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Measuring bond price volatility |
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Bond Price Volatility refers to the fluctuations in the price of a bond due to changes in various underlying factors. An optimal bond portfolio should be able to effectively factor in such volatilities and keep resulting price risk to a minimal. However, estimation of such volatilities in the bond price is not easy. Moreover, volatility in the prices of different securities varies with the yield, maturity and the duration of these respective securities. Thus to effectively estimate volatility of a portfolio, various measures of such estimation need to be resorted to. Some of these are discussed here.
Price Value of a Basis Point
Price Value of a Basis Point refers to the change in the price of a bond if the yield changes by 1 basis point (0.01%). If the price of Security A falls by 20 paise when the yield rises by 0.01% and the price of Security B falls by 25 paise for the same rise in the yield, then Security B would be said to be more volatile than Security A. This volatility, of course, holds good even on the positive side; that is when price of Security B rises more than that of Security A for the same fall in yield. Therefore, a portfolio manager's job is to optimize positive volatility while minimizing downside volatility.
Yield Value of a Price change
Yield Value of a Price change refers to the change in the yield of a security for a specified change in the price of the security. The smaller the yield value, the price volatility would be greater since even a small change in the yield would change the price considerably.
Duration of the Bond
Duration of the bond, in simple terms, is the measure of time to its maturity. It is a measure of the bond's price risk. Higher the duration of the bond, higher is the bond's sensitivity to market interest rate movements. The concept is of extreme importance in the context of bond volatility. In case of a bond having fixed term to maturity with no intermittent coupon payments, the duration of the bond is simply its tenor to maturity. However in case of coupon paying bonds, the investor receives interest payments before the maturity date and hence the duration of the bond is lower than its tenor. The present values of the cash flows are taken as the weights for calculating the duration of the bond.Generally, bonds with longer terms to maturity have higher durations than bonds with shorter maturities. Bonds with lower coupons have higher durations than bonds with higher coupons.
Modified Duration
Modified Duration establishes a direct mathematical relationship between bond price and interest rate changes. It is a direct measure of the interest rate sensitivity of the bond.Mathematically, percentage change in bond price is the product of Modified Duration of the bond and the change in its yield. The concept can be used effectively to manage portfolio volatility since the modified duration of a bond and the sensitivity of its price to interest rate movements are inversely related.
Convexity
Duration and Modified Duration of the bond assume a linear relationship between price and yield. However, since the actual yield curve is usually convex, measurement of the bond risk using its duration may not give a perfect picture. Convexity takes into account the shape of the Price yield relationship when making price sensitivity calculations. It is the rate of change of duration with a change in the yield. |
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