We all understand returns as what is earned on our capital. If your capital of Rs.1000 grows to Rs.1120 at the end of 1 year then Rs. 120 is your return on the investment. This can also be expressed in percentage terms as 12% (120/1000). This is a very simple measure of returns. In practice, the returns are normally calculated over a longer period of time. Whether you are measuring your personal portfolio or the returns generated by a mutual fund, the concept essentially remains the same. Returns, by definition, have different connotations. There are different definitions of returns that can be applied in different circumstances. How to measure fund performance and how to calculate returns? Let us also look at a unique technique of measuring return of mutual funds. But first, let us look at returns in greater detail.

1. Arithmetic mean of investment returns

This is the simplest way of calculating returns on an investment. Let us consider the case of an investment where we invested Rs.10,000 in a stock and then evaluate the price after 5 years. Here is how it looks..

Year 0Year 1Year 2Year 3Year 4Year 510,00011,50016,00017,20015,50018,900Profits / Loss1,5004,5001,200-1,7003,400Returns (%)15.00%39.13%7.50%-9.88%21.94%Arithmetic Mean Returns =14.74%(73.69 / 5)

What the above table indicates that the return on the investment over a 5 year period was 14.74%. The only problem with using an arithmetic measure is that this mean is very vulnerable to large numbers. The massive profit earned in Year 2 has sharply distorted the returns into positive territory.

2. Compounded Annual Growth CAGR (CAGR)

The second approach to calculating returns on your investment is the CAGR of returns. Here we assume that when you hold the asset for a period of 5 years then the returns made each year does not matter. Instead, what matters is what returns were generated over a period of 5 years and how that translated into an annualized IRR. In the above case, Rs.10,000 invested at the beginning of year 1 grew to Rs.18,900 at the end of year 5. What does that translate into in terms of annualized compounded returns? We can use the standard compounding formula in this case as under:

Corpus at year 5 = Investment at Year 0 X (1 + R)5

In the above case we need to find the missing compounding rate of “R”, which will be the 5th root of the wealth ratio i.e. (1.89)1/5 = (1 + R). Thus R = 13.58%

The above formula works very well for long period returns when the asset price is moving in a secular trend. When the trend is volatile and unpredictable then CAGR does not give clear results.

Geometric returns when there are intermittent losses

The arithmetic measure of returns can be misleading in the case of losses. However, there is an alternate method called the Geometric returns. This tends to smoothen out the positive and negative returns by converting them into relative numbers. Here is how it works..

DetailsYear 1Year 2Year 3Year 4Year 5Year Returns12%-8%15%-3%21%Factor of 11.120.921.150.971.21

Geometric Mean = {(1.12*0.92*1.15*0.97*1.21)1/5} - 1

Geometric Returns = 6.82%

The big advantage of the geometric mean approach is that it smoothens out the vagaries of the stock over a longer period. Under normal growth it gives the same rate of return as the CAGR returns and close to what the Arithmetic mean gives.

Return on average sum invested

This is a very useful measure of returns when your principal invested keeps changing. Here the returns are not being seen in terms of price movement on a year on year basis but the profits earned by you net of costs is measured against your corpus. But what is your corpus since it keeps shifting through the year. That is why the average corpus is used.

DetailsCapital on Jan-01Capital on Jan-30Gross ReturnsNet Returns

Rs.100,000Rs.150,000Rs.31,000Rs.25.400Average CapitalRs.1,25,000

Return on Average Sum Invested20.32%25,400/1,25,000

Return on average sum invested is more relevant when we are taking a portfolio approach and therefore the net returns are of greater importance.

Dollar adjusted return on investment

The dollar adjusted returns may not be too relevant to Indian investors. But this matters to international investors like NRIs, foreign portfolio investors etc who need to measure their returns in dollar terms. Therefore, apart from the domestic rupee returns, the movement of the dollar also matters. Let us take the case of 2 investors who invested the same amount and earned the same returns but at different points of time. While Investor A faced a strong dollar, Investor B faced a weak dollar.

Investor A

Investor BBasic InvestmentRs.1,00,00,000Basic InvestmentRs.100,000Rupee / Dollar65/$Rupee / Dollar65/$Dollars Paid$153,846Dollars$153,846Value after 1 YrRs.1,25,00,000Value after 1 YrRs.1,25,00,000Rupee / Dollar68/$Rupee / Dollar63/$Dollars Received$183,824Dollars Received$198,413Rupee Returns25%Rupee Returns25%Dollar Returns19.49%Dollar Returns28.97%

As can be seen in the above instance, Investor B has benefited by the dollar depreciation which has actually enhanced his rupee return by 3.97%. On the other hand Investor A has lost (-5.51%) due to the impact of the dollar appreciation. The dollar movement makes a big difference to international investors.

You need to choose your returns based on the objective. That is the key!

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