Financial Risk Management of Insurance Enterprises Review of Bond Pricing

Overview Determine the value of a stream of payments Determine the correct discount rate “Stripping” the yield curve Adjusting the risk-free discount rate Non-fixed cash flows

Some Definitions Valuation: Determining the fair value of a cash flow Cash flow: Stream of payments of a financial instrument Zero coupon security: All interest is paid at maturity with no periodic interest payments

Fixed Cash Flows No variations in payment amount or maturity –Assumes no default Examples: –Zero coupon bonds are the most basic –Noncallable US Treasury bonds All cash flows are a package of zero coupon bonds

Discounting the Cash Flow Investors demand a minimum (market) rate of interest for the use of their money –Minimum is default-free US Treasury rate Traditional discounting –Use one rate for the entire cash flow Better approach –Use one rate for each “zero coupon” payment –Market rate is determined by maturity of payment

Determining the minimum market rate of interest The treasury yield curve depicts the relationship between yields on Treasury securities and their maturities –This is the benchmark interest rate On-the-run issues: Mostly recent auction

The US Treasury Curve 3-month, 6-month, and 1-year Treasuries are discount securities –Essentially zero coupon instruments –Sold below face value with no coupons paid Longer maturity Treasuries pay coupons Yield curve is a combination of zero coupon bonds and coupon-paying bonds

Some More Definitions Yield/yield-to-maturity: Discount rate used to equate cash flow and market value –Same discount rate for all maturities Spot rate: Discount for zero coupons –One spot rate for each maturity Basis point: 0.01%, 100 b.p. = 1% Yield (or spot rate) curve: Graph of bond yield (or spot rate) by maturity

Determining the Spot Rate Curve In valuing cash flows, we discount the package of zero coupon payments –We need the discount rates for zero coupons Bootstrap method uses shorter maturity spot rates for coupon payments and determines the spot rate at the bond’s maturity

Assumptions under the Bootstrap Method No arbitrage opportunities –No one can strip coupons and sell zeroes for more than the entire bond All Treasury yields are compounded semi- annually All cash flows are fixed –No options

Example 1: Data

Example 1: Solution

Example 2: Bootstrap Method

Credit risk Up to now, we have been discounting at US Treasury yields –These are “default free” Most cash flows have risk from investors standpoint –State Farm, Allstate do not have power to tax Investors require additional payment to offset probability of default

Credit risk (p.2) Form of additional payment through coupon or market rate of interest Traditional approach to credit risk –Compare yields Modern approach –Static spread to all spot rates –Term structure of credit spreads

Example of Credit Spread Using the US Treasury curve from before, determine the static spread of an issuer whose 1½ year, 8% coupon bond is currently priced at Use trial and error –Some spreadsheet packages have a “solver”

Credit Spread Solution

Variable Cash Flows Actuarial projections predict cash flow amount and timing, but these estimates are not exact –Pensioners may request a lump sum if interest rates decrease –Life annuitants may not lapse if market rates drop –A court case may decrease the long-term liability of property/casualty companies

Common Provisions that can Alter Cash Flow Call provision –Issuer can retire entire bond early –Investors may have call protection Sinking fund –Issuer can retire bonds periodically Put feature –Investor can force redemption Prepayment provisions

Next time... Forward rates of interest Hedging and the relationship between spot rates and forward rates Term structure theories