2016年-世界发展银行全球_Pricing_Partially_Guaranteed_Bonds___Valuation_of_Bonds_Benefitting_from_a_World_Bank_Partial_Guarantee_13页_874kb

Summary of "Pricing Partially Guaranteed Bonds" Occasional Paper 001/16

Core Content

This paper discusses the valuation of bonds that benefit from a partial guarantee by the World Bank, using a fictional case study of a 15-year, USD 1 billion bond issued by the fictional low-income country, Emergistan, with a USD 400 million World Bank first loss guarantee. The paper outlines four methodologies for valuing such bonds and evaluates their effectiveness in capturing the features of the guarantee.

Main Points

• World Bank Guarantee Structure: The guarantee is non-accelerable and covers the bond's interest and principal payments. It is available from the first day of issuance and rolls over as the bond amortizes, with the full guarantee amount remaining available as long as the bond is outstanding.

• Valuation Methodologies:

  1. Nominal Weighted Average Yield: A simple method that calculates a blended yield based on the proportion of guaranteed and uncovered cash flows. It does not account for the rolling feature or time value of money.
  2. Rolling Nominal Weighted Average Yield: Improves on the first method by considering the rolling nature of the guarantee, recalculating the yield each year based on the remaining guaranteed cash flows.
  3. Discounted Cash Flow (DCF): Breaks the bond cash flows into two streams and discounts them using different rates. It accounts for the time value of money but not the rolling feature.
  4. Recovery Analysis: The most comprehensive method, involving the calculation of implied annual default probability, simulation of recovery scenarios, and adjusting the bond yield to reflect the risk-adjusted yield equal to the risk-free rate plus liquidity premium.

Key Information

• Emergistan's Yield Curve: The paper provides a fictional yield curve for Emergistan, IBRD, and US Treasuries, with Emergistan's yields significantly higher than the risk-free rate, reflecting its higher credit risk.

• Guarantee Features:

  • Non-accelerable: The guarantee does not accelerate upon default.
  • First Loss Arrangement: The World Bank covers missed payments until the guarantee is fully exhausted.
  • Soft-bullet Amortization: The bond amortizes in three equal installments over the last three years.

• Results from Methodologies:

  • Methodology #1: Bond Yield = 9.4%, Implied Guarantee Value = 142 bps.
  • Methodology #2: Bond Yield = 8.2%, Implied Guarantee Value = 262 bps.
  • Methodology #3: Bond Yield = 8.2% - 9.9%, Implied Guarantee Value = 91 - 264 bps.
  • Methodology #4: Bond Yield = 7.0% - 8.1%, Implied Guarantee Value = 270 - 383 bps.

• Recovery Analysis Details:

  • Assumes a recovery rate of 25% in case of default.
  • Calculates the implied annual probability of default for Emergistan, which is 8.6% in the first year, decreasing each subsequent year based on the formula: $ P_{d_i} = 8.6% \times (1 - 8.6%)^{Y - 1} $.
  • The yield derived from this method is adjusted to reflect the risk-adjusted yield equal to the risk-free rate plus liquidity premium.

• Liquidity Premium Sensitivity:

  • A sensitivity analysis is conducted with different liquidity premiums, showing the impact on the bond yield and the implied guarantee value.
  • The yield reduction compared to a naked bond ranges from 383 bps to 270 bps depending on the liquidity premium.

Methodology Comparison

Methodology	Blending of WB and EM Yields	Rolling Feature	Time Value of Money	Bond Yield	Implied Guarantee Value
#1	✓	×	×	9.4%	142 bps
#2	✓	✓	×	8.2%	262 bps
#3	✓	×	✓	8.2% - 9.9%	91 - 264 bps
#4	✓	✓	✓	7.0% - 8.1%	270 - 383 bps

Conclusion

• Recovery Analysis is the most comprehensive method, fully capturing the time value of money and the rolling feature of the guarantee, leading to the lowest bond yields and highest implied value for the World Bank guarantee.
• The paper emphasizes that the valuation method should be chosen based on the specific features of the guarantee and the bond structure.
• A financial model is available for further analysis of planned bond issues with World Bank guarantees.