserve fund has been exhausted, Country X will reallocate existing budgets to fund the losses. The base case assumes that Country X is able to reallocate budgets equal to US$20m, such that, together with the reserve fund, the maximum budget available to finance losses is US$40m (equivalent to a 1 in 10.7 year event). It is assumed that the cost of reallocating budgets is 20 percent. 62 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE Annex X3 – Sensitivity Analysis: Economic and Financial Assumptions Marginal cost – base case scenario Figure AX3.1 compares the marginal cost (as a multiple of expected loss in layer) for the various finance sources under the base case assumptions. The marginal cost represents the additional cost of each risk finance instrument per unit of annual average loss in layer, for a specific return period. Figure AX3.1 – Marginal Cost as a Multiple of Loss, Base Case Assumptions 3.5 per $1 of annual average scale up expenditure Annual average economic cost of nancing, 3.0 2.5 2.0 1.5 1.0 Budget reallocation - 20% hurdle rate Insurance Multiple o 1.35 0.5 Post Disaster Financing Delay actor o 3 0.0 Reserves -2% spread 0 5 10 15 20 25 30 35 40 45 50 Return period of scale up expenditure Source: Clarke, Cooney, Edwards, and Jinks (2016). • The reserve fund has an increasing marginal cost due to the difference between the cost of borrowing funds (the interest rate) and the investment return earned on funds held in reserves, which is lower. At losses at higher return periods, the reserve fund is less likely to be called on and therefore more likely to incur a cost of holding funds. • Post-disaster debt has a cost of exactly 3 times the loss at all return periods by definition of the delay factor of 3. It is assumed that US$1 of aid provided early costs US$3 when the response is provided late. • Insurance has a cost of 1.35, reflecting the constant assumed 1.35 insurance pricing multiple. • Budget reallocation has a constant marginal cost of 1.14 under the base case scenario, representing the spread between the hurdle rate (20 percent) and the discount rate (5 percent). The marginal cost does not reflect the limitations and budgetary constraints of various finance sources – most notably funds available through some instruments are cost-effective but very limited. The graph implies that theoretically, budget reallocation is most cost-effective for high finance cost return periods. However, this ignores the fact that there might be a limit on the extent to which government budgets can be reallocated. EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 63 Where the different lines of marginal cost intersect is where one finance strategy becomes marginally more cost-effective than another: • Reserves are the cheapest finance instrument up the 1 in 8.5 year return period. • For losses greater than the 1 in 8.5 year loss, budget reallocation is always marginally the cheapest finance instrument. • Reserves remain the second cheapest between the 1 in 8.5 year and the 1 in 19.4 year loss, after that insurance is the second cheapest. Marginal cost - sensitivities Figures AX3.2 and AX3.3 consider the impact on the marginal cost of adjusting economic and financial assumptions: Figure AX3.2 – Marginal Cost as a Multiple of Loss, Sensitivity to the Spread on the Reserve Fund and budget Reallocation Hurdle Rate 3.5 per $1 of annual average scale up expenditure Annual average economic cost of nancing, 3.0 2.5 2.0 Insurance Multiple o 1.35 1.5 Post Disaster Financing Delay actor o 3 Reserves -2% spread 1.0 Reserves -4% spread Budget reallocation - 20% hurdle rate 0.5 Budget reallocation - 10% hurdle rate Budget reallocation - 40% hurdle rate 0.0 0 5 10 15 20 25 30 35 40 45 50 Return period of scale up expenditure Source: Clarke, Cooney, Edwards, and Jinks (2016). • Increasing the spread between the interest rate and investment return of the reserve increases the slope of the marginal cost line, such that the reserve becomes less cost-effective. • Similarly, increasing (decreasing) the budget reallocation hurdle rate increases (decreases) the marginal cost of budget reallocation and increases (decreases) the point to which the reserves remain the cheapest instrument. 64 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE Figure AX3.3 – Marginal Cost as a Multiple of Loss, Sensitivity to the Post-Disaster Debt Delay Factor and the Insurance Multiple 5.0 per $1 of annual average scale up expenditure Annual average economic cost of nancing, 4.5 4.0 3.5 3.0 2.5 Insurance Multiple o 1.35 2.0 Insurance Multiple o 2 1.5 Post Disaster Financing Delay actor o 3 Post Disaster Financing Delay actor o 1.5 1.0 Post Disaster Financing Delay actor o 5 0.5 Budget reallocation - 20% hurdle rate Reserves -2% spread 0.0 0 5 10 15 20 25 30 35 40 45 50 Return period of scale up expenditure Source: Clarke, Cooney, Edwards, and Jinks (2016). • Increasing the insurance pricing multiple increases the point at which insurance becomes marginally the least cost- effective strategy compared to reserves and budget reallocation. In fact, increasing the multiple to 2 means that the reserve fund and budget reallocation always has a lower marginal opportunity cost than insurance. • Increasing the post-disaster finance delay factor shifts up the horizontal line showing the post-disaster finance cost, such that it is now significantly more expensive than the other strategies. Annex X4 – Sensitivity Analysis: