There are two ways in which an investment in a debt mutual fund grows: (1) by buying bonds with high coupon rates and holding them until maturity. The growth in this case is by accrual of interest. (2) by choosing long-term bonds issued by the government and aim for capital gains when the bond price increases due to decrease in interest rates.

Higher the coupon rate, lower the credit rating. Therefore the accrual strategy is subject to risk of default. Most investors do not recognize that the accrual strategy is also subject to interest rate risk. That is, the value of the high coupon rate bonds can also change value depending on interest rate movements.

If the fund manager buys only government bonds (long or short-term), there is no risk of default and only risk of capital loss due to increase in interest rates.

When interest rates increase, new bonds will have a higher coupon rate than existing ones. Since the demand for existing bonds decreases, they will have to be priced lower in order to be sold in the bond market. In fact the price has to drop to ensure the yields matches that of the new bonds.

Similarly if interest rates decrease, new bonds will have a lower coupon rate than existing ones. The demand for the old bonds increases and so does the price until the yields match.

**Yield**

Yield is a measure of the interest income generated by a bond.

Yield = coupon amount / bond price.

If a bond is priced at 100 with a coupon rate of 10%, the coupon amount is 10% of 100 = 10

The *initial yield * = 10/100 = 10%

For debt funds, the weighted average of portfolio bond yields is calculated. This is known as **running yield** or **yield to maturity**.

It is the expected yield* if the bonds in the folio are held to maturity. *

**Modified Duration**

There is a simple metric which the investor can use to understand how sensitive a debt mutual fund is to interest rate changes: **the modified duration****.**

The modified duration is measured in years and gives us two pieces of information:

- For 1% change in interest rates, what would be the expected increase or decrease in fund NAV. A modified duration of 2 years implies, a possible NAV change of 2% for 1% change in interest rate. So longer the modified duration, higher the interest rate sensitivity.
For a given yield to maturity, how long would the fund take to recover, if there is a loss due to increase in interest rates.

Change in bond price = **-1** x Modified Duration x (change in interest rate)

For debt funds, the formula is

Change in NAV = **-1** x Modified Duration x (change in interest rate)

If the modified duration is 4 years and if the interest rates have increased by 1%,

change in interest is +1% (it would be -1% if the rates had dropped by 1%)

So the change in bond price or NAV =(-1) x 4 x (+1%) = -4%

The -**1** is included in the formula to show that interest rate movement and bond price or NAV movement are opposite to each other.

Higher the modified duration, higher would the gain or loss due to rate movements.

Suppose the *current* annual yield to maturity of the debt fund (net of expenses) is 10% per year. This means that each day the NAV will increase by

10%/365 = 0.03% each day.

If the interest rate has increased by 1% in a day, a debt fund with a modified duration of 4 years would suffer a NAV loss of 4%.

The fund NAV will continue to increase 0.03% a day. To recover from the change in interest rate, the fund will take

4%/0.03% = 133 days or about 4.5 months.

Thus modified duration gives you an idea of how much you stand to lose or gain when the rates change and along with the current yield to maturity of the fund, it gives you an idea of how long the fund would take to recover from a rate hike.

Here are some numbers for a few funds in each debt fund category listed by VR online.

The time to recover here is in response to a 1% increase in interest rates.

Note that that values can vary widely within a category. Would be a good idea to *always *choose a fund with low modified duration and reasonable yield to maturity. High yield to maturity implies the fund is invested low rated bonds. So tread with caution.

When it comes to debt fund selection, the modified duration is the most important metric that I would look at.

Here is a something I wrote about an year ago:

**How to Select Debt Mutual Funds Suitable For Your Financial Goals?**

References:

Raghu RamamurthyVery good input.I have invested in Gilt Funds.

Raghu RamamurthyVery good input.I have invested in Gilt Funds.

BharaniGood information. I have 2 comments:

1. "High yield to maturity implies the fund is invested low rated bonds. So tread with caution."

I think this is not always true; long-term g-secs (sovereign rating) has high YTM and high modified duration, so sensitivity is high. Not to mention interest rate risk though 🙂

2. In absolute terms, with 1% leading to 2% diff in NAV is good. But if I want to apply this directly in today's market, I won't be, since most inc/dec in NAV occur in anticipation of future rate dec/inc! And when it happens in steps over a period of time, difficult to correlate, say, an actual rate dec with the NAV increases already happened!

Please correct me if I am wrong.

BharaniGood information. I have 2 comments:

1. "High yield to maturity implies the fund is invested low rated bonds. So tread with caution."

I think this is not always true; long-term g-secs (sovereign rating) has high YTM and high modified duration, so sensitivity is high. Not to mention interest rate risk though 🙂

2. In absolute terms, with 1% leading to 2% diff in NAV is good. But if I want to apply this directly in today's market, I won't be, since most inc/dec in NAV occur in anticipation of future rate dec/inc! And when it happens in steps over a period of time, difficult to correlate, say, an actual rate dec with the NAV increases already happened!

Please correct me if I am wrong.

Pattabiraman MurariThank you sir.

Pattabiraman MurariThank you sir.

KarthikeyanSir, thank you for explaining this concept clearly, I read about modified duration in an academic course, but reading it here gave me some sense of how it can applied in the world of debt mutual funds.

I'm not sure if its ideal to always choose a fund with low modified duration, wouldn't a high MD serve better in a scenario where interest rates are coming down? Is it better to diversify one's debt portfolio with investments in both categories?

KarthikeyanSir, thank you for explaining this concept clearly, I read about modified duration in an academic course, but reading it here gave me some sense of how it can applied in the world of debt mutual funds.

I'm not sure if its ideal to always choose a fund with low modified duration, wouldn't a high MD serve better in a scenario where interest rates are coming down? Is it better to diversify one's debt portfolio with investments in both categories?

NithinIf you see "Franklin India Ultra Short Bond Fund - Super Institutional Plan" in value research, on 10/05/2015 the NAV change is shown as 0.01%. But the YTM is 9.75% and 9.75% / 365 = 0.026% (per day). Then why is it displayed 0.01% ? Am I missing something ?

NithinIf you see "Franklin India Ultra Short Bond Fund - Super Institutional Plan" in value research, on 10/05/2015 the NAV change is shown as 0.01%. But the YTM is 9.75% and 9.75% / 365 = 0.026% (per day). Then why is it displayed 0.01% ? Am I missing something ?