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Last Updated : Apr 08, 2019 09:16 AM IST | Source: Moneycontrol.com

# Viewpoint | Don't rely on heuristics, do the math for compounded return on investments

## A lot of mischief and harm is caused by unscrupulous sellers by using simple interest in place of compound interest.

Rajeev Thakkar

Rajeev Thakkar

Most people come across the compound interest formula in high school. It is usually memorised for the test and quickly forgotten. Over decades of interacting with clients and others, this is one kind of mathematics that does not come naturally to most people. Because of this, as a substitute for mathematically accurate calculation of the actual compounded rate of return (XIRR for the excel geeks) on financial instruments, most people rely on heuristics (mental shortcuts).

The following are some of the heuristics used and the harm which it causes over the long term.

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1. Thinking in absolute return terms

Rajeev Thakkar
CIO & Director |PPFAS Mutual Fund

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This kind of thinking goes like this “Investment A tripled and Investment B doubled.” Seems legit, right? However, it ignores the time taken to do that. If investment B doubled in 20 years, it is a terrible return whereas if that was done in 5 years, it is a great return. A lot of insurance sold as investments uses these kind of heuristics where the annual compound rate of return is neither conveyed by the seller nor calculated by the purchaser.

2. Using simple return as a substitute for compound return

Investment P doubled in 5 years. That means 100% returns over 5 years. That means 20% returns annually....right? Wrong. Using the compound interest formula, it is clear that the return is 14.86% per annum.

A lot of mischief and harm is caused by unscrupulous sellers by using simple interest in place of compound interest. As an aside, I have even seen some superior court judgements use simple interest to calculate compensation for delayed payments by one party to another for periods as long as a decade and half.

3. Overweighing returns on long term investments and under-weighing returns on short to medium term investments

In this kind of thinking, what happens is that say investment D which has gone up 4 times in value over 20 years (7.18% return per annum) is seen as a better investment than investment E which has “just” doubled in 7 years (10.41% return per annum).

4. Overweighing returns on larger investments and under-weighing returns on smaller investments

When investors think of returns, they think in terms of Rupees and Paise. An investment which gave a profit of Rs 1 crore is obviously better than an investment which gave a return of just Rs 10 lacs right? Even assuming that the period of investment is the same, one has to look at the amount of principal invested.

Given the large amounts of investments that a lot of people have in real estate and gold, the returns from those assets seem larger in absolute amounts. Investments in equities or fixed income securities (financial assets) are of lower amounts and returns seem poor on an absolute basis even though on a percentage return basis the returns could be higher.

5. Calculating returns pre expenses and pre tax

On many occasions, investors just remember some arbitrary purchase price for say an apartment. The repairs and renovation and improvements done on the property, stamp duty, registration charges and brokerage paid and the tax paid on the gains are ignored.

By such arbitrary methods of calculation, many a times, selection of the correct asset classes gets distorted and a wrong conclusion is drawn.

Solution

The ideal solution for most people would be to use a readily available tool called XIRR in Google spreadsheet, Microsoft Excel or any other spreadsheet program. Here, all one needs to do is input the dates for each cashflow and the corresponding cashflow. Outflows (investments) are input as negative amounts. Inflows like interest, dividend, rent, sale value are input as positive values and the XIRR function gives the correct annualised return.

This is not too difficult to learn and one get a grasp of this in under 30 minutes.

If this sounds like too much work and one wants to rely on Heuristics, using the rule of 72 is a good way of going about it rather than using the heuristics listed above.

Rule of 72 gives you the time it would take to double your money given an annual rate of return. It can also give you the annual rate of return if you know the time period in which your investment has doubled in the past.

For example,

a) If you are investing at the rate of 8% p.a. according to the rule of 72, you will double your money in approximately 72 / 8 that is 9 years.

b) If you had invested Rs 100 ten years back and it has now doubled, the approximate annual rate of return that you have generated as per the rule of 72 is 72 / 10 or 7.2% per annum.

Do brush up on your high school mathematics and happy investing in the new financial year.

(The author is Chief Investment Officer & Director, PPFAS Mutual Fund. Views are personal.)
First Published on Apr 8, 2019 09:16 am

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