Anup is a financial advisor and a sincere one. He advises people on mutual funds investment as per their requirement. Anup, in his interaction with many clients, has come to realize that many of the investors want to preserve their capital as well as earn an average return. It is fine for them to receive average returns as long as the capital is preserved. Investors, however, do want better returns than the banks. Anup realised that there in the market there is a significant set of investors who are risk averse and want a fund that not only preserves their capital but provides returns at least as good as banks. Anup, to satisfy and to do justice with the requirement of his clients started suggesting debt funds to his clients. It was all good. Debt funds usually don’t lose money. They provide periodic returns as well as chances of capital appreciation when interest rates go down.

 

Then something happened

Government, in order to lower inflation, started playing with monetary policy. There were 13 hikes in interest rates in 2 years. Whenever interest rates go up, bond prices go down. Since debt funds mainly invest in bonds, their prices also went down. It was still fine. However, few of the bonds went down much lower while few lost little and few did not lose anything. There were questions about this by his clients.

Typically when interest rates go up, bond prices go down and hence NAV of debt funds also go down because their underlying assets are bonds.

 

A brief about Duration

Duration of any bond is weighted average of the time during which the cash is received. Let’s do this with an example. Suppose you have two bonds, bond A and bond B. Both bonds pay a coupon rate of 8% annually. This means both bonds pay Rs 80 (8% of face value of bond which is assumed Rs 1000 in this case).

Suppose the time to maturity of bond A is 6 years while it is 4 years for bond B. Let’s take a look at cash flow of these bonds.

Year

1

2

3

4

5

6

Bond A

80

80

80

80

80

1080

Bond B

80

80

80

1080

   

The last payment in each case includes the final payment of face value as well as coupon payment.

Let’s assume the YTM in each case is 10%. Hence price of bond A will be 912.8 while price of bond B will be 936.6. (Don’t worry about how the prices have come. This is beyond the scope of this article, though it is simple). Alternatively, you can add the present value for bond A and bond B (shown below) to get the price of the bond.

Present Value calculation with discount factor of 10%

Bond A

72.73

66.12

60.11

54.64

49.67

609.63

Bond B

72.73

66.12

60.11

737.65

   

Let’s find out the duration of each bond. To find duration of the bond, multiply the year number (or period) with the present value of the payment and sum all of them. Then divide with the price of the bond.

Duration of bond A = [(72.73*1) + (66.12*2) + (60.11*3) + (54.64*4) + (49.67*5) + (609.63*6)] / 912.8 = 4.94 years

Duration of bond B = [(72.73*1) + (66.12*2) + (60.11*3) + (737.65*4)] / 936.6 = 3.56 years

 

Impact of duration on price change

% Change in Price = ((-Duration) * (% Change in Rates))

The negative sign shows reverse relationship. When interest rates change, prices change in opposite direction.

Now suppose that interest rate changes by 2%.

Change in price of bond A = 4.94 * 2% = 9.88%

Change in price of bond B = 3.56 * 1% = 7.12%

Now you can see how bond prices change when the interest rates change.

 

How to interpret this

This means if a debt fund has underlying assets in the form of bonds with shorter duration (bonds whose time to maturity is nearby), the change in price will be less compared to a debt fund with underlying assets as bonds with longer duration (bonds whose time to maturity is far).

The example shown above has two bonds A and B with a very small difference in time to maturity. In reality, the variation in maturity can be much longer. Bonds come in maturity of few months to 30 years.

 

 

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