# Actual Rate of Return, Explained

## What is actual return?

Actual return is the nominal gain or loss made by investment within a specified period.

### How does actual return work?

The actual return is the exact amount of money gained or lost during a period relative to the initial investment value. For example, the actual return on a stock purchased at \$100 and its value at the end of the year is \$120 is said to have a return of 20%.

The formula for actual return is: (ending value-beginning value)/ beginning value = actual return.

The expected return is the projected return on investment based on the historic performance combined with predicted market trends.

## The basics of actual return

Actual return is what investors receive from their investments, unlike the expected or assumed returns. For instance, a mutual fund’s disclosure could say that you get 5% annual returns from your investment. The actual returns may be different. The discrepancy between the expected returns and actual returns is explained by the systematic(market’s) and the idiosyncratic(manager’s/fund’s) risk factors on the portfolio returns.

Drivers of actual returns include trading costs, managers fees, investment timeframe, additional investment or withdrawals, inflation, and taxes over a given period.

Both the Government Accountability Office (GAO) and the Securities and Exchange Commission (SEC) have made proposals to require mutual fund companies to improve disclosures they provide to investors over the years. In a Final Rule issued in February 2004, the SEC mentions differences between actual and expected returns. For example, a mutual fund describing and illustrating the costs and performance of a hypothetical investment over a five-year period must reference actual return numbers and actual cost figures.

## Why does actual return matter?

The disparity between the expected return and actual return on investment provides an analytical framework that explains how an investment performed and why it performed differently than expected.

### The formula for rate of return ROR

The standard formula for ROR is as given:

Return= Ending value of an investment – Beginning value of investment X 100

Beginning value of investment

Remember, any gains made during the holding period of an investment must be included in the formula. For example, if a share costs 410 and its current price is \$15 with a dividend of \$1 is paid, it must be included in the ROR formula. The calculation is as follows.

((\$15+ \$1- \$10)/ \$10) x 100 = 60%

### Example rate of return calculation

John, a retail investor, buys ten shares of Company A at a per-unit price of \$20. He holds the shares for two years. Company A paid a yearly dividend of \$1 per share. After the two years, he decides to sell the ten shares at an ex-dividend price of \$25. What is the rate of return during the two years?

To determine the rate of return, first, calculate the number of dividends he received over the two years:

10 shares x (\$1 annual dividend x 2) = 420 in dividends from 10 shares

Next, calculate how much he sold shares for:

10 shares x \$25 = \$250 (Gain for selling 10 shares)

Lastly, determine how much it cost to purchase ten shares from Firm A:

10 shares x \$20 = \$200 (cost of buying 10 shares)

Put the numbers into the ROR formula

= ((\$250 + \$20- \$200)/ \$200)x 100 = 35%

Therefore, John realized a 35% return on his shares over the two-year period.

## Annualized rate of return

The regular ROR describes the gain or loss, which is expressed as a percentage of an investment over an arbitrary period. The annualized ROR is also known as the Compound Annual Growth Rate (CAGR), is the return of an investment over each year.

### The formula for annualized ROR

The formula is given as follows:

Gains earned at holding period an investment must be included in the formula.

### Example of annualized rate of return

Let us use the previous example to determine annualized ROR. Recall John purchase ten shares at a per-unit price of \$20, received \$1 in dividends per year. He sold the shares at a price of \$25 after two years. The annualized ROR is computed as follows:

((\$250 + \$20)/ \$200)1/2 – 1 =16.1895%

John made an annualized return of 16.1895% on his investment

### Alternative measures of return

Common alternatives include:

## Why calculate it?

There are many benefits of calculating return on investment. You tell whether the investment was a wise choice. For example, if the rate of returns stocks you have invested in is good after a short time, you can invest in more stocks. If the stocks show a substantial loss, you can find a better performing stock.

Calculating the rate of return helps you gauge the investment and decision-making skills. If an investment has high gains, it is great. If it has huge losses, you may want to change your investment strategies. Understanding how to calculate the rate of return helps investors change strategies.

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