1. Portfolio Management Professor Brooks BA 444 02/18/08

2. From this Chapter… Bonds and Risk Credit (default), Interest Change, Reinvestment Duration and Stripping of a Bond Excel Worksheet Immunization Bullet and Bank Duration Changes Asset Allocation Changes Bonds, Stocks, and Cash

3. Bond Risk Credit Risk Probability of Default Built into the Yield-to-Maturity Interest Rate Risk When rates increase, bond prices fall Sensitivity of the price change is duration Higher the coupon, lower the sensitivity Longer the maturity, higher the sensitivity Reinvestment Risk When interest rates fall, coupons are reinvested at lower rates Zero-coupon bonds do not have reinvestment risk

4. Duration as a measure of Sensitivity What is duration? Weighted average of the wait… Take present value of each payment as a percent of the value of the bond price (weight) Take the maturity of each payment (wait) Duration = Σ Weight x Wait Example with Stripping to find the YTM Spreadsheet: 10-Year, 7.5% Coupon Bond, paying semi-annual coupons, YTM is 4.77%

5. Immunization Inoculation of the bond portfolio from movements in interest rate movements Note, does not impact credit risk Offset combined effects of interest rate risk (changes) and reinvestment risk Bullet Immunization Target ending value of the bond portfolio Offsetting the interest rate risk and reinvestment risk Build Bond Portfolio with yield-to-maturity at desired rate and duration at target maturity date

6. Bullet Immunization Example From Text…Target is 10% return over six years with initial investment of $93,600 Target: $93,600 x (1.10) 6 = $165,818.11 Find a Bond (Bond Portfolio) with a yield-to-maturity of 10% and a duration of six years. Perfect Match…Zero-coupon bond with 10% yield and six years to maturity If Zero-coupon Bond not available… Book found 8-Year coupon bond with 8.8% coupon rate and 10% yield to maturity…hence it has a six year duration…(Table 12-1, pg. 260)

7. Bank Immunization Have both assets and liabilities that are interest rate sensitive Nomenclature RSA – Rate Sensitive Assets RSL – Rate Sensitive Liabilities Funds Gap – the dollar value of its RSA minus the dollar value of its RSL Bank Immunization Target $ (assets) x D (assets) = $ (liab.) x D (liab.)

8. Bank Immunization Equation 12 -1 : $ A x D A = $ L x D L What the “bank” needs to do… If $ A x D A > $ L x D L Bank has asset sensitive portfolio and net worth will fall if interest rates rise Need to reduce asset value, or asset duration or raise liability value or liability duration If $ A x D A < $ L x D L Bank has liability sensitive portfolio and net worth will fall if interest rates fall Need to raise asset value, or asset duration or reduce liability value or liability duration Because it is difficult to change liability side of the portfolio, most actions are on changing the assets

9. Changing Duration To Increase Duration… Sell short-term bonds and buy long-term bonds Sell high-coupon bonds and buy low-coupon bonds To Decrease Duration (reduce risk) Sell long-term bonds and buy short-term bonds Sell low-coupon bonds and buy high-coupon bonds Using Futures…to offset risk of rising interest rates on a bond portfolio Pages 264-265 example, will buy 99 T-Bond contracts Using Futures…to increase risk Basis point value (BPV), example on pages 265-266, will sell 58 T-Bond contracts

10. Altering Assets Just worked through the bond adjustments with hedge ratios (equations 12-2, 12-3, and 12-4) and basis points (equations 12-5, 12-6, and 12-7). Can also adjust a stock portfolio…this was from Chapter 9 using stock index futures What about cash? This is a non-employed asset of the portfolio Can use futures to increase beta (index futures) or T-Bonds to decrease duration