# Fixed Income - Yield Curve Risk

For a nonparallel shift in the yield curve, the yields on different bonds in a portfolio can change by different amounts, and duration alone cannot capture the effect of a “yield change” on the value of the portfolio. Why doesn’t duration capture the effect alone?

Also, why does a lower coupon = higher duration?

Let me start this way: Duration basically is a measure of Interest Rate Risk. Meaning, if Interest Rates in the market change/fluctuate, they have an affect on the Price of the bond you hold and hence a Risk that value/price of your holdings may go down. Now, in a Portfolio of Bonds, this fluctuation in Interest Rates will affect Prices of different bonds differently. This is because Bonds in a Portfolio could be different from each other in terms of their maturities, coupon rates or embedded options. Thus prices of these bonds will fluctuate differently for a given change in Interest Rate. So, Duration becomes a weak measure for measuring Interest Rate risk of a PORTFOLIO of different bonds. To answer your other question: why does a lower coupon = higher duration? Say, there are 2 bonds; Bond A paying 5% annual coupon and Bond B paying 8% annual coupon. Now, if market interest rate goes up to 10%, Bond A will sell at a bigger discount than Bond B, right? Meaning, prices of Bond A will go down more than Prices of Bond B. So, as a holder of Bond A, you loose more money than as a holder of Bond B. This explains why lower coupon bonds have higher Interest Rate Risk (duration). Hope this helps.

Further to your 1st question: Why doesn’t duration capture the effect alone? Duration measures risks arising from interest rate fluctuations that cause Parallel changes in the Yield Curve. If shape of the Yield Curve itself changes (that is, it flattens or steepens), then Duration alone cannot measure Interest Rate Risk completely. In that case, Duration together with Yield Curve Risk is a complete measure of Interest Rate Risk. This can be a little confusing. Yield Curve is expected Interest Rates over time; short term and long term. And a long term bond price would be based on this Yield Curve. Then, if say there is an increase in Market Interest Rate, say by 1%, and it increases both short term and long term rate by the same %age, then it will be a parallel shift in the Yield Curve, and Duration would be a good measure for this. But, if say, short term interest rates increase by 1% and long term interest rates increase by 2%, then yield curve would shift up and also would steepen and Duration alone would not be a good measure to calculate complete Interest Rate Risk. Hope this helps.

In a more simpler way, Duration is the “weighted avg” % change in bond prices to market interest. If different bonds change differently then duration becomes meaningless.