Managing Interest Rate Risk Risk vs Return l

Managing Interest Rate Risk

Risk vs. Return l As a portfolio manager, your job is to maximize your risk adjusted return Risk Adjusted Return = Nominal Return – “Risk Penalty” You can accomplish this by 1 of two methods: 1) Maximize the nominal return for a given level of risk 2) Minimize Risk for a given nominal return

The one year interest rate is currently 5% and is expected to stay constant. Further, there is no liquidity premium Yield 5% Term P $5 $5 + + = 2 3 4 (1. 05) … = $100 All 5% coupon bonds sell for Par Value and YTM = Coupon Rate = Spot Rate = 5%

Available Assets 1 Year Treasury Bill (5% coupon) l 3 Year Treasury Note (5% coupon) l 5 Year Treasury Note (5% coupon) l 10 Year Treasury Note (5% coupon) l 20 Year Treasury Bond (5% coupon) l STRIPS of all Maturities l How could you maximize your risk adjusted return on a $100, 000 Treasury portfolio?

Suppose you buy a 20 Year Treasury $100, 000 P(Y=5%) = 20 Year $5000/yr $105, 000 $5000 + + + 2 3 (1. 05) $4, 762 1+ $100, 000 $4, 535 2 + $100, 000 Macaulay Duration = 12. 6 … + $4, 319 $100, 000 $105, 000 (1. 05) 20 $39, 573 3+ …+ $82, 270 $100, 000 20

Alternatively, you could buy a 20 Year Treasury and a 5 year STRIPS $50, 000 20 Year $2500/yr 5 Year $63, 814 $52, 500 5 Year $63, 814 (Remember, STRIPS have a Macaulay duration equal to their Term) Portfolio Duration = $50, 000 12. 6 + $100, 000 $50, 000 $100, 000 5 = 8. 8

Alternatively, you could buy a 20 Year Treasury and a 5 year Treasury $50, 000 20 Year $50, 000 5 Year $2500/yr 5 Year $52, 500 (5 Year Treasuries have a Macaulay duration equal to 4. 3) Portfolio Duration = $50, 000 12. 6 + $100, 000 $50, 000 $100, 000 4. 3 = 8. 5

Even better, you could buy a 20 Year Treasury, and a 1 Year T-Bill $2500/yr $50, 000 20 Year $50, 000 1 Year $52, 500 … (1 Year Treasuries have a Macaulay duration equal to 1) Portfolio Duration = $50, 000 12. 6 + $100, 000 $50, 000 $100, 000 1 = 6. 3

Alternatively, you could buy a 20 Year Treasury, a 10 Year Treasury, 5 year Treasury, and a 3 Year Treasury $25, 000 D = 12. 6 20 Year $25, 000 D = 7. 7 10 Year $25, 000 D = 4. 3 5 Year $25, 000 D = 2. 7 3 Year $25, 000 $100, 000 $1250/yr 12. 6 + $25, 000 $100, 000 Portfolio Duration = 6. 08 7. 7 + $25, 000 $100, 000 4. 3 + $25, 000 $100, 000 2. 7

Obviously, with a flat yield curve, there is no advantage to buying longer term bonds. The optimal strategy is to buy 1 year T-Bills $100, 000 1 Year … $105, 000 Portfolio Duration = 1 However, the yield curve typically slopes up, which creates a risk/return tradeoff

Also, with an upward sloping yield curve, a bond’s price will change predictably over its lifetime

A Bond’s price will always approach its face value upon maturity, but will rise over its lifetime as the yield drops Pricing Date Coupon YTM Price ($) Issue 2005 2006 2007 2008 2009 2010 2011 3. 87% 3. 69 3. 48 3. 28 3. 04 2. 78 2. 55 Matures 100. 00 100. 96 101. 77 102. 20 102. 35 102. 11 101. 29 100. 00 3. 75% 3. 75 3. 75

Also, the change is a bond’s duration is also a non-linear function Length of Bond Initial Duration Percentage after 5 Years Change 30 Year 20 Year 15. 5 12. 6 7. 8 14. 2 10. 5 4. 4 -8% -17% -44% As a bond ages, its duration drops at an increasing rate