Varying Maximum Funding by Finance Instrument Reduced reserve fund coverage Figure AX4.1 and AX4.2 show the cost of the three strategies above over different return periods, assuming the reserve fund is reduced to US$10m (1 in 1.4 year return period). For the alternative finance strategies considered: • Strategy B assumes that insurance still attaches after the reserve fund and is assumed to cover losses up to the 1 in 30 year event. • Strategy B assumes that the government is still able to reallocate budgets equal to US$20m, such that, together with the reserve fund, the maximum budget available to finance losses is US$30m (equivalent to a 1 in 5.1 year event). EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 65 Figure AX4 .1 – Relative Cost Saving of Reduced Reserve Fund 100% 90% 82% 80% Percentage cost decrease (relative to Strategy A) 70% 65% 60% 53% 50% 42% 40% 37% 30% 27% 20% 10% 0% B C B C B C Average 1 in 5 year return period of loss 1 in 30 year return period of loss Source: Clarke, Cooney, Edwards, and Jinks (2016). Figure AX4.2 – Total Cost of Reduced Reserve Fund 160 140 120 Total cost (US$m) 100 80 60 40 20 0 A B C A B C A B C Average 1 in 5 year return period of loss 1 in 30 year return period of loss Reserve Fund Insurance Budget reallocation Post-disaster debt Source: Clarke, Cooney, Edwards, and Jinks (2016). • Decreasing the reserve fund increases the average costs for all three strategies as there are more losses met from post- disaster debt in Strategies A and C (which is the least cost-effective strategy) and there is an increase in the premium in Strategy B. • Strategy B is still the cheapest, both on average and at the return periods considered. Decreasing the reserve fund increases the cost savings of Strategy B relative to Strategy A as the additional losses previously covered by the reserve fund are ceded to the insurer (at the marginal cost of the assumed insurance price multiple of 1.35), which is cheaper than the additional losses covered by post-disaster debt (at a marginal cost of the assumed delay factor of 3). • Strategy C is still cheaper than Strategy A, but the relative savings at the higher return periods are reduced as post-disaster debt begins to dominate the total cost of both strategies. 66 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE Increased reserve fund coverage Figure AX4.3 and AX4.4 show the cost of the three strategies above over different return periods, assuming that the reserve fund is increased to US$30m (1 in 1.4 year return period). For the alternative finance strategies considered: • Strategy B assumes that insurance still attaches after the reserve fund and is assumed to cover losses up to the 1 in 30 year event. • Strategy C assumes that the government is still able to reallocate budgets equal to US$20m, such that, together with the reserve fund, the maximum budget available to finance losses is US$50m (equivalent to a 1 in 24.7 year event). • Increasing the reserve reduces the average costs for all three strategies as there are more losses met from the reserve in all strategies, which is the most cost-effective strategy at lower return periods. • While Strategy B is still the cheapest on average, at the 1 in 5 return period Strategy A is now more cost-effective. This is because the reserve is sufficient to meet 1 in 5 year events and hence the insurance is not called on but the premium is still payable. • As in the baseline assumptions, costs at the 1 in 5 year period are higher than the average costs for all strategies. This is because the average loss under the assumed distribution is smaller than the 1 in 5 year loss (see Annex 1 for the assumed distribution of losses). • At the 1 in 5 return period, the cost of Strategy A and C are identical because there is no need for budget reallocation. • At higher return periods, Strategy B is still the cheapest strategy. EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 67 Figure AX4 .3 – Relative Cost Saving of Increased Reserve Fund 70% 66% 60% Percentage cost decrease 50% (relative to Strategy A) 40% 28% 30% 20% 15% 14% 10% -10% 0% 0% -10% -20% B C B C B C Average 1 in 5 year return period of loss 1 in 30 year return period of loss Source: Clarke, Cooney, Edwards, and Jinks (2016). Figure AX4.4 – Total Cost of Increased Reserve Fund 120 100 Total cost (US$m) 80 60 40 20 0 A B C A B C A B C Average 1 in 5 year return period of loss 1 in 30 year return period of loss Reserve Fund Insurance Budget reallocation Post-disaster debt Source: Clarke, Cooney, Edwards, and Jinks (2016). 68 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE Country Y Annexes Annex Y1 – Underlying Contingent Liability Figure AY1.1 represents the undiversified total payout/cost function in Strategy A. There is a discrete increase at approximately 90 percent to a multiple of 4 times the premium. This is consistent with the fact the initial payout is triggered at the 1 in 10 return period, which corresponds to a 90th percentile (slightly greater for some regions due to multiple events occurring in one year). There is a plateau at payouts of 10 times the premium after approximately the 96.7th percentile (corresponding to 1 in 30), with a step in between of 8 times the premium for years with multiple events. Figure AY1.1 – Cumulative Distribution Function for Undiversified Total Payouts/Costs 10 9 Payment as a multiple of premium 8 7 6 5 4 3 2 1 0 - region perils (undiversi ed) Sum all 70% 75% 80% 