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CHAPTER 4 BOND PRICE VOLATILITY CHAPTER SUMMARY To use effective bond portfolio strategies, it is necessary to understand the price volatility of bonds resulting from changes in interest rates. The purpose of this chapter is to explain the price volatility characteristics of a bond and to present several measures to quantify price volatility. REVIEW OF THE PRICE-YIELD RELATIONSHIP FOR OPTION-FREE BONDS An increase (decrease) in the required yield decreases (increases) the present value of its expected cash flows and therefore decreases (increases) the bond’s price. This relationship is not linear. The shape of the price-yield relationship for any option-free bond is referred to as a convex relationship. PRICE VOLATILITY CHARACTERISTICS OF OPTION-FREE BONDS There are four properties concerning the price volatility of an option-free bond. (i) Although the prices of all option-free bonds move in the opposite direction from the change in yield required, the percentage price change is not the same for all bonds. (ii) For very small changes in the yield required, the percentage price change for a given bond is roughly the same, whether the yield required increases or decreases. (iii) For large changes in the required yield, the percentage price change is not the same for an increase in the required yield as it is for a decrease in the required yield. (iv) For a given large change in basis points, the percentage price increase is greater than the percentage price decrease. An explanation for these four properties of bond price volatility lies in the convex shape of the price-yield relationship. Characteristics of a Bond that Affect its Price Volatility There are two characteristics of an option-free bond that determine its price volatility: coupon and term to maturity. First, for a given term to maturity and initial yield, the price volatility of a bond is greater, the lower the coupon rate. This characteristic can be seen by comparing the 9%, 6%, and zero- coupon bonds with the same maturity. Second, for a given coupon rate and initial yield, the longer the term to maturity, the greater the price volatility. MEASURES OF BOND PRICE VOLATILITY Money managers, arbitrageurs, and traders need to have a way to measure a bond’s price volatility to implement hedging and trading strategies. Three measures that are commonly 1
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employed are price value of a basis point, yield value of a price change, and duration. Price Value of a Basis Point 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. 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). Typically, the price value of a basis point is expressed as the absolute value of the change in price. Price volatility is the same for an increase or a decrease of 1 basis point in required yield. Because this measure of price volatility is in terms of dollar price change, dividing the price
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