##### June 29, 2017

### Estimation of Debt Fund Returns

###### Amit Trivedi

###### Owner, Karmayog Knowledge Academy

# Estimation of Debt Fund Returns…

**“Kitna return milega?”** This is a very common question majority of investment advisers and distributors of investment products face. Very regularly. Many simply look at the historical numbers and gave some projections based on the past. Some others stick to various thumb rules, e.g. equity returns = GDP growth plus inflation. In the case of fixed income mutual funds, many assume that the fund should return net YTM to the investors (Net YTM = YTM – fund expenses).

Is there a better way to estimating the future returns from an investment? Well, if we understand how the investments work, there is a scientific way to estimation. However, please be very clear that investing is not a complete science and even with a scientific approach, there are few assumptions involved. You could be completely wrong in your assumptions.

With that background and disclaimer, let us start with the debt funds. This is a bit easier than explaining equity returns. Later we will look at how to estimate returns from equity funds and hybrid funds, too.

**The debt fund returns come from two sources:** (1) the YTM of the securities held in the portfolio, and (2) any capital gains or losses incurred by the portfolio. Mathematically speaking:

*Debt fund returns = Net YTM on the portfolio +/- capital gains (or losses)*

*Debt fund returns = Net YTM on the portfolio +/- capital gains (or losses)*

The capital gains/losses could either be booked or only on paper due to marking of the portfolio to market.

Out of the above, the first one is easy to find out, i.e. the net YTM, which is the portfolio YTM minus the expenses. Both the numbers are available from the fund fact sheet in most cases.

However, estimating the capital gains/losses are tricky. At the same time, **the capital gain/loss arises in the case of the following situations:**

- Change in interest rates in the economy
- Change in the credit rating of a paper
- Change in the credit spread

Out of the above, only the first can be estimated. The other two are event based and there is no way to predict these events in advance. At the same time, I am not saying that predicting the movement of interest rates is any easier. However, even if we simply do some guesswork, the Mathematics of bonds allows us to estimate the range of future returns from debt funds.

As we all know, there is a relationship between the interest rates in the economy and the prices of bonds. We also know that the prices of bonds are more sensitive if the bond maturity is long as compared to short maturity bonds.

As the bond prices move, the NAV of the fund would get the move in the same way.

For every change in interest rates in the economy, the bond prices move in opposite direction. The exact relation can be calculated with the help of a factor known as modified duration.

*Change in fund NAV = (-1) X change in interest rates X modified duration*

*Change in fund NAV = (-1) X change in interest rates X modified duration*

Assuming that a fund’s modified duration is 2 years and the interest rate in the economy rises by 0.25% then the fund’s NAV should drop by 0.5% (calculated with the above formula: (-1)*2*0.25%).

**Please understand this is just an estimate and not an exact prediction, since:**

- The fund’s modified duration is the average of all securities in the portfolio, and hence different portfolios may have a similar modified duration even with investments in securities with different maturity profile.
- The interest rates may also change at different rates and different time periods for different maturities. For example, while RBI may reduce the interest rate by 0.25% during one of its monetary policies; the market might have already adjusted for longer maturity papers in anticipation of such a cut. At the same time, if the market had adjusted the bond prices in anticipation of a larger cut, the prices would fall after the lower-than-expected cut announced by the RBI.
- While you may look at the month-end factsheet to check the fund’s modified duration, the portfolio might have changed between the last date of the previous month and the day the interest change in announced.

The two equations mentioned in ** Orange fonts** above would help you estimate the debt fund returns. However, you still need to find the basic inputs for the right side of the equations, in order to get the value for the left side.

**You need the following values or estimates:**

- Fund YTM
- Fund expense ratio
- Modified duration
- Estimate of capital gains/losses (which can be derived with the help of 3 above and 5 below)
- Expected change in the interest rates

The first three are available from the fund factsheet. However, the fourth and the fifth can only be based on assumptions. Some of you may be able to take an informed view on the direction of interest rates, but most cannot.

If you can take an informed view on the interest rates, please use your estimated change. However, if you cannot, you may consider taking a range of possible change, say 0.5% increase or decrease in interest rate and then you would get a range of possible returns if the interest rates change within the range you have assumed.

**Let us take an example:**

Say,

- Fund’s modified duration = 2 years
- YTM = 8.2% p.a.
- Expense ratio = 0.5% p.a.
- Expected change in interest rate = 0.5% up or down

In this case, if the interest rate rises by 0.5%, then the fund should deliver

**(YTM – Expense ratio) + ((-1) * change in interest rate * modified duration)**

= (8.2% – 0.5%) + ((-1) * 0.5% * 2)

= 7.7% – 1% = 6.7%

However, if the interest rate falls by 0.5%, then the fund should deliver

**(YTM – Expense ratio) + ((-1) * change in interest rate * modified duration)**

= (8.2% – 0.5%) + ((-1) * (-0.5%) * 2)

= 7.7% + 1% = 8.7%

You may say that, over the next year if the interest rates move within 0.5%, the fund should deliver between **6.7% and 8.7%.**

Having said that, there is another important perspective that one must be aware of. In the example given above, both the YTM and expense ratio are mentioned as % p.a., whereas the change in interest rate could be sudden, and due to that the capital gain/losses would also be sudden.

That means, the above calculation would be true in case of change in interest rate over a year. However, if in the above example, the change in interest rate happens within six months from the date of investment, the investment returns for the six months period would look very different. Let us do a calculation for the same.

Say,

- Fund’s modified duration = 2 years
- YTM = 8.2% p.a.
- Expense ratio = 0.5% p.a.
- Expected change in interest rate = 0.5% up or down

Now, the change in interest rate is assumed to happen in six months. During this period, one would have earned only half of the net YTM, i.e. ½ * (8.2% – 0.5%). Since the YTM and expenses ratio are mentioned on per annum basis, both would be only half of the annualized number.

In this case, if the interest rate rises by 0.5%, then the fund should deliver

**(YTM – Expense ratio) + ((-1) * change in interest rate * modified duration)**

= (4.1% – 0.25%) + ((-1) * 0.5% * 2)

= 3.85% – 1% = 2.85% for six months = 5.7% p.a.

However, if the interest rate falls by 0.5%, then the fund should deliver

**(YTM – Expense ratio) + ((-1) * change in interest rate * modified duration)**

= (4.1% – 0.25%) + ((-1) * (-0.5%) * 2)

= 3.85% + 1% = 4.85% for six months = 9.7% p.a.

As you can see, the range of returns changed from between **6.7% p.a. and 8.7% p.a**. to between **5.7% p.a. and 9.7% p.a.**

It is important to understand this and explain to your clients that even debt fund returns could be highly sensitive in shorter periods of time. This is true in case of all debt funds, whether duration funds or accrual funds.

**Understand how debt funds work and help your clients in managing their investments.**

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