85% 90% 95% 100% Probability Source: Clarke, Cooney, Edwards, and Jinks (2016). Figure AY1.2 demonstrates the diversified individual distributions, summed by simulated year. Some correlation exists between neighbouring regions, as expected, but there is an overall diversification benefit. The pooled portfolio demonstrates an overall smoother loss function profile, with sharp increase to a total aggregate 10 times the premium loss; that is, even the 1 in 200 loss at the 99.5th percentile is significantly lower than the maximum loss (unlike in Figure AY1.1, where the 1 in 200 loss is also the maximum loss). EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 69 Figure AY1.2 – Cumulative Distribution Functions for Pooled Cover (by Peril and in Aggregate) Individual Pooled Pooled Fully Insurance Earthquake Tropical Pooled 10 Payment as a multiple of premium Contracts Only Cyclone 9 Only 8 1 in 200 10 6.3 5.4 3.8 loss 7 6 (as multiple of base 5 premium) 4 Maximum 10 8.1 8.0 5.9 3 simulated (1 in 10,000) 2 loss 1 (as multiple 0 of base 70% 75% 80% 85% 90% 95% 100% premium) Probability Sum Tropical Cyclone Sum Earthquake Sum All Source: Clarke, Cooney, Edwards, and Jinks (2016). Annex Y2 – Base Case Scenario Assumptions Economic assumptions Initial payouts (in Strategy C) are retained through a reserve fund. The cost of reserve funds reflects the assumption that Country Y has to borrow to fund the reserves and has to pay interest on the amount borrowed. While this is offset by the investment returns achieved on the reserves, the investment returns are typically assumed to be lower than the borrowing rate. The economic assumptions required for calculating the cost of reserve fund are therefore: • Discount rate used to discount costs incurred in the future into present day terms • Interest rate on amounts that are borrowed to fund reserves • Investment return earned on reserve not used to fund payouts. The retained payouts are assumed to be fully capitalised; that is, the pooled facility is assumed to hold capital reserves at a level equal to the maximum expected payout in the retained layer. For simplicity and because the focus of this case study is on different insurance strategies, the discount rate, interest rate, and investment return are assumed to all be equal. The simplifying result of this combination of assumptions is that the cost of financing the retained payouts is equal to the costs occurred in the retained layer, with no cost charged on the capital reserves held in excess of the loss incurred. Risk transfer assumptions Under Strategy A the average insurance pricing multiple based on the individual insurance contracts is 1.64 (determined based on the premium divided by the average annual loss). 70 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE Two key assumptions were made in comparing the insurance price of Strategies B and C: • Diversification benefit (Strategy B): The diversification benefit that can be achieved by moving from Strategy A to Strategy B and pooling the risks of all regions • Reinsurance pricing (Strategy C): The (re)insurance pricing multiple applied to excess losses in Strategy C. Strategy B diversification benefit Based on a pool of the cumulative underlying risk, the resulting cumulative distribution function (CDF) follows a smoother distribution (than the individual risks) and there is a diversification benefit arising from the pooling of all risks. This is demonstrated in Figure AY1.2 in Annex Y1. With the evidence that a diversification benefit exists, assumptions were made about the size of this benefit (that is, the discount on premiums charged) through consideration of the following metrics: • The insurance pricing multiple (premium divided by average annual loss) • The implied risk volatility loading to demonstrate the premium charged to compensate for the level of volatility in the underlying losses (see Glossary). Strategy A assumes a summation of all CDFs across all regions and perils with no diversification benefit (see Figure AY1.1 in Annex Y). Strategy B has an inherent diversification benefit incorporated, as it is summing across 13 regions by simulated year rather than by CDF ranked from best scenario (no losses) to worst scenario (maximum payout for each region). Some correlation exists between neighbouring regions, as expected, but there is an overall diversification benefit (see Figure AY1.2 in Annex Y1). Therefore, as a starting point, comparing Strategy B with Strategy A, it is intuitively expected that: • The risk volatility loading to be higher: This is because Strategy A would have a relatively high standard deviation value due to the nature of the defined payouts being a step function with a more extreme maximum than any pooled loss distributions in Strategies B. A relatively greater standard deviation value would result in a relatively lower risk volatility loading base amount. • The pricing multiple to be lower, due to the diversification benefit achieved in Strategy B. The initial parameter for the diversification benefit from Strategy B was set as 10 percent: • It is evident that there should be some level of diversification, but without real-time market pricing insight it is difficult to set an initial parameter. Ten percent was chosen for simplicity and to demonstrate the difference in cost between Strategy A and B. • It is intuitive that any diversification benefit greater than 2.5 percent (which is the additional fee