Lecture_15 - InterestRateRisk v Money managers arbitrageurs...

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Interest Rate Risk Professor Ruslan Goyenko
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Measures of Bond Price Volatility v Money managers, arbitrageurs, and traders need to have a way to measure a bond’s price volatility to implement hedging and trading strategies. v Three measures that are commonly employed: 1) price value of a basis point 2) yield value of a price change 3) duration
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Measures of Bond Price Volatility  (continued) v Price Value of a Basis Point Ø The price value of a basis point, also referred to as the dollar value of an 01, is the change in the price of the bond if the required yield changes by 1 basis point. Ø Note that this measure of price volatility indicates dollar price volatility as opposed to percentage price volatility (price change as a percent of the initial price). Ø Typically, the price value of a basis point is expressed as the absolute value of the change in price. Ø Price volatility is the same for an increase or a decrease of 1 basis point in required yield. Bond Initial Price (9% yield) Price at  9.01% Price Value of  a Basis Point 5-year 9% Coupon 100.00 99.9604 0.0396 5-year 6% coupon 88.1309 88.0945 0.0364 5-year zero-coupon 64.3928 64.3620 0.0308
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Measures of Bond Price Volatility  (continued) v Yield Value of a Price Change Ø Another measure of the price volatility of a bond used by investors is the change in the yield for a specified price change. Ø This is estimated by first calculating the bond’s yield to maturity if the bond’s price is decreased by, say, X dollars. Ø Then the difference between the initial yield and the new yield is the yield value of an X dollar price change. Ø The smaller this value, the greater the dollar price volatility, because it would take a smaller change in yield to produce a price change of X dollars.
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Duration ]
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4-6 Measures of Bond Price Volatility  v Duration Ø The Macaulay duration is one measure of the approximate change in price for a small change in yield: where P = price of the bond C = semiannual coupon interest (in dollars) y = one-half the yield to maturity or required yield n = number of semiannual periods (number of years times 2) M = maturity value (in dollars) ( 29 ( 29 ( 29 ( 29 1 2 1 2 1 1 1 1 Macaulay duration + + + + = n n C C nC nM + + . . .+ + y y y y P
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