Understand Modified duration for bond & Mutual Fund.

 

Modified duration is a measure of how much the price of a bond or a mutual fund changes when the interest rate changes. It is based on the concept that bond prices and interest rates move in opposite directions. Higher modified duration means higher sensitivity to interest rate changes.

For example, if a bond has a modified duration of 4%, the bond price will rise by 4% with a decrease in interest rate by 1%

 

We can calculate the modified duration by dividing the Macaulay duration (which is the weighted average time until cash flows are received) by one plus the yield to maturity (which is the potential return of a bond) divided by the number of coupon periods per year.

 

Let us understand first the concept of Macaulay duration. 

 

Macaulay Duration = Face Value / Annual Interest Payout 

The below table shows the Macaulay Duration calculation of Bond A based on these features of the bond:

Macaulay Duration Calculation of Bond A
Face Value of Bond A	₹1000
Coupon Rate	8%
Annual Interest Payout	₹80
Macaulay Duration	1000 / 80 = 12.5 years

 

Based on the Macaulay Duration formula mentioned earlier, the Macaulay Duration of Bond A is 12.5 years. However, in real life, when considering future cash flows from a Bond, you also must consider the Present Value (PV) of the future cash flows considering the Discount Rate. So assuming that the Maturity of Bond A is 15 years and assuming a Discount Rate of 10%, you can calculate the Present Value of Future Cash Flow. By considering how many years in the future a payout will be made by the Bond, you can also calculate the Present Value of the Time Weighted Cash Flow of Bond A as below:

Present Value of Cash Flow Calculations for Bond A
Year	Cash Flow	PV of Future Cash Flow	PV of Time Weighted Cash Flow
1	80	72.72	72.72
2	80	66.10	132.20
3	80	60.10	180.30
4	80	54.64	218.56
5	80	49.67	248.35
6	80	45.16	270.96
7	80	41.05	287.35
8	80	37.32	298.56
9	80	33.93	305.37
10	80	30.84	308.40
11	80	28.04	308.44
12	80	25.49	305.88
13	80	23.17	301.21
14	80	21.07	294.98
15	1080	258.54	3878.10
Total Cash Flow	2200	847.90	7411.50

 

In this case, Macaulay Duration of Bond A is: Macaulay Duration = (Total PV of Time Weighted Cash Flow) / (Total PV of Future Cash Flow) = 7411.50 / 847.90 = 8.7 years While you do not need to calculate the Macaulay Duration for your Debt Funds as you can find it from the Debt Fund Factsheet, do keep in mind that a higher Macaulay Duration indicates higher Interest Rate sensitivity.

In order to understand how high Macaulay Duration indicates Higher Interest Rate Sensitivity of a Debt Fund, let’s take a close look at the Modified Duration of Debt Investments.

The modified Duration of a bond is a measure of how much the price of a Bond changes because of a change in its Yield To Maturity (YTM) or interest rate. In the simplest terms, if the Modified Duration of a Bond is 5 years and the market Interest Rate decreases by 1%, then the Bond’s price will increase by 5%. On the other hand, if the market Interest Rate increases by 1%, the price of the same Bond will decrease by 5%. The Yield to Maturity (YTM) of a Debt Fund indicates the potential returns of a Debt Fund and the quality of the Bonds that the scheme invested in. A higher YTM typically indicates that the scheme is invested in low-quality Bonds that can potentially give higher returns but carry a higher degree of risk investments as compared to Debt Funds with a lower YTM.

 

You might have noticed that in the above examples, Bond prices have moved in the opposite direction to Interest Rates. This happens because of the inverse relationship between Interest Rates and Bond prices, i.e., a decrease in Interest Rates increases Bond prices while an increase in Interest Rates leads to a reduction in Bond prices. The Modified Duration formula applicable to a Bond is:

Modified Duration = (Macaulay Duration) / {1 + (YTM / Frequency)}

In the above formula for Modified Duration, YTM = Yield To Maturity and Frequency = How frequently Coupon Interest is distributed by the Bond Issuer Using this formula, the Modified Duration calculation of Bond A from our earlier example will be like this:

 

Modified Duration Calculation of Bond A
Macaulay Duration	8.7 Years
Yield to Maturity	10%
Frequency	Once every year
Modified Duration of Bond A	7.9 years

 

In the above example, the Modified Duration of Bond A = 8.7 / {1+ (10 / 1)} = 7.9 years This means that in the case of Bond A, if the Interest Rate increases by 1%, the price of the Bond A will decrease by 7.9%. Similarly, a 1% decrease in Interest Rates will lead to a 7.9% increase in the price of Bond A.

 

Using Modified Duration to Fine-tune Debt Investing Strategies

Using the Modified Duration information of a Debt Fund, you can understand the Fund Manager’s view regarding future interest rate movements.

For example, if the Fund Manager is anticipating an increase in Interest Rates, he/she might decide to reduce the Modified Duration of the portfolio by investing in short-maturity Debt Instruments. This will help reduce the adverse impact of the Interest Rate increase on the Debt Fund. On the other hand, when the Fund Manager anticipates a decrease in Interest Rates, he/she might decide to maintain a high Modified Duration in the portfolio by investing in long-maturity Bonds. This will help the Debt Fund generate high returns when Bond Prices increase due to the decrease in Interest Rates.

You can use this same concept to select Debt Funds that are in line with your investment objectives. For example, suppose you want to reduce the Interest Rate Risk in your Debt Portfolio. In that case, you can do so by increasing your investment in Debt Funds with a low Modified Duration of up to 2 years and decreasing your exposure to Debt Investments with a higher Modified Duration.