charged for pooling) will result in Strategy B being more cost-effective. • While this approach may not be robust enough for market pricing purposes, it is sufficient for the purposes of the evaluation of the finance strategies in this case study and will allow us to reach a reasonable conclusion, keeping the limitation on parameter robustness in mind. EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 71 Strategy C pricing multiple The resulting assumption for the pricing multiple in Strategy C was set based on a reasonable level of the risk volatility loading compared to Strategy B. The pricing multiple is expected to be greater in Strategy C than Strategy B due to the higher layer of risk being written and the greater volatility in the layer. A summary of the base case scenario assumptions and diagnostics are outlined in Table AY2.2. Table AY2.2 – Diagnostics of Insurance Pricing Assumptions, Base Case Strategy A Strategy B Strategy C Diversification benefit 10% Pricing multiple 1.64 1.47 2.00 Risk volatility loading 52% 38% 25% Source: Clarke, Cooney, Edwards, and Jinks (2016). Market and administration fees There are fees assumed to be placed on the risk transfer mechanisms: • Strategy B and C both have a 2.5 percent market fee charged on the premium for the layer placed in the insurance market. • Strategy C has a 5 percent administrative fee charged on the retained layer. Annex Y3 – Sensitivity Analysis The analysis considered sensitivities to key assumptions as follows: • Strategy B diversification benefit: increase from 10 percent to 20 percent • Strategy C insurance pricing multiple: reduce from 2.0 to 1.47 • Strategy C economic assumptions relevant to the risk retention: increase the spread (between the interest rate and investment return) from 0 percent to 5 percent. For the first two sensitivities, the insurance pricing assumptions are considered, in Table AY3.1 were considered which decrease the cost of insurance premiums in both Strategy B and C, as outlined by the resulting pricing multiples in Table AY3.1. 72 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE Table AY3.1 – Diagnostics of Insurance Pricing Assumptions, Sensitivities Strategy A Strategy B - sensitivity Strategy C - sensitivity Diversification benefit N/A 20% N/A Pricing multiple 1.64 1.31 1.47 Risk volatility loading 52% 25% 12% Source: Clarke, Cooney, Edwards, and Jinks (2016). For the third sensitivity, the following dynamics with the economic assumptions apply: • Increasing the discount rate and/or decreasing the investment rate (that is, increasing the spread between the investment rate and the discount rate) will increase the cost. To demonstrate this, a spread of 5 percent (such that the discount rate is 5 percent higher than the investment rate) is assumed. Additional parameters and sensitivities that have not been considered are outlined in Table AY3.2. Table AY3.2 – Assumptions with Sensitivity Analysis Not Considered Assumption Base Parameter Justification for Not Considering Sensitivity Analysis Spread between 0% No sensitivity analysis considered as a more material and relevant spread is interest rate & (interest rate = 4%; the one between investment return and interest rate. discount rate discount rate = 4%) Market fee 2.5% The magnitude of how much these assumptions will vary is likely to be significantly smaller than the assumptions around premium pricing for Strategy B and C. Administration 5% fee The direction of movement in overall cost is intuitively obvious and there is minimal additional insight to be gained in varying these assumptions – the costs will increase proportionally and evenly for all return periods (since premiums are consistent) as the fees increase. EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 73 Country Z Annexes Annex Z1 – Contingent Liability Figure AZ1.1 demonstrates the cumulative distribution function of the public capital losses relating to tropical cyclone damage. This cumulative distribution function of the contingent liability demonstrates a long tail of extreme potential losses, which is the nature of catastrophic tropical cyclone exposure. It is the same shape as the underlying total tropical cyclone losses (the losses are just a 30 percent proportion of total tropical cyclone losses). Public capital losses have been capped at the 1 in 50 year return period (approximately US$300m or 2.5 percent of GDP). Losses beyond this magnitude are assumed to require significant donor support in any finance strategy – the cost of this donor support would be consistent for all strategies and is excluded from this analysis. Figure AZ1.1 – Cumulative Distribution Function of the Public Losses 100% 90% 80% 70% Cumulative probability 60% 50% 40% 30% 20% 10% 0% 0 50 100 150 200 250 300 Loss ($USD millions) Source: Clarke, Cooney, Edwards, and Jinks (2016). 