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# How and why does duration matter for debt funds?

One of the key measures in evaluating debt funds is the concept of duration. Normally, funds with higher duration tend to have a greater sensitivity to change in the rate of interest. For example, if the rate of interest were to go down by 50 basis points, then the price appreciation in a bond with duration of 7 years will be more than a bond with 5 years duration. That is why fund managers prefer to buy bonds with longer duration when interest rates are expected to go down and they prefer to buy bonds with lower duration when interest rates are either likely to stay stable or go up. To understand the application of the concept of duration, it is essential to first understand the concept of duration. In technical parlance, the duration is referred to as Modified Duration (MD) and the fact sheet of debt funds will necessarily disclose this each month.

Understanding what duration is all about..
To understand and calculate the Modified Duration, the first step is to calculate the Macaulay Duration. Macaulay Duration is the term to maturity weighted by the present value of intermediate cash flows.  The calculation of the Macaulay Duration can be best understood with the help of this example

Let us assume a Bond with a face of Rs.1000 bearing coupon of 9% payable annually for a period of 5 years. It is also assumed that the market yield is currently 8%...

YearCash FlowPV FactorPV of Cash FlowWeightTime X Weight1900.9259383.33370.0801340.0801344212900.8573477.16060.0741980.1483966283900.7938371.44470.0687020.2061055624900.7350366.15270.0636130.254452081510900.68058741.83220.7133523.566761952   1039.9241.004.255850644

A few points to be noted in the above example! The market price of the bond will be at a premium because the coupon interest paid by the bond is more than the market yield. Secondly, the duration is nothing but timing of cash flows weighted by the present value of cash flows. Therefore, if there are big balloon payments in the early years then duration will be lower. In this case since the principal is repaid at the end of 5 years, the duration at 4.2558 years is closer to the maturity of 5 years. The Macaulay duration of a bond will always be lower than the term to maturity, except in case of a deep discount bond where the duration will be equal to the term to maturity. That is because a deep-discount bond is issued at a discount and redeemed at face value. However, since there is no intermediate interest payments involved, the term to maturity of the bond and its duration will be one and the same.
Modified Duration is nothing but the Macaulay Duration divided by the yield. Therefore Modified Duration (MD) will be (4.2558/1.08) = 3.94 years
In the above case, a 1% increase in the interest rates will result in a 3.94% fall in bond prices and vice versa.

Applying Duration in practice: when and how
For fund managers and investors in debt, the concept of duration is extremely important. Here are the key applications of the concept of duration in debt market investing

Duration is a measure of bond risk. Just as risk of equities is measured through Beta, the risk of bonds is measured using duration. Duration helps investors to numerically quantify the risk for the bond price due to change in interest rates. Typically, long term bonds with lower interest payouts tend to have a higher duration compared to shorter term bonds with higher interest payouts.

Normally government bonds tend to have longer maturity and lower interest payouts to bond holders considering their low perception of default risk. As a result government bonds tend to have longer durations and therefore they also tend to be more sensitive to shifts in interest rates.

When the fund manager is normally expecting the interest rates in the market to soften (as is the case in India currently), the tendency will be to switch towards longer duration G-Secs as they are normally more sensitive to cuts in interest rates. In such cases, the impact of fall in interest rates in the form of price appreciation will be much larger. That is why fund managers tend to prefer government bonds over private bonds when rates are expected to go down.

The reverse holds true in case interest rates are expected to go up. That will mean a fall in the price of bond s and therefore government bonds with longer durations will be impacted most in the form of price depreciation. That is why when fund managers expect interest rates to rise, they shift out of long duration bonds and park in short duration bonds so that the impact on price will be minimal.

Lastly, there is a very important role that duration plays in maturity matching. For example, if you have a liability payable after 5 years, how do you hedge your risk by investing in a bond with a similar maturity? The answer is to match your duration with your payout frame and not your term to maturity. So instead of buying a 5-year bond, you must buy a bond with Duration of 5 years so that your risk of maturity mismatch is almost entirely eliminated.

Duration forms the foundation of trading and investing in bonds. In terms of maturity profile and liability matching, duration plays a key role for bond investors.