##### August 29, 2017

### How to Estimate Equity Mutual Fund Returns?

###### Amit Trivedi

###### Owner, Karmayog Knowledge Academy

# How to Estimate Equity Mutual Fund Returns?

Equity markets are at all time high levels. On one hand, many are flocking to investing in equity, while some others are developing cold feet. **“Is this the right time to invest?”** – This is the common question facing investment advisors and mutual fund distributors, alike.

In the last article, we looked at how to estimate returns from your debt funds. In this one, we will do the same exercise for equity funds. **Understanding how much to expect should be able to help us evaluate various investment options.**

An investment in equity shares of a company gives one part-ownership of a business. An owner of the business is entitled to the profits of the company in proportion to one’s share of the ownership. The management of the firm normally shares part of the profit with the shareholders in the form of dividends, whereas the other part is retained for funding the growth of the business. Such a retention of earnings should help the company grow the business and hence the profits. That means, over the years the company should be able to grow the profits and shares part of the same in form of dividends.

Assuming that the market prices of the shares are fair, the percentage growth in share prices should then be a function of the percentage growth in profits as well as the dividend yield calculated as dividends received dividend by the current market price. To put it mathematically:

**Investment Return = Growth in Profits + Dividend Yield**

Let us call the above **“Equation I”.**

So, according to the above equation, if a company’s share is giving the dividend of 3% of the current market price and if the profits of the firm grow at 12% per year, the expected return should be 15% p.a.

Similarly, if we were talking about the broader market, we would look at the overall dividend yield and the growth in profits of a larger cross-section of companies to arrive at the expected return from the equity market. This means if the broader market is offering the dividend yield of 2% and if the profits grow at 10% every year, the equity markets should deliver 12% p.a. to the investor.

This relationship is more or less true, so long as we remember the assumption we made earlier – that the market price of the share is fair. This is an impractical assumption since it is very difficult for anyone to estimate the fair price.

**If the current price is not fair, it is obvious that the share is either cheap or costly.** In such a case, the returns earned by an investor should be different from what we have seen above.

Logically, if one buys a share cheap, the returns should be higher than those arrived at earlier. Let us go back to the same example of the company growing profits at 12% p.a. and offering the dividend yield of 3%. We saw that the investment return would be 15% in such a case. However, what if the investor buys such a share cheap, say at a discount of 20% to the fair price? Logically, the investor should earn more than 15% p.a. Similarly, if the shares are costly when the investor buys, the subsequent return should logically be lower than 15%.

**What would be the impact of the 20% discount that we mentioned earlier on how much the investor makes?** Shouldn’t that depend on the holding period? Well, the discount (or premium, as the case may be) would be distributed across the holding period. If the holding period is one year, the entire 20% is available for that period. At the same time, if the holding period were five years, the 20% would be distributed across the period, which means there would be an increase (or decrease) of roughly 4% per year in the returns earned by the investor.

So, going back to our example of the company offering a dividend yield of 3% and growing profits at 12% per year, if the shares are currently trading in the market at a discount of 20% to the fair price, should the investor expect closer to 19% (15% as calculated earlier, plus the 4% additional return on account of buying at discount) per year?

Once again, this is logically true so long as the shares start trading at a fair price when the investor sells. Practically, there is no guarantee that such a thing would happen. What if the shares are not trading at a fair price when the investor sells? Again, it is obvious that when the investor sells the shares in the market, the same could be cheap or costly.

We must factor that. If the investor buys the shares cheap, the investor’s returns would go up, but if these were cheap at the time of getting out, the returns would reduce. And if the shares are bought when they are costly, the investor’s returns reduce, but if these are sold costly, investor’s returns go up.

This understanding is important. Now, it is no longer about whether the shares are cheap or costly in comparison to a fair price. Estimation of a fair price is impossible and the best of the investors have admitted their inability to do that. However, an investor can and should focus on the comparison – whether both the buying and selling prices are high or low in relation to a stable reference point.

**Just to summarise, we would put four different scenarios:**

- Buying cheap and selling costly would enhance the investment returns
- Buying costly and selling cheap would negatively impact the investment returns
- Buying cheap and selling cheap – well, we need to check which leg was the relatively cheaper one
- Buying costly and selling costly – exactly like the point 3 above, we need to check the costly price in relative terms.

**How do we determine the relative price** – whether something is cheaper or not? We would look at the P/E ratio for our discussion here. If this ratio moves up over the period, we may say that the share has become costlier and if the ratio drops, it would mean that the share has become cheaper compared to the earlier time.

This change in P/E ratio would contribute to the money that the investor makes.

**Let us then add the impact of such a change in the P/E ratio to the investor’s returns. How much is the change in investor’s returns on account of this factor?**

If an investor invests when the price is P_{0} and sells when the price is Pn, after a holding period of ‘n’ years, we can calculate the investment returns with the help of the future value equation as under:

The future value equation is given as under for a quick and ready reference:

**FV = PV * (1 + r) ^ n**

In the above case: ‘r’ or the rate of return is something we want to find out, ‘n’ is the holding period, P_{0} is the PV and P_{n} is the FV. Let us rewrite the future value equation and solve it for finding ‘r’.

**P _{n} = P_{0}* (1 + r) ^ n**

**(1 + r) ^ n = P _{n}/P_{0}**

**(1 + r) = (P _{n}/P_{0}) ^ (1/n)**

**r = (P _{n}/P_{0}) ^ (1/n) – 1**

In the above equation, if we replace the ‘P’ (the price) with the ‘PE’ (the P/E ratio), the equation would be as under:

**r = (PE _{n}/PE_{0}) ^ (1/n) – 1**

Let us call the above “Equation PE”.

Here, the PE_{n} is the PE ratio after the holding period of ‘n’ years and PE_{0} is the PE ratio in the beginning of the period (or the PE ratio at the time of investing). This is the additional return over and above the investment return we saw in the beginning (see Equation I).

**Adding the investment return from Equation PE to the Equation I gives us the return an investor would get buy buying and selling shares in the capital market. Let us rewrite the equation mathematically:**

Return on investment = Profit growth + dividend yield + change in valuation

**Return on investment (%)** = **EG _{n} + **DY

_{n}+ [(PE_{n}/PE_{0}) ^ (1/n) – 1]EG_{n} = Compounded Annual Growth Rate in profits of the firm (or the market) over ‘n’ years

DY_{n} = Dividend yield offered by the firm (or the market) over ‘n’ years

So, let us return to the question: **“Is it prudent to buy currently when the markets are at all time high levels?”**

First of all, the market indices are at all time high levels, but the valuations are not at the historically highest levels. Second, while the valuations may not be the highest, the same are at high levels as compared to historical averages. Thus, someone buying equity today would be buying at relatively costly valuations. Third, while one may be buying at high valuations, can the profits and dividends contribute enough to make up for the high price one has paid? It is possible. However, there is a risk here: what if the profits do not grow at the fast pace? Fourth, can the P/E ratios expand from here? Is there a possibility for one to sell at even higher valuations? The answer is: yes, it is possible. However, one is looking at a reduced probability.

**Finally, what should an investor do? Or, what should an advisor advise at current levels?** Well, the contribution of profit growth and the dividend yield is measured in % p.a. basis, whereas the change in valuation, would be distributed over the years. As we saw earlier if one is buying a share 20% cheaper and is able to get out at the fair valuation, the discount distributed to the holding period. So, if the valuations return to normal levels within a year, the investor’s returns jump by 20%; whereas if the valuations take five years to return to normal levels, the discount is spread over the holding period, thus bringing down the contribution to roughly 4% per years. The change in valuation can have a bigger impact in the short term, but it reduces as the holding period is increased. As compared to that the profit growth and dividends may have a small impact in the short term, but they account for a large part of the long term returns.

**With this background, an advisor should consider two things in order to set the right expectations:**

**The total returns may be lower than in the past****The minimum holding period should be longer than what one considered in the past**

**If these two are set properly, one may be in a better position to manage the investor’s emotions.**

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