74 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE Annex Z2 – Assumptions Reserve fund assumptions (all strategies) Under all strategies, initial losses are retained through a reserve fund. The base case assumes that the reserve fund is assumed to be equal to 0.2 percent of GDP, which is broadly equivalent to a 1 in 6 year event. The cost of reserve funds reflects the assumption that Country Z has to borrow to fund the reserves and has to pay interest on the amount borrowed. While this is offset by the investment returns achieved on the reserves, the investment returns are typically assumed to be lower than the borrowing rate. The economic assumptions required for calculating the cost of reserve fund are therefore: • Discount rate used to discount costs incurred in the future into present day terms • Interest rate on amounts that are borrowed to fund reserves • Investment return earned on reserve not used to fund finance costs. The interest rate charged on amounts borrowed to fund the reserves is assumed to be 6.75 percent, which is the yield on long- term bonds issued by Country Z in US$. The fund is assumed to be invested in low risk assets, hence it is assumed that the investment return earned is equal to the borrowing rate, minus a spread of 3 percent. For simplicity, it is assumed that the discount rate is the same as the borrowing rate – varying this assumption does not have a material effect on any conclusions drawn in this case study. Post-disaster debt assumptions (all strategies) All strategies assume that large losses (that is, those that exhaust the additional financial instruments described below) are met by post-disaster debt issued by Country Z. A post-disaster debt delay factor of 18.44 percent is assumed based on assumptions that: • Emergency public losses account for 23 percent of losses. • The internal rate of return for emergency public losses is 40 percent. • The internal rate of return for non-emergency public losses is 12 percent. • There is a one-year delay in building both emergency and non-emergency reconstruction. Insurance assumptions (Strategy B) Strategy B assumes that insurance will start to pay out once the reserve fund has been exhausted. The base case insurance contract structure is defined as follows: • Insurance Coverage: The attachment point is 1 in 6 year loss when the reserve fund is exhausted. The insurance layer is assumed to cover losses up to the 1 in 30 year event. EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 75 • Insurance Premium: The annual premium payable is US$23.5m for tropical cyclone cover. The assumed premium was set with consideration of the following metrics: • The pricing multiple (premium divided by annual average loss) • The implied risk volatility loading to demonstrate the premium charged to compensate for the level of volatility in the underlying losses (see Glossary). The base case assumes a constant risk volatility loading of 25 percent. For the assumed attachment point and layer, this is equivalent to a pricing multiple of 1.85. It should be noted that if the risk volatility loading is assumed to be constant then the equivalent pricing multiple increases (decreases) as the assumed attachment point increases (decreases) and the assumed layer decreases (increases). This is because the volatility of insured losses increases as the attachment point increases, and hence insurers charge a higher premium for the extra volatility. Fees and expenses associated with insurance mechanisms are assumed to be included within the premium. Budget reallocation assumptions (Strategy C) Strategy C assumes that once the reserve fund has been exhausted, Country Z will reallocate existing budgets to fund the losses. The base case assumes that Country Z is able to reallocate budgets equating to 0.8 percent of GDP, such that, together with the reserve fund, the maximum budget available to finance losses is 1 percent of GDP (roughly equivalent to a 1 in 17 year event). It is assumed that the cost of reallocating budgets is 37 percent, based on economic modelling. Contingent credit assumptions (Strategy D) Strategy D assumes that Country Z has contingent credit arrangements to provide immediate liquidity in the aftermath of a tropical cyclone event. It is assumed that Country Z can secure contingent credit of up to a maximum of US$30m, which is approximately 0.25 percent of GDP, consistent with current World Bank arrangements.1 To derive the cost of contingent credit, it is assumed that Country Z would otherwise have to borrow the amount of the line of contingent credit from the commercial market (at the government’s ex-ante borrowing rate) in order to finance the same portfolio of expenditures. As a result, the cost of contingent credit depends not only on the assumed contingent credit interest rate but also the spread between the interest rate on amounts borrowed and the contingent credit interest rate. The economic assumptions required for calculating the cost of contingent credit are therefore: • Discount rate used to discount costs incurred in the future into present day terms • Interest rate on amounts that are borrowed (the ex-ante borrowing rate) • The interest rate charged on contingent credit. Contingent credit interest rates, such as catastrophe risk deferred drawdown options are set based on a spread over LIBOR. Based on current US$ LIBOR rates and IBRD lending rates, a contingent credit interest rate of 2.5 percent is assumed. 