Sam Ghosh
Founder and SEBI Regd. Investment Adviser at Wisejay Private Limited
Bangalore, Karnataka

How to know how much return you got from your investment? Calculations for Holding Period Return, Annualised Return, CAGR, Real Return and Total Return.

In Investment Advisory

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01:05:55 PM, 3rd January, 2019

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HOLDING PERIOD RETURN

This is the most straight forward way to calculate returns. If you have invested Rs. 10 and current value is Rs. 12, the growth is 20% and this is the holding period return.

Holding Period Return =((End Value – Beginning Value) / Beginning Value) x 100%

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ANNUALISED RETURN

While, holding period return is easy to calculate, it is not comparable. Consider you are comparing two investments, one of which grew from Rs. 10 to Rs. 20 in 5 years and another from Rs.10 to Rs. 30 in 10 years. The holding period return from the first investment is 100% and the second one is 200%. The second investment looks better on the basis of holding period return but it was invested for a much longer period.

Now, let us convert the return to an annual return using the following formula

Annualised Return

= (End value - Beginning value)/Beginning value) x 100% x (365/ holding period of investment in

days)

Annualised Return for First Investment: 20%

Annualised Return for Second investment: 20%

So, the reality is that the annualised return for both the securities are same.

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COMPOUNDED ANNUAL GROWTH RATE (CAGR)

The issue with the above mentioned Annualised Return is that it does not consider the effect of compounding. To calculate the annulised return with consideration to the effect of compounding, we have to calculate the CAGR which is given as

= ((End Value / Benginning Value) ^(1/Number of Years))-1

or

= ((End Value / Benginning Value) ^(365/Number of days))-1

How do we know that our calculated CAGR is right. Well, let us see.

Consider the investment which grew from Rs. 10 to Rs. 20 in 5 years.

CAGR = ((20 / 10) ^(1/5)) – 1 = 14.87%

Now, if we invest Rs. 10 at a compounding rate of 14.87%,

Value after one year = Rs. 10 x ( 1 + 14.87%) = Rs. 11.49

Value after two years = Rs. 11.49 x ( 1 + 14.87%) = Rs. 13.20

Value after three years = Rs. 13.20 x ( 1 + 14.87%) = Rs. 15.16

Value after four years = Rs. 15.16 x ( 1 + 14.87%) = Rs. 17.41

Value after five years = Rs. 17.41 x ( 1 + 14.87%) = Rs. 20.00

So, we are getting the End Value same.

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TOTAL RETURN

The issue with the approaches mentioned above is that they do not consider any intermediate cash flow. Value stocks and coupon bonds give dividends and coupons before the redemption and that adds to the return. For example, consider that the investment which grew from Rs. 10 to Rs. 20 in five years gave Rs. 1 dividend at the end of first, second and third year. We cannot just ignore these cash flows for the return calculation because the dividend paying investment is not comparable to an investment which does not pay any dividend.

We can use the Internal Rate of Return (IRR) to calculate the total return. For the above mentioned investment the IRR is 20.39%, considerably higher than the CAGR calculated above.

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REAL RETURN – EFFECT OF INFLATION

Till now, we have considered the return in nominal terms – i.e. growth in monetary terms. But, just because the investments is increasing in monetary (nominal ) terms does not mean that we will benefit from the growth.

Consider, you have invested Rs. 100 in September 2017 and in September 2018, the value increased to Rs. 103. Does that mean the value of the investment grew 3%. Not really.

Let us introduce the purchasing power of money. It indicates the amount of goods and services we can purchase using money.

Now, the Year to Year increase in consumer prices was 3.8%. So, practically you lost around 0.8% purchasing power of your investments.

Real return = ((1+ Nominal Return) / ( 1+ Inflation rate)) – 1

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EFFECT ON INCOME TAX ON RETURN

All the above calculations ignored the effect of taxes. A simple way to calculate the after tax return

After Tax Return

= Before Tax Return x ( 1- Marginal Tax Rate)

This formula cannot be used directly in the calculation of the total return because of time value money. All the cash flows needs to be adjusted for tax and then the IRR needs to be calculated.

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