Glossary

# Return Calculations

Return calculations quantify the profits and losses from investments. Return calculations measure the performance of individual assets or overall portfolios. There are multiple ways to calculate investment performance.

## Dollar Return

Total dollar return calculates the returns from portfolio investments over a defined time period. Dollar return is the actual aggregate profit and loss realized in an account. Dollar returns can be calculated on individual positions or the entire portfolio.

Total dollar return considers the capital gain or loss on an investment plus interest, dividends, and distributions. The total return is based on the change in the market value of an asset. The total return includes the reinvestment of dividend payments and capital gains.

For example, an investor purchases 100 shares of a \$50 stock for a net cost of \$5,000. If the stock pays a 5% dividend, the investor receives \$250 of dividend income at the end of the one-year holding period. If the stock price increases to \$60, the investor has a capital gain of \$10 x 100 shares, or \$1,000. The total value of the asset is now \$6,250. The total dollar return is \$250 + \$1,000 = \$1,250.

Total dollar return is important because it considers many factors of stock ownership, not just the change in an asset’s price.

## Percentage Return

Percentage return measures the percentage gain or loss on an asset or portfolio relative to its starting value.

In the example above, the investor earned a \$1,250 total dollar return on a \$5,000 investment. To calculate the total return in percentage, simply divide the total gains (\$1,250) by the starting value (\$5,000) = 25%.

Total percent return can be a better indicator of return on investment because it shows growth relative to the initial investment.

Dividend yield refers to the percentage amount of a security that is paid to shareholders as dividend income.

For example, a \$100 stock with a 5% annual dividend yield will pay the investor \$5 per share owned every year the security is held, and the company continues to pay the dividend.

Not all companies pay dividends. Dividend yield decreases as the underlying asset’s share price increases, and vice versa, assuming the dividend amount is constant.

## Annualized Return

An annualized return is the annualized amount of money earned by an investment or portfolio over a year. Annualized returns are calculated to represent what an investor would earn if the returns were compounded.

To calculate the annual return, divide the total returns by the number of years in the holding period. For example, if an investment has yielded 10% over a five year period, the annualized return would be 2%.

Investment returns can be compared to determine the volatility within the holding period, as not all returns are created equally.

A holding period return is the total return earned on an investment for the period of time it was held. Holding period return helps compare two assets’ return that were purchased and held at different times.

To calculate the holding period return as a percentage, subtract the asset’s current value from the purchase price, plus any dividend earned, and divide by the asset’s original value. For example, if an investor purchased one share of a \$100 stock, earned a 5% dividend yield, the stock increased to \$110, and was sold one year after the initial purchase, the investor earned \$15 for the year: \$5 + (\$110-\$100) = \$15/\$100 = 15% holding period return for the one year holding period.

The effective annual return includes the effects of multiple compounding periods and is higher than the annual percentage rate of return. The effective annual return calculates the return when compounded semi-annually.

For example, if a 15% return was made in 6-months, the annualized return would be higher than 15%.

The effective annual return is calculated using the following formula: 1 + Effective Annual Return = (1 + Holding Period Percentage Return)^m where m is the number of holding periods in a year. So, the 15% holding period return earned in 6-months would have an effective annual return equal to 1 + EAR = (1 + .15)^2 or 1.3225, for an annualized return of 32.25%.

## Average Returns

Average returns may be calculated using different methods.

The arithmetic average is the sum of returns divided by the number of holding periods. The arithmetic average is not typically a useful tool for calculating investment returns, as the value can be misleading because arithmetic returns ignore the effects of compounding. If a large portion of the portfolio’s account is lost in a single year, the percentage return on less capital is skewed because the results are not compounded.

For example, if an investor has returns of 20%, 40%, and -30% over a three year period, the arithmetic average return would equal 10% (20% + 40% - 30% = 30%/3 = 10%). But the 30% loss is significantly larger than the 20% gained in the first year.

Instead, the geometric average is often used in finance. Geometric average factors compound growth into its equation. Geometric return is calculated by adding 1 to each number, then multiplying all the numbers together and raising the sum to a factor of 1 divided by the total amount of periods calculated, and then subtracting 1.

In the above example, the calculation would appear as follows: (1.2)*(1.4)*(0.7)^1/3 - 1 = 1.1761/3 - 1 = 5.6%, much lower than the arithmetic return of 10%.

Dollar weighted returns include cash inflows and outflows. If money is deposited or withdrawn from an account, gains or losses are realized with the purchase and sale of assets, or dividends are received or reinvested, the dollar-weighted return will include these cash flows in the total return. The dollar-weighted return helps measure the overall performance of an investment.

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## FAQs

### What is the difference between a dollar return and a percentage return?

The total return is based on the change in the market value of an asset. Total dollar return calculates the returns from portfolio investments over a defined time period.

Dollar return is the actual aggregate profit and loss realized in an account and can be calculated on individual positions or the entire portfolio. Total dollar return considers the capital gain or loss on an investment plus interest, dividends, and distributions.

Percentage return measures the percentage gain or loss on an asset or portfolio relative to its starting value. Total percent return can be a better indicator of return on investment because it shows growth relative to the initial investment.

### How do you calculate the percentage return?

To calculate the total return in percentage, simply divide the total gains by the starting value. For example, if an investor earns \$1,250 return on a \$5,000 investment, divide the total gains (\$1,250) by the starting value (\$5,000) = 25%.

### How do you calculate annualized returns?

Annualized returns are calculated to represent what an investor would earn if the returns were compounded. To calculate the annual return, divide the total returns by the number of years in the holding period.

For example, if an investment has returned 10% over five years, the annualized return would be 2%.

For holding periods of less than one year, returns can be annualized to determine the compounded return. The effective annual return is equal to one plus the percentage return raised to the number of periods in a year minus one.

For example, if an investor made a 5% return in six months, the effective annual return would be (1 + 0.05)2 -1 or 10.25%.

### How do you calculate annualized returns in excel?

To calculate the annual return, divide the total returns by the number of years in the holding period. This can be calculated in Excel by inputting the values into cells and using the software’s functions to divide the values.

### What is the average rate of return on stocks?

The average return rate for stocks varies by market capitalization with small-cap and mid-cap stocks having higher average annual returns but increased volatility compared to large-cap stocks.