1 http://treasury.worldbank.org/bdm/pdf/Handouts_Finance/CatDDO_Product_Note.pdf 76 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE In addition to the contingent credit interest rate, contingent credit arrangements such as catastrophe risk deferred drawdown options charge fees for establishing these lines of credit. For simplicity, a single front-end fee of 0.5 percent of the maximum loan amount is assumed. Annex Z3 – Sensitivity Analysis: Economic and Financial Assumptions Marginal cost – base case scenario Figure AZ3.1 compares the marginal cost (as a multiple of expected loss in layer) for the various financial instruments under the base case assumptions. The marginal cost represents the additional cost of each risk finance instrument per unit of annual average loss in layer, for a specific return period. Figure AZ3.1 – Marginal Cost as a Multiple of Loss, Base Case Assumptions 3.5 Annual average economic cost of nancing, 3.0 per $1 of annual average respose cost 2.5 2.0 1.5 Insurance Risk Volatility Loading o 25% 1.0 Post Disaster Financing Delay actor o 1.18 Contingent Credit - 2.50% interest 0.5 Budget reallocation - 37% hurdle rate 0.0 Reserves -3% spread 0 5 10 15 20 25 30 35 40 45 50 Return period of loss Source: Clarke, Cooney, Edwards, and Jinks (2016). • The reserve fund has an increasing marginal cost due to the difference between the cost of borrowing funds (the interest rate) and the investment return earned on funds held in reserves, which is lower. For losses at higher return periods, the reserve fund is less likely to be called on and therefore more likely to incur a cost of holding funds. • Contingent credit similarly has an increasing marginal cost due to the difference between the cost of borrowing funds (interest/discount rate) and the investment return earned on the amount of contingent credit unused, which is lower. This spread (4.25 percent being the difference between 6.75 percent and 2.5 percent) is greater than for the reserve fund and so the marginal cost increases more sharply. EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 77 • Post-disaster debt has a cost of 1.18 times the loss at all return periods. • Budget reallocation has a constant marginal cost of approximately 1.30 under the base case scenario, with 30 percent being approximately the spread between the hurdle rate (37 percent) and the discount rate (6.75 percent). • The marginal cost for insurance is derived from the change in insurance premium that results from insurance attaching US$1 higher. Attaching insurance at a higher return period increases the marginal cost of insurance (note that the unsmooth curve of the insurance marginal cost is a result of the number of simulations used). This is because a constant risk volatility loading is assumed and as the attachment point increases, the uncertainty in the loss increases. When expressed relative to the loss amount, it is therefore cheaper for insurance to attach at a lower level. The marginal cost does not reflect the limitations and budgetary constraints of various financial instruments – most notably funds available through some instruments (for example, contingent credit) are cost-effective but very limited. The graph implies post-disaster debt is most cost-effective for high loss return periods. Where the different lines of marginal cost intersect is where one finance strategy becomes marginally more cost-effective than another: • Reserves are the cheapest finance instrument up the 1 in 7.6 year return period. • For losses greater than the 1 in 7.6 year loss, post-disaster debt financing is always marginally the cheapest finance instrument. • Reserves remain the second cheapest between the 1 in 7.6 year and the 1 in 11.1 year loss, after that budget reallocation is the second cheapest. • Beyond the 1 in 5 year, insurance and contingent credit are marginally the most expensive finance instruments (assuming that insurance attaches at these higher return periods). Note that the last bullet may at first sight appear inconsistent with Figure Z3.4, which shows that at higher return periods, Strategy B (insurance) is the cheapest strategy. This is because the marginal cost presented in Figure AZ3.1 assumes that insurance attaches at the return period shown on the x-axis. In our baseline assumptions, Strategy B assumes that insurance attaches at the 1 in 6 year loss. As a result, Strategy B ‘locks in’ the marginal cost of insurance at the 1 in 6 year level, which is much lower. Or alternatively, Figure AZ3.1 demonstrates that it is much more cost-effective for insurance to attach at lower return periods. Marginal cost - sensitivities Figures AZ3.2, AZ3.3 and AZ3.4 consider the impact on the marginal cost of adjusting the following economic and financial assumptions: 78 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE Figure AZ3.2 – Marginal Cost as a Multiple of Loss, Sensitivity to the Spread on the Reserve Fund and The Budget Reallocation 3.5 Annual average economic cost of nancing, per $1 of annual average response cost 3.0 2.5 2.0 Insurance Risk Volatility Loading o 25% Post Disaster Financing Delay actor o 1.18 1.5 Contingent Credit - 2.50% interest Budget reallocation - 50% hurdle rate 1.0 Budget reallocation - 10% hurdle rate Budget reallocation - 37% hurdle rate 0.5 Reserves -1% spread Reserves -5% spread 0.0 Reserves -3% spread 0 5 10 15 20 25 30 35 40 45 50 Return period of loss Source: Clarke, Cooney, Edwards, and Jinks (2016). • Increasing (decreasing) the spread between the interest rate and investment return of the reserve increases (decreases) the slope of the marginal cost line, such that the reserve becomes less (more) cost-effective. • Increasing (decreasing) the budget reallocation hurdle rate shifts up the horizontal line showing the budget reallocation marginal cost, such that budget reallocation becomes less (more) cost-effective. Figure AZ3.3 – Marginal Cost as a Multiple of Loss, Sensitivity to the Post-Disaster Debt Delay Factor and the Insurance Multiple 3.5 Annual average economic cost of nancing, per $1 of annual average response cost 3.0 2.5 2.0 Insurance Risk Volatility Loading o 25% 1.5 Insurance Risk Volatility Loading o 45% Insurance Risk Volatility Loading o 12.5% 1.0 Post Disaster Financing Delay actor o 1.18 Post Disaster Financing Delay actor o 1.38 0.5 Contingent Credit - 2.50% interest Budget reallocation - 37% hurdle rate Reserves -3% spread 0.0 0 5 10 15 20 25 30 35 40 45 50 Return period of loss Source: Clarke, Cooney, Edwards, and Jinks (2016). EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 79 • Increasing (decreasing) the risk volatility loading decreases (increases) the point at which insurance becomes marginally the least cost-effective strategy. • Increasing the post-disaster finance delay factor shifts up the horizontal line showing the post-disaster finance cost, such that it becomes a less cost-effective option. Figure AZ3.4 – Marginal Cost as a Multiple of Loss, Sensitivity to the Contingent Credit Assumptions 3.5 per $1 of annual average scale up expenditure Annual average economic cost of nancing, 3.0 2.5 2.0 1.5 Insurance Risk Volatility Loading o 25% Post Disaster Financing Delay actor o 1.18 1.0 Contingent Credit - 2.50% interest Contingent Credit - 1.00% interest Contingent Credit - 2.00% ee 0.5 Budget reallocation - 37% hurdle rate Reserves -3% spread 0.0 0 5 10 15 20 25 30 35 40 45 50 Return period of loss Source: Clarke, Cooney, Edwards, and Jinks (2016). • Reducing the interest rate charged on contingent credit investment return increases the slope of the marginal cost line, such that contingent credit becomes less cost-effective. • Increasing the fee to 2 percent of the contingent credit maximum, increases the marginal cost slightly, such that contingent credit becomes less cost-effective. Annex Z4 – Sensitivity Analysis: Varying Maximum Funding by Finance Instrument Reduced insurance layer Figures AZ4.1 and AZ4.2 show the relative cost savings and overall costs of the four strategies over different return periods, assuming that the insurance layer covers only finance costs up to the 1 in 15 year return period. 80 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE Figure AZ4.1 – Relative Cost Saving of Reduced Insurance Layer 30% 27% 26% 25% Percentage cost decrease 20% (relative to Strategy A) 15% 10% 6% 5% 2% -11% -3% 1% -4% -4% 0% -5% -10% -15% B C D B C D B C D Average 1 in 10 year return period of loss 1 in 30 year return period of loss Source: Clarke, Cooney, Edwards, and Jinks (2016). Figure AZ4.2 – Total Cost of Reduced Insurance Layer 300 250 Total cost (US$m) 200 150 100 50 0 A B C D A B C D A B C D Average 1 in 10 year return period of loss 1 in 30 year return period of loss Reserve Fund Contingent Credit Insurance Budget reallocation Post-disaster debt Source: Clarke, Cooney, Edwards, and Jinks (2016). • Decreasing the insurance layer shows that at higher return periods, post-disaster debt is now required, hence increasing the total cost of Strategy B. While it is still cheaper than the other strategies at higher return periods, consistent with the base case scenario results, the saving is not as great due to the requirement for post-disaster debt. • On average and at lower levels of losses, the total cost of Strategy B is now lower compared to the base case scenario as the premium has reduced. On average, Strategy B is still the most expensive (consistent with the base case scenario). • At the 1 in 10 year return period Strategy B becomes more cost-effective strategy (contrary to the base case scenario where Strategy D was cheapest at this level of loss) since losses are fully covered up to the 1 in 10 year loss, but the premium is lower than the base case scenario premium (due to the overall reduced coverage). EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 81 Increase layers of non-insurance finance arrangements Figure AZ4.3 and AZ4.4 demonstrate the relative cost savings and overall costs of the four strategies over different return periods, assuming that the layers of non-insurance arrangements are doubled. Figure AZ4.3 – Relative Cost Saving of Increasing Non-Insurance Layers 80% 72% 60% Percentage cost decrease (relative to Strategy A) 40% 20% 2% 4% -25% -4% -42% 0% -1% -7% 0% -20% -40% -60% B C D B C D B C D Average 1 in 10 year return period of loss 1 in 30 year return period of loss Source: Clarke, Cooney, Edwards, and Jinks (2016). Figure AZ4.4 – Total Cost of Increasing Non-Insurance Layers 300 250 Total cost (US$m) 200 150 100 50 0 A B C D A B C D A B C D Average 1 in 10 year return period of loss 1 in 30 year return period of loss Reserve Fund Contingent Credit Insurance Budget reallocation Post-disaster debt Source: Clarke, Cooney, Edwards, and Jinks (2016). 