Question

1. What is bond convexity, how is it measured and how does it con- tribute to a bond trader understanding the manner in which her port- folio might react to yield changes? Do duration and convexity to- gether give a perfect picture of a bond’s likely reaction to changes in yields? [Write no more than 15 sentences in your answer.]

Answer 1

Bond Convexity:

Bond convexity refers to the relation between a bond's price and its yield with every change in the interest rates. Thus it measures how the duration of the bond changes, with respect to the fluctuations in the interest rates.

C=d2(B(r)) / B∗d∗r2

​where,

C=convexity

B=the bond pricer

r=the interest rated

d=duration​

Higher the coupon rate, lower the convexity; this is because a 5% coupon bond is way more sensitive to changes in interest rates than a 10% coupon bond.

Zero coupon bonds have the highest convexity since relationships are dependent on the fact that whether the compared bonds have the same duration and yields to maturity. Thus, a high convexity bond is more sensitive to changes in interest rates and should consequently witness larger fluctuations in price when interest rates move.

Duration refers to the bond's sensitivity to interest rate changes. Duration of a bond generally increases with the time to maturity (keeping the coupon rate constant). Only exception being the deep discount bonds where the duration may fall with increase in maturity. Thus, duration and convexity together do help an investor by giving a perfect picture of a bond’s likely reaction to changes in yields and thus quantifying the uncertainty in fixed income investing.

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