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Holding other factors constant, which one of the following bonds has the smallest price volatility? 1)...

Holding other factors constant, which one of the following bonds has the smallest price volatility? 1) 5- year, 0% coupon bond 2) 5- year, 12% coupon bond 3) 5- year, 14% coupon bond 4)5- year. 10% coupon bond 5) Cannot tell from the information given.

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Answer #1

For a given term to maturity and initial yield, the smaller the coupon rate, the greater will be the price volatility. So, among the given bonds, the 5-year 14% coupon bond will have the least price volatility.

Let us assume that the given bonds have a YTM of y (annual) and have the same par value M, then price volatility is given by the Macaulay Duration

where C = coupon per period, n = number of payments and P = current bond price

For the same YTM, the current price will be highest for the bond with the highest coupon rate which is the 5-year 14% bond here. Therefore, the duration for the 5-year 14% bond will be lowest.

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