Return calculations quantify the profits and losses from investments and measure the performance of individual assets or overall portfolios. 

Dollar returns, percentage returns, holding period returns, annualized returns, average returns, and more are used to measure investment performance.

What is annualized return?

The annual return is simply the return earned over one year. However, not all investments are held for one year. Some are held longer, and some are held much shorter. 

An annualized return is the annualized