82 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE • In this sensitivity scenario, the average costs of Strategies A, C, and D increase slightly. This is because losses up to the 1 in 11 year return period are met by reserve funds which become marginally more expensive than post-disaster debt beyond the 1 in 7.6 year loss (see Figure AZ3.1). • The average cost of strategy B reduces slightly, because there is a reduction in the premium payable, due to the higher attachment point (though this is partially offset by the higher equivalent pricing multiple that results from the assumed constant risk volatility loading). • At the 1 in 10 year return period, the cost of Strategies A and C are identical because losses are met by reserve funds in both strategies. Although losses are also met by reserve funds in Strategies B and D, the cost is higher due to the contingent credit arrangement fee and insurance premium. For Strategy D, the difference is small; however, for Strategy B, the insurance premium means the cost is 42 percent higher than Strategy A. • At the higher return periods, Strategy B continues to be the most cost-effective; however the cost savings of Strategy B relative to Strategy A are reduced. This is because losses up to the 1 in 11 year return period are met by reserve funds, which become marginally more expensive, and because it is less cost-effective to attach insurance at a higher level. EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE 83 Glossary Average A number expressing the central or typical value in a set of data. In this report, average refers to the mean, which is calculated by dividing the sum of the values in the set by the number of values (data points) in the set. Average Annual The average (mean) annual loss to a layer, calculated by summing all losses above the layer Loss minimum and below the layer maximum in the relevant simulations and dividing by the total number of simulations. Budget The release of resources originally designated for a different purpose to cover costs associated reallocation with financing losses due to disasters considered. Capital reserves The funds held in respect of a potential contingent liability, typically held by insurers or any party taking on an element of risk. Contingent credit Financing credit available from a source to a recipient which is contingent on a trigger (for example, a natural disaster occurring), and for which the recipient pays a set-up fee as a percentage of the total credit available. Contingent liability A potential payment obligation that may be incurred depending on the outcome of a future event. Cost / Opportunity The cost of an alternative use of the finance that must be forgone in order to pursue a certain cost strategy. Throughout this report, references to cost imply opportunity cost. Delay factor The assumed cost increase due to delayed response. A delay factor of 1.5 corresponds to a situation where delayed response of US$1.50 has the same impact as US$1 of fast response cost. This delay factor is applied to financial or budgetary instruments assumed to be slow in situations where slow response is less cost-effective than fast response. Ex-ante Before an event – based on forecast results rather than actual results. For example, the ex-ante investment return is the expected return on an investment portfolio. Ex-post Subsequently to an event – based on actual results rather than forecast results. For example, the ex-post investment return is the known investment return that was achieved on an investment portfolio. Hurdle rate Rate of return on foregone investments, specifically considered in the context of budget reallocation. This rate is also used to calculate the (opportunity) cost of the insurance premiums that will need to be paid by government or development partners. Insurance (risk An arrangement by which a company undertakes to provide a guarantee of compensation for transfer product) specified loss in return for payment of a specified premium. Insurance The trigger point at which insurance will start to pay, for example an insurance attachment of attachment US$5m, means that losses that are smaller than US$5m would not trigger a payout from the insurance contract. Insurance The maximum point to which insurance will cover losses, for example, phrased as up to the 1 in 30 exhaustion year loss or up to a loss of US$100m. (insurance limit) 84 EVALUATING SOVEREIGN DISASTER RISK FINANCE STRATEGIES: CASE STUDIES AND GUIDANCE Marginal cost The additional average opportunity cost of each risk finance instrument (such as, insurance) per unit of annual average loss, for losses at a specific return period. Opportunity cost The cost of an alternative use of the finance that must be forgone in order to pursue a certain strategy. Parametric A type of insurance that does not indemnify the pure loss (that is, the pure response costs insurance incurred), but ex ante agrees to make a payment upon the occurrence of a triggering event. This is common for natural disaster insurance where the trigger might be the severity of a windstorm or the magnitude of an earthquake on a Richter scale. Pricing multiple Premium Pricing multiple = Average Annual Loss A factor applied to expected losses by an insurance company to determine the premium required for the insured risk. This factor would reflect the cost of capital and expense costs of the insurance company. Return period (of An indication of the likelihood of an event occurring; a recurrence interval demonstrating how loss) frequently an event is expected to occur. For example, an event or a loss with a return period of 5 years is statistically expected to recur every 5 years on average over an extended period of time (or has a 20 percent probability of occurrence). Risk finance A set of finance instruments combined to provide funds to cover the financial effect of potential strategy losses. Risk volatility Premium charged - Average Annual Loss loading Risk volatility loading = Standard deviation of loss The factor applied to the chosen measure of risk (in this case the standard deviation) by the party accepting the risk (in this case insurers), in a set of simulated losses. With Technical Input From