# Yield Curve Risk

We know that the bond prices are sensitive to changes in interest rates. When interest rates increase, the bond prices fall and vice versa. A bond’s maturity also influences its price sensitivity to interest rate changes.

When we are looking at a single bond, measuring the interest rate risk (sensitivity) is relatively easier because we are talking about one bond with one maturity. However, in case of a portfolio, things become a bit complex. A bond portfolio will usually have bonds with different maturities. For example, there could be two bonds with 2-years of maturity, 2 bonds with 5-year maturity, and 2 more bonds with 10-year maturity.

While measuring the interest rate risk in such a portfolio, we can make a simple assumption such as, “Change in price of the portfolio if the interest rates increase by 50 basis points”. This will do the job, but there is one problem. In the real world, the interest rates or yields are different for different maturities. There is a structural relationship between the yield and the maturity, and the graph that plots maturity on x-axis and yield on y-axis is called the yield curve. If we simply say that the interest rates have increased by 50 basis points, we are assuming that interest rates have risen by 50 bps across the yield curve for all maturities. This is also called a parallel shift in the yield curve. This may not always be the case. It could be so that yields for different maturities change by different percentage. For example, the 5 year rate rises by 50 bps while the 10-year rate rises by just 25 basis points. This is called a non-parallel shift in yield curve and is a more commonly seen phenomenon.

Due to this reason the bond portfolios will have different exposures to how yield curve shifts, and this risk is called the yield curve risk.

This also brings us to one problem with calculating duration. Duration doesn’t account for yield curve risk because it assumes a single change in yield across all maturities on the yield curve. As per the definition of duration, it measures the approx. change in the price of a bond or a portfolio, for a 1% change in the yield. Due to this drawback, we need to look at other measures of interest rate risk that could capture the exposure even in case of a non-parallel shift in yield.  One such measure is ‘rate duration’. Rate duration measures the change in the value of a portfolio considering the change in yield of only a particular maturity, the yield of all other maturities remaining constant. For example, 10-year rate duration of 3% means that the portfolio value will change by 3% for a 1% change in the 10-year yield.

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