# How You Should Actually Measure Your Investment Returns

# What is the annualized return? There are two ways to approach the problem

Sandeep Raj Bhardwaj

Let us start off the debate on returns with a simple question. If the stock price went up from INR100 to INR125 in one year then what would be the return on the stock. The answer is obviously 25per cent. When we are talking of a single year, the calculation of returns is quite simple. The real complication of returns arises when we look at multiple time periods like 3 or 5 years. To understand this point, let us consider a stock that went up from INR100 to INR148.15 over three years. What is the annualized return? There are two ways to approach the problem and this difference lies at the core of understanding returns.

- When the stock price moves from INR100 to INR148.15 in a span of 3 years, then the total return over a 3 year period is 48.15per cent. In terms of arithmetic annual returns, we can express it as 16.05per cent(48.15 / 3) per annum.
- Let us look at the same price movement differently. If we say that annual returns are 16.05per cent then the price at the end of 3 years should have been INR156.29 (100 * 1.1605 * 1.1605 * 1.1605). But, that is not adding up. That is because you need to use the compounded return or CAGR which would have been 14per cent in the above case. The CAGR captures the time value and the compounding of money more effectively as a measure of returns.

Now let us look at some popular measures of returns in the context of financial markets.

**Arithmetic Mean of Investment Returns**

As we saw above, this is the simplest method of calculating returns on investment. The only problem is that just considers simple return and does not factor in time value of money or the power of compounding. The arithmetic mean of returns can be very deceptive. The problem with arithmetic mean is that it is very vulnerable to large numbers. For example, if the stock gave negative returns in four years and gave a 100per cent return in the fifth year, then the average return will still look healthy. But that is very misleading if you are going to use that data point for investment. The dispersion is just too much.

**Compounded Returns on Investments(CAGR)**

As we saw in our first illustration, the CAGR returns is an improvement over the arithmetic return in the sense that it considers the time value of money and also the power of compounding. What the CAGR implies is that if you hold the asset for a period of 5 years then the returns made each year does not matter. Instead, what matters are the total returns over a period of 5 years converted into an IRR return. What about annual fluctuations?

**Benchmarking Returns With a Representative Index**

Arithmetic means returns and CAGR returns are still returns on an absolute basis. It looks at the returns of that asset class in isolation. But what really matters is how the fund has outperformed with respect to the benchmark or a representative sample. There are two aspects to this debate.

- Firstly, you need to benchmark returns of a fund with the index, which could be the Sensex or the Nifty. Again benchmark has to be selected based on the portfolio nature. For example, if you are holding a portfolio of metal stocks then benchmark it to the metal index. Same implies for a portfolio of mid-cap stocks or thematic stocks. Here benchmarking with the Nifty can give a wrong picture. The idea of benchmarking with the index is that you can earn index returns by just buying a passive index fund. Hence an active fund needs to earn higher than the benchmark to justify the higher risk.
- The second type of benchmarking is the peer group comparison. For example, if you have bought a diversified equity fund, then the basic benchmarking is with the Nifty or the Sensex. The second level is you must also compare with returns of other equity funds in the market. At least ensure that your fund is in the top 10 percentile in the group in terms of returns and if it is not in that group then you must seriously consider switching out of the fund. As well be with the leaders in the group than the laggards.

When it comes to benchmarking with the peer group there are 2 further variants to consider. Firstly, you need to consider benchmarking on consistency than just purely on CAGR returns. Check the table below:

**Particulars End of Year 1 End of Year 2 End of Year 3 CAGR Returns**

Fund A – Starting NAV INR.114.00 INR..131.10 INR.152.08 14.997%

of INR.100

Fund Returns 14.00% 15.00% 16.00%

Fund B – Starting NAV INR.111 INR.106 INR.159.30 16.790%

of INR 100

Fund B Returns 11.00% -4.50% 50.28%

In the above instance, A and B are in the same peer group. If you are holding Fund A, then should you shift to Fund B? The answer is a clear “No”. That is because while Fund B has given higher returns, it is highly inconsistent. That makes Fund B highly unpredictable. That is why benchmarking with peer group should be done on returns and also consistency.

The second aspect of benchmarking is a risk. We have measures like which help calculate the risk-adjusted returns. Earning higher returns by taking inordinately higher risk is not a smart idea. This is one more thing to keep mind when benchmarking.

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Sandeep Raj Bhardwaj

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