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Unformatted text preview: Measuring Interest Rate Risk Lecture Notes for Actsc 445/845  Fall 2009 Department of Statistics and Actuarial Science University of Waterloo Notes by Prof. K.S. Tan/Actsc 445/845 Chapter 9: Measuring Interest Rate Risk p. 1 Chapter Summary Recall that yieldtomaturity (ytm) is the internal rate of return. Such yield will be realized only if: the coupon payments can be reinvested at the yieldtomaturity if the bond is held to maturity What are the associated risks ? This chapter introduces ways of measuring the sensitivity of bonds: full valuation approach price value of a basis point duration/convexity approach Notes by Prof. K.S. Tan/Actsc 445/845 Chapter 9: Measuring Interest Rate Risk p. 2 Four Hypothetical Optionfree Bonds Yield 5%/5year 5%/15year 10%/5year 10%/15year 3.00% 109.2222 124.0158 132.2776 184.0554 4.00 104.4913 111.1982 126.9478 167.1894 4.50 102.2166 105.4113 124.3821 159.5247 4.90 100.4387 101.0535 122.3755 153.7298 4.99 100.0438 100.1047 121.9296 152.4654 5.00 100.0000 100.0000 121.8802 152.3257 5.01 99.9563 99.8954 121.8308 152.1863 5.10 99.5635 98.9604 121.3873 150.9390 5.50 97.8400 94.9377 119.4402 145.5609 6.00 95.7349 90.1998 117.0604 139.2009 7.00 91.6834 81.6080 112.4749 127.5881 Notes by Prof. K.S. Tan/Actsc 445/845 Chapter 9: Measuring Interest Rate Risk p. 3 Price Sensitivities of the 4 Bonds Instantaneous % change in bond prices with initial ytm 5% Yield 5%/5year 5%/15year 10%/5year 10%/15year 3.00% 9.22 24.02 8.53 20.83 4.00 4.49 11.20 4.16 9.76 4.50 2.22 5.41 2.05 4.73 4.90 0.44 1.05 0.41 0.92 4.99 0.04 0.10 0.04 0.09 5.010.040.100.040.09 5.100.441.040.400.91 5.502.165.062.004.44 6.004.279.803.958.62 7.008.3218.397.7216.24 Notes by Prof. K.S. Tan/Actsc 445/845 Chapter 9: Measuring Interest Rate Risk p. 4 Bonds Price Sensitivity The bonds price sensitivity/volatility measures how sensitive a bond is with respect to changes in market interest rates Properties of bonds price sensitivity: asymmetric percentage price change, particularly more pronounced with larger change in yield for a given (large) change in yield, the % price appreciation is of greater magnitude than the % price depreciation The degree of sensitivity of a bonds price depends on various features of the issue, e.g. maturity coupon rates yield level embedded options* Notes by Prof. K.S. Tan/Actsc 445/845 Chapter 9: Measuring Interest Rate Risk p. 5 Bonds Price Sensitivity The Impact of Maturity: lower coupon rate implies greater bonds price sensitivity Premium bond Par bond Discount bond Zerocoupon bond The Impact of Maturity: the longer the bonds maturity, the greater the bonds price sensitivity (except for some deepdiscount bonds) The Impact of Yield Level: the higher the level of interest rates, the lower the price sensitivity Notes by Prof. K.S. Tan/Actsc 445/845 Chapter 9: Measuring Interest Rate Risk p. 6 Quantifying Interest Rate Exposure Three approaches of quantifying interest rate exposure:...
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 Spring '09
 ChristianeLemieux

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