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Measuring Returns – Simple, Annualised and Compounded (Part 1 of 2)

Investments are made with a basic principle of generating returns. Based on the risk appetite of an individual they invest in different asset classes. Returns is the amount of money one earns from an investment over a period of time. Every rupee earned on an investment is called a return. The outperformance or underperformance of an investment is measured based on the returns of different asset classes.


The returns are compared with different asset classes and at times against the benchmarks. One must be wondering, how to calculate and measure returns generated by any asset? There are different methods to calculate and measure returns, let us understand those in detail.


The first part talks about the simple, annualised and compounded returns. On the other hand, the second part talks about the importance of compounded annual growth rate (CAGR), holding period returns and rolling returns.


When we speak about calculating or measuring returns, there are three important factors: amount invested (known as principal invested), returns generated on the principal and time one has been invested for. For time, it is usually considered as a one year period, but based on the time frame there are few other concepts as well. We have discussed this in detail below.


Simple returns


When we speak about simple returns, as the name suggests, it is calculated by returns generated. However, the time frame is not considered or provided. Usually, the returns are calculated over a one year time frame basis.


For example, Mr. X had invested Rs. 1,000 in a mutual fund and the current value of the same stands at Rs. 1,200.


Here the principal is Rs. 1,000.


Returns generated are Rs. 200 (Rs. 1,200 – Rs. 1,000).


(Current Value - Initial value) * 100 / Initial value

(Rs. 1,200 – Rs. 1,000) * 100 / Rs. 1,000


= Rs. 200 * 100/Rs. 1,000


= 20%


Thus, simple return is simply the change in the value of an investment over a period of time. There is no specific time frame here. The returns may have come in one month, one year or even five years. Hence, while simple returns are easier to calculate returns, it is not considered the best way to measure returns.


Annualised returns


In simple returns, we only calculate the returns generated in percentage terms while the time factor was missing. In investment, the time factor is very important. Financial goals are mostly time based. Hence, to rationalise the time factor usually a one year basis is considered.

In the above example, if the amount invested of Rs. 1,000 becomes Rs. 1,200 in exactly one year. Then the yearly returns would be 20%. However, consider if Rs. 1,000 invested becomes Rs. 1,200 in just six months, then how do we rationalise the returns generated?


Here the equation would be as follows


(Simple returns *12 Month)/ Period of simple returns in months

Here, simple returns are 20 % and the period of simple returns holding is 6 months.


Hence,


(20 *12)/6


= 240 /6


= 40%.


To be specific, in six months the mutual fund investment had generated 20% returns. To rationalise the same it was converted into a yearly time frame, thus becoming 40%.


While we used months here, we could also use the number of days to calculate the same. In that case, the equation would be = (Simple returns * 365days)/ Period of simple returns in Days.


The advantages of annualised returns is that it gives a comparative analysis based on the time frame. For instance, if there are two different asset classes; investment X generated 5% return and investment Y generated 4% returns. However, it is just simple returns and there is no time frame mentioned about it. If one calculates based on simple returns, X seems to have performed well. However, if we attach the third factor of time, things may change. Like investment X generated 5% in 6 months and investment Y generated 4% in four months.

Here’s how we calculated the same for annualised returns of


Investment - X


= (5*12)/6


= 10%


Investment - Y


= (4*12)/4


= 12%


So on an annualised basis, investment Y is the better option. This means, with an element of time being involved in analysis, the perspective changes completely.


Compounded returns


Now that we are aware of time being the utmost important factor, let us understand compounding. Compounding is a series of gains on initial value of investment over a period of time. For instance, Mr. X has invested Rs. 10,000 at 10% per annum for three years. In compounding the returns would look like as follows.



If we had calculated by normal simple interest way of calculating returns, 10% per annum would have been like,


Rs. 10,000 *10% = Rs. 1,000 per year.


For three years it would have generated Rs. 3000 in three years and the closing balance of investment value would be Rs 13,000. In compounding, however, the closing balance is Rs. 13,310. The difference of Rs. 310 (Rs. 13,310 – Rs. 13,300) is because of the compounding effect. As the returns generated are reinvested the compounding returns are higher. Longer the period of investment holding, higher would be the difference.


There is an Excel Sheet formula provided for calculating compounding returns. The formula here would be put as:

A= P(1+r/n)^t

A - Accrued Amount, P - Principal Amount, r- Rate of interest, n - number of times interest applied and t - Time period


Let us understand the compounding in a different way. If someone has invested Rs. 10,000 and in next five years it doubles to Rs. 20,000. The returns are 100%. Annualised won’t work here as the time frame is more than one year. But if we put it in the compounding formula, the compounding has happened at 18.92% per annum. So, it is a series of 18.92% returns generated over the five-year period.


Challenges faced by investors


Conceptually, these calculations give one only the return in the form of change in net asset value (NAV). As we know, another form of return for an investor in a mutual fund scheme is dividend. Remember, NAV of a scheme goes down after a dividend is paid to the investor. Therefore, in the above examples, if dividends were paid, then that has not been captured in any of the three kinds of returns calculated, vis-à-vis, simple, annualised and compounded. So, the above three formulas are thus applicable only for growth schemes or for dividend schemes that have not paid a dividend during the period. Whenever a dividend is paid then the compounding must be considered. The compounded annual growth rate (CAGR) technique prescribed by SEBI is used. We’ve explained this in the second part of this blog.



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