Question

Explain the importance of modified duration as a measure of interest sensitivity.What are the main assumption under this concept?

Answer 1

Modified duration as a measure of interest sensitivity:

Modified duration continues to be an important tool in measuring the sensitivity of bond prices with respect to interest rate. We all are aware there are many factors that influence the bond price and interest rate being one of them. The price of the bond is inversely and non linearly proportional to interest rate. In fact the formula for price involves handling "N"th power of interest rate where N is the time left to maturity. Now imagine a situation where interest rate changes. The analyst has to recalculate the bond price with the revised interest rate to figure out the impact of interest rate on price of the bond. This task is simplified by the concept of modified duration. It measure s the sensitivity of the price changes with changes in interest rate. it indicates by what %age price of a bond will change for 1% change in interest rate.

Needless to say, every method has its own advantages and disadvantages. This concept is also no exception.

We therefore now need to understand the key assumptions behind the modified duration concept.

What are the main assumption under this concept?

1. The main assumption behind this concept is that Price to interest rate relationship is linear. This is not true. In fact the relationship is highly complex and non-linear. However for a decently small range of interest rate, the relationship is indeed linear. Modified duration concept exploits this property of linear relationship for a small range of interest rate fluctuation.
2. Modified duration can thus be effective in predicting the changes in bond prices if interest rate changes are small. In case of large changes in interest rate, the modified duration concept will not be able to predict the impact on bond prices correctly. The second derivative of bond prices with respect to interest rate as explained by the concept of "Convexity" then comes into the picture.
3. Further we assume that while calculating the price of bond, all the cash flows are discounted by the same interest rate. This in a way translates into an assumption that yield curve is flat and interest rate shifts are parallel. This assumption may not always hold true in real life.
4. The modified duration concept is helpful and relevant in case of pure vanila bonds. In case of bonds with embedded option, the change in interest rate may change the cash flows of the bond and in that case the concept of duration loses its applicability.