In our first part of measuring returns, we had discussed the calculation of simple returns, annualised returns and compounded returns. In this part we are going to focus on compounded annual growth rate (CAGR).

**Understanding CAGR**

The CAGR calculation is based on an assumption that the dividend would be reinvested in the same scheme at the ex-dividend net asset value (NAV). The following example will clarify the calculation.

Mr. X invested Rs. 10,000 in a scheme at Rs. 10 per unit on June 30, 2014.

On January 1, 2015, the scheme paid out a dividend of Re. 1 per unit. The ex-dividend NAV was Rs. 12.50.

On January 1, 2016, the scheme paid out another dividend of Re. 1 per unit. The ex-dividend NAV was Rs. 15.

Let us now calculate the CAGR, which captures the impact of both dividend payments and compounding.

Formula for CAGR is

**CAGR= ((Current Value/Initial Value)^(1/t) -1)**

*t is time in years*

We know that the initial value of investment by Mr. X is Rs. 10,000.

If Rs. 10,000 was invested at Rs. 10 per unit, then Mr. X would have 1,000 units (Rs. 10,000/Rs. 10) of the mutual fund. The first dividend of Re. 1 per unit on 1,000 units would amount to Rs. 1,000. As per the compounding rule, if this amount were reinvested in the same scheme at the ex-dividend NAV, then Mr. X would have 80 additional units (Rs. 1000/Rs. 12.50). Thus, Mr. X unit-holding would have gone up from 1,000 to 1,080 units.

The second dividend of Re. 1 per unit, on the revised unit-holding of 1,080 units would amount to Rs. 1,080. If this amount were re-invested in the same scheme at the ex-dividend NAV, then you would have 72 additional units (Rs. 1,080/Rs. 15). Thus, unit-holding of Mr. X would have gone up from 1,080 to 1,152 units. At Rs. 15 per unit, this would be valued at Rs. 17,280.

Therefore, the current value of units is Rs. 17,280.

Let us now analyse the time period. From June 30, 2014 to January 1, 2016 the investment was held for 550 Days around 1.51 years. Putting in the formula of compounding interest, the per annum returns would be 43.65%. When longer period returns of different mutual funds are shown in open domain, it is given in the CAGR format.

**Holding period and rolling returns**

Holding period returns (HPR) is calculated for a fixed period such as one month, three months, one year, three years or since inception. The return is calculated using CAGR if the holding period is over one year and simple absolute returns for less than one year. Holding period returns may not present an accurate picture of the returns from a fund if the initial value or the end value used for calculation was too high or low. But still the holding period return is a fundamental metric in investment management.

The HPR measure provides a comprehensive view of the financial performance of an asset or investment because it considers the appreciation of the investment, as well as the income distributions related to the asset like dividends paid, etc. The HPR can be used to compare the performance of different investments or assets.

For instance, if Mr. X had invested Rs. 10,000 and after two years the investment value stands at Rs. 14,400. The CAGR would be 20%. However, during this period he also got a dividend of Rs. 300 in first year and Rs. 300 in second year. Now the returns would be Rs. 15,000 (Rs 14,400 + Rs 300+ Rs 300). So, the CAGR here for two years would be 22.47%.

**Rolling Returns**

Rolling returns, also known as rolling period returns are annualised average returns for a period, ending with the listed year. To simplify, all consecutive one year returns in a three-year period with a daily, weekly and monthly rollover is calculated and averaged.

For instance, the five-year rolling return for 2015 covers January 1, 2011, to December 31, 2015. The five-year rolling return for 2016 is the average annual return for January 1, 2012 to December 31, 2016. Some investors will break down a multi-year period into a series of rolling 12-month periods or even 36-month (3 years) periods.

By looking at rolling returns, investors are able to understand how a fund's returns stacked up at a more particular point in time. If an investment displays a 9% annualised return over a 10-year period, this shows that if one had invested on January 1 in a base year (start of investment), and sold his investment on December 31 at the conclusion of year 10, they earned the equivalent of 9% per year. During those 10 years, returns could have varied drastically.

In year 4, the investment could have moved up 35%, while in year 8 it could have dropped 20%. Averaged out, one earned 9% per year (the ‘average annualised’ return), yet this 9% might misrepresent the investment’s performance. Rolling returns help us in finding out how the scheme or asset class performed during a particular period.

If one is looking at investing in a large-cap equity fund for 5 years, they should check the historical 5-year rolling return for that particular fund. By doing so, they will get a perspective of historical return range plus its average. Based on the asset cycles rolling period returns should be checked. If some are looking at investing in equity oriented funds, then please consider at least 5 years rolling returns or higher.

**Scheme returns and investor returns**

The discussion so far focused on mutual fund scheme returns. However, one must understand that investors might have a return profile that is different, on account of the role of loads charged by the asset management company (AMC).

In the earlier example, the CAGR was calculated with the closing NAV as Rs. 15. However, if an exit load of 1% was applicable, then Mr. X will receive only 99% of Rs. 15 i.e., Rs. 14.85 on repurchase. Thus, the return as an investor would be lower than the scheme returns.

Similarly, if the original investment had suffered an entry load of 2%, Mr. X would have bought the units at 102% of Rs. 10 i.e., Rs. 10.20. This would have brought down the returns. (Fortunately for the investor, entry load is no longer permitted). Loads thus drag down the investor’s return below the scheme return. Even taxes can pull down the investor’s post-tax returns. The returns generated from the scheme are taxable and as per regulation it would be taxed. So, one must reduce the taxation impact as well while calculating returns.

All in all, investor returns might vary from the scheme returns also on account of choices regarding investment schedule, i.e., additional investment being made during the period or redeeming a portion of the investment. In such a case, for the same period investor’s returns may be different from the published returns of the scheme.