Equity funds and equity instruments are already well understood. What is less understood is the aspect of how debt instruments and debt funds are evaluated. Most of us know that interest rates and bond prices are inversely related. That means; if the interest rates go up then the bond prices come down and when the interest rates go down then the bond prices go up. Have you ever wondered why that happens? Let us look at it as an illustration.

Assume that you invested in a 9% bond for 3 years where interest is paid semi-annually and the bond will be redeemed at the end of 3 years.  The par value of the bond is Rs.1000, which is the price at which the bond will be redeemed. Now what happens if the interest rates go down by 50 bps after you buy the bond? Note that the market yields are down by 50 basis points but your bond is still paying 9%. That makes your bond more valuable and that will take your bond price up to Rs.1005/- in the bond markets. The idea is that for fresh buyers of this bond, the interest rate will still be 9% but since they are paying a premium of Rs.5 to buy this bond, the effective yield will be closer to the lower market yields. For you the holder, it is a benefit because the price of the bond will go up and give you trading opportunities. This is the crux of most strategies surround bonds and an important concept to note in bond analysis is Duration or Modified Duration. Let us understand how to evaluate debt funds using duration. Let us also look at how to use the concept of modified duration in debt funds and how the duration debt funds impact the bond trading decision.

 

Calculation of Modified Duration..

Modified Duration (MD) is critical for testing the sensitivity of the bond or fund to changes in interest rates. Higher the Modified Duration (MD), higher is the fund’s sensitivity to changes in interest rates. That means higher duration bonds will fall more when interest rates rise and it will rise more when interest rates fall. But how exactly is MD calculated?

 

To understand and calculate the Modified Duration, the first step is to calculate the Macaulay Duration. 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 is 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. Since there are no intermediate cash flows in a deep discount bond, it will have a duration that is exactly equal to the time to maturity of the bond.

 

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.
 
Why is the concept of Duration so important?
Duration has important implications when we evaluate opportunities in the bond markets and also within bond funds. Here are a few key applications of the concept of duration

Normally, your decision to sell or buy bonds is based on the duration of the bond. For example, when rates rise or when rates fall, the bonds with a higher duration are more vulnerable to shifts in interest rates. As a result, when rates are rising you shift to low duration bonds and when interest rates are falling then you shift to high duration bonds so that the impact on your capital can be optimized.

Bond duration is a good barometer to compare funds on risk parameters. For example, two bonds with the same duration will react similarly to changes in interest rates. Hence, while creating your portfolio you make buckets of bonds with similar duration and not bonds with similar term to maturity.

Finally, duration has very important applications in asset liability matching. Suppose you have a payable maturing after 7 years. How do you plan for the same? A simple method will be to use zero coupon bonds but the problem is that zero coupon bonds are not found so easily in the market. A better method will be to match the duration with the liability. For example, if you want to pay a liability after 7 years then cover it with a bond having duration of 7 years not a term to maturity of 7 years. This is where duration is extensively used.