1. Managing Interest Rate Risk

2. Risk vs. Return As a portfolio manager, your job is to maximize your 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

3. $5 = ++++ (1.05) 234 P = $100 The one year interest rate is currently 5% and is expected to stay constant. Further, there is no liquidity premium Term Yield 5% All 5% coupon bonds sell for Par Value and YTM = Coupon Rate = Spot Rate = 5% …

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

5. 20 Year $100,000 $5000 =++++ (1.05) 23 … 20 P(Y=5%) $4,762$39,573$4,319$4,535 $4,762 $100,000 $4,535 $100,000 $4,319 $100,000 $82,270 $100,000 ++++ 12320 Macaulay Duration = 12.6 Suppose you buy a 20 Year Treasury … $5000/yr$105,000

6. 20 Year $50,000 Alternatively, you could buy a 20 Year Treasury and a 5 year STRIPS 5 Year $50,000 $63,814 5 Year $63,814 $2500/yr$52,500 (Remember, STRIPS have a Macaulay duration equal to their Term) Portfolio Duration = $100,000 $50,000 5 = 8.812.6 + $100,000 $50,000

7. 20 Year $50,000 Alternatively, you could buy a 20 Year Treasury and a 5 year Treasury 5 Year $50,000 5 Year $2500/yr$52,500 (5 Year Treasuries have a Macaulay duration equal to 4.3) Portfolio Duration = $100,000 $50,000 4.3 = 8.512.6 + $100,000 $50,000 $2500/yr $52,500

8. 20 Year $50,000 Even better, you could buy a 20 Year Treasury, and a 1 Year T-Bill $50,000 $2500/yr$52,500 (1 Year Treasuries have a Macaulay duration equal to 1) Portfolio Duration = $100,000 $50,000 1 = 6.312.6 + $100,000 $50,000 1 Year … $52,500

9. 20 Year $25,000 Alternatively, you could buy a 20 Year Treasury, a 10 Year Treasury, 5 year Treasury, and a 3 Year Treasury 10 Year $25,000 5 Year 3 Year $1250/yr Portfolio Duration = 6.08 $100,000 $25,000 12.6 + $100,000 $25,000 $1250/yr $25,000 D = 12.6 D = 7.7 D = 4.3 D = 2.7 7.7 $100,000 $25,000 4.3 + $100,000 $25,000 2.7 +

10. 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 Portfolio Duration = 1 1 Year … $105,000 However, the yield curve typically slopes up, which creates a risk/return tradeoff

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

12. Pricing DateCouponYTMPrice ($) Issue3.75%3.87%100.00 20053.753.69100.96 20063.753.48101.77 20073.753.28102.20 20083.753.04102.35 20093.752.78102.11 20103.752.55101.29 20113.75Matures100.00 A Bond’s price will always approach its face value upon maturity, but will rise over its lifetime as the yield drops

13. Length of Bond Initial Duration Duration after 5 Years Percentage Change 30 Year 15.514.2-8% 20 Year 12.610.5-17% 10 Year 7.84.4-44% Also, the change is a bond’s duration is also a non-linear function As a bond ages, its duration drops at an increasing rate