Bond portfolio convexity

We will discuss two approaches for assessing the interest rate risk exposure of a bond or a portfolio. The first approach is the full valuation approach that involves selecting possible interest rate scenarios for how interest rates and yield spreads may change and revaluing the bond position. The second approach entails the computation of measures that approximate how a bond s price or the portfolio s value will change when interest rates change. The most commonly used measures are duration and convexity. We will discuss duration/convexity measures for bonds and bond portfolios. Finally, we discuss measures of yield curve risk. 

Convexity comes into play when yield curve changes are moderate to large and serves to increase the value of the bond irrespective of whether the yield rises or falls. In other words, if yields rise, then bonds with positive convexity fall less than expected from duration alone, and when yields fall, bond prices rise more than expected. To put it bluntly, convexity is good for a bond portfolio, but it is exceptionally hard to actively manage a credit portfolio and maximise convexity at the same time. 

Portfolio convexity depends on the distribution of cash flows in the portfolio. A portfolio with an even distribution of cash flows has higher convexity than one where cash flows are concentrated in a particular maturity bucket, assuming equal duration and no optionality. By extension, considering a bond to be a portfolio of cash flows, the obvious conclusion is that bonds with higher coupons have higher convexity than bonds with low or zero coupons. 

We calculate the convexity of the portfolio in the same way as the duration, by averaging the convexities of the constituent bonds weighted by their market values as recommended by EFFAS and shown below ... 

As we mentioned earlier, it is difficult for credit portfolio managers (where the market is overwhelmingly noncallable) to actively manage convexity of their holdings. However, preferring higher coupon instruments and premium bonds over lower coupon and discount bonds tends to increase the convexity of the portfolio and in turn increases its total return. 

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