Portfolio Management

Portfolio Management Professor Brooks BA 444 02/18/08

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

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

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%

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

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)

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.)

Bank Immunization • Equation 12 -1 : $A x DA = $L x DL • What the “bank” needs to do… • If $A x DA > $L x DL 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 DA < $L x DL 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

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

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

Portfolio Management