Managing Interest Rate Risk

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

$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% …

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?

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, Macaulay Duration = 12.6 Suppose you buy a 20 Year Treasury … $5000/yr$105,000

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 = $100,000 $50,000

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, = $100,000 $50,000 $2500/yr $52,500

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 = $100,000 $50,000 1 Year … $52,500

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, $100,000 $25,000 $1250/yr $25,000 D = 12.6 D = 7.7 D = 4.3 D = $100,000 $25, $100,000 $25,

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

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

Pricing DateCouponYTMPrice ($) Issue3.75%3.87% Matures A Bond’s price will always approach its face value upon maturity, but will rise over its lifetime as the yield drops

Length of Bond Initial Duration Duration after 5 Years Percentage Change 30 Year % 20 Year % 10 Year % 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