# What is an Average Annual Return - AAR

### Average Annual Return

Average Annual Return (AAR): is a measure of money gained or money lost by a mutual fund. It is calculated over a set period to evaluate long-term performance.

## Average Annual Return Details

A mutual fund is a financial company that accumulates money from several investors to invest in assets and securities such as bonds, stocks, short-term debt, and other money market instruments. The combined holdings that the mutual fund possess are referred to as its portfolio. Investors buy shares in mutual funds because;

- it's a relatively low amount for the initial investment.
- of the ease of redeeming their shares.
- of the ability to spread risk over several investments.

For the Average Annual Return to be calculated, one needs to know the Annual Rate of Return. The Annual Rate of Return is derived by dividing the surplus or deficit at the end of the year by the initial investment at the beginning of the year.

The Average Annual Return is calculated by:

AAR = [(1+X1) * (1+X2) * …*(1+Xi)1/n

Where X = Annual Rate of Return for years one, two, and so on.

And n = number of years of the period in view.

## Example of Average Annual Return

For example, if an investment company, Cloudcom, began its fiscal year with $10 million and ended the year with $10.5 million, the Annual Rate of Return is:

The Annual Rate of Return is X = ($10.5 million - $10 million)/$10 million

The calculation above gives us 5% or 0.05.

For example, if the Annual Rates of Return for the first, second, and third year of an InfoTech start-up are 0.02, 0.03, and 0.05, respectively, the Average Annual Return will be:

AAR = [(1 + 0.02) * (1 + 0.03) * (1 + 0.05)]1/3

AAR = [1.10313]1/3 or 1.033.

To obtain the rate, subtract 1 from the determined value.

The Average Annual Return is 0.33 over three years.

## Types of Average Annual Return Elements

One of the elements of the Average Annual Return is the share price appreciation. This arises from the unrealized stock gains and losses within the mutual fund's portfolio. Over a year, the share price of a stock fluctuates. These fluctuations contribute positively (increase value) or negatively (decrease the value) to the Average Annual Return.

Another element of the Average Annual Return is the dividends. Shareholders of corporations earn profits called dividends. When quarterly dividends are paid from the investment earnings, they can improve the Average Annual Return but reduce the portfolio's net asset value. The shareholders can choose to receive the dividend allocations in cash or to reinvest them in the fund.

The third element of the Average Annual Return is capital gain distribution. The sale of stocks or generation of income from which an investment manager derives profit is usually paid to investors as capital gains. Like dividends, the shareholder can choose to receive the distributions in cash or reinvest them in the fund, and the distributions to shareholders are taxable. It is important to note that a mutual fund can negatively affect Average Annual Return and still make taxable distributions.

## Net Present Value vs. Average Annual Return

The Net Asset Value (NAV) of an investment company is the difference between its assets and securities and its liabilities. The Net Asset Value can be negative. This usually happens when the company borrows and spends a significant part of its income, servicing the debts, thus reducing the net income value. Negative Net Asset Values can also occur when the value of the assets reduces drastically.

For example, company A previously used wired infrastructure to provide service to their customers, then rival companies started using more effective wireless solutions. A’s major assets, including wires, poles, large equipment, and backup devices, lose value drastically.

For example, if Sambisa Investment Company has assets worth $5 million and securities worth $7 million, with liabilities of $4 million, the Net Asset Value is calculated as:

NAV = (Assets and Securities) - (Liabilities)

NAV = ($5 million +7 million) - ($4 million)

NAV = ($12 million) - ($4 million) = $8 million

The Net Asset Value is $8 million.

The knowledge of the Average Annual Return calculation helps to inform investment decisions and help stakeholders manage risks.