Every investor has one goal in mind when they invest: to make money. Due to this reason many investors are interested to know what kind of return they are going to get before investing in anything. In this regard, annual return is used as a measure to report the historical rate of return of investments.

Here is a list of the most important tools used to measure rate of return on a investment;

- Return On Investment (ROI)
- Compound Annual Growth Rates (CAGR)
- Annual return
- Annualized return or Average Annual Return (AAR)

In case of a mutual fund, the average annual return measures the money lost or gained over a period of time. It’s a percentage calculated to know a mutual fund’s historical average return.

Not only in the case of mutual funds, you can use Average annual return of any investment portfolio and index. Many investors calculate the average annual return of the index to compare with their own return on investment to measure their performance.

Sensex and Nifty 50 are two indices which act as a benchmark of the performance of the indian stock market overall.

Similarly the S & P 500 index acts as a benchmark of the performance of the overall U.S. Stock market.

Investors use average annual return as a helpful guide for measuring a mutual fund’s long term performance. They compare AAR of a mutual fund with other similar mutual funds as a part of their investing strategy.

We have already discussed Return On Investment (ROI) and Compound Annual Growth Rates (CAGR) in our earlier articles. In this article we will be discussing what is annual returns and annualized returns.

## What is the annual return?

The annual return is the percentage of profit or loss an investment has generated over a year.

Annual return over a period of 12 months for an investment can be calculated by using following formula;

**Annual return = [ (ending value – beginning value of investment) / beginning value of investment ] *100**

Suppose you purchased 100 shares of XYZ limited at Rs 10 per share. Now shares are traded at Rs 11.5 per share. To calculate the performance of the share, you need to find out annual return.

Beginning value of your investment = 100 shares * Rs 10 per share = Rs 1,000

Ending value = 100 shares * Rs 11.5 per share = Rs 1,150

Annual return of your investment = [ (1,150 – 1,000) / 1,000] * 100 = 15%

Now the question arises, how to calculate the annual return when the investment period is more than one year.

In this case, annual return is calculated by taking the ending value, beginning value and the number of years for which you are calculating the return.

Here is the formula you have to use to calculate annual return for more than one year time period;

**Annual return = [(EV / BV) ^ (1/n)] – 1**

Where,

BV = Beginning value, its the value of the investment at the beginning of the period

EV = Ending value, its the value of the investment at the end of the period

n = number of years for which you want to calculate annual return

Let’s calculate annual return by taking following example;

Suppose Mr Kumar buys stocks of XYZ limited at Rs 500 on 1st January 2013. The price of the stock as of 31st December 2021 is Rs 1,500.

The annual return from the investment is

[(1500/500) ^ (1/8)] – 1 = 14.72%

Mr Kumar’s annual return from XYZ stock is 14.72%.

If the result is positive then it’s considered a gain, otherwise a loss.

In our above calculation we have only considered the share appreciation of an individual.

However, investment can have multiple sources of income. Here are the components that you need to consider while calculating annual return of your investment.

## Components to be considered while calculating annual return of your investment

For calculating annual return of a mutual fund or a investment portfolio, you can have following three components;

- Share price appreciation,
- Capital gain, and
- Dividends

Now, let us understand each of such components to calculate the return of a portfolio of assets.

### Share price appreciation

Share price appreciation is the unrealised gain or loss of the underlying security in a mutual fund or investment.

You can get share price appreciation by deducting the purchase price from the current market price of the stock or security.

A fund manager can change the proportion of each holdings based on its objective by adding or subtracting assets from the fund based. Therefore, it won’t be an easy task for a large fund house to calculate share price appreciation unless and until systematic records are maintained.

### Capital gain

Capital gain is the amount that the mutual fund has realized as a profit. The capital gain distribution by the mutual fund will reduce the fund value by the amount that is distributed.

A shareholder of the mutual fund can opt to receive cash or reinvest them in the fund.

### Dividends

Quarterly or yearly dividend received by the mutual fund from the company’s earnings can decrease the overall net asset value (NAV) of the mutual fund.

Like capital gain, you can opt to receive a dividend distributed in cash or reinvest the same in the mutual fund.

## What is annualized return or average annual return

Mutual funds, institutional investors and even individual investors do not invest in only one stock. They invest their money in different assets with different time periods. In order to compare returns on such investments with a one year return, you require to annualize them, which is also referred to as average annual return or annualized return.

Here is the formula to calculate annualized total return of an investment;

**Annualized return = [(1+a1) x (1+a2) x (1+a3) x … x (1+an)]^(1/n) – 1**

where a is the annual rate of return and n is the number of years in the period.

a1 is the rate of return for year 1

a2 is the rate of return for year 2

a3 is the reate of return for year 3…. and so on.

Result has to be multiplied with 100 to get the annualized return in percentage.

Suppose you have invested 100 shares at a price of Rs 10 each for 3 years. For the first year the stock has given 14% price hike, then increases 10% next year and finally falls by10% in the 3rd year. The rate of return for the 3 years of holding the stock is calculated as follows;

Annualized return = { [ (1+14%)*(1+15%)*(1-10%)]^(⅓) } – 1 = 5.669%

You might consider a AAR of 12% more attractive, however, if the yearly returns were 50%, 30%, -10%, -15% and +5%, then performance of the last three years should be looked in to know exactly the underperformance of the fund’s manager and the investment strategy.

Instead of giving a yearly rate of return, if you have only the end and beginning value, then you should use the following formula instead. We have already discussed it.

**Annualized rate of return = [(EV / BV) ^ (1/n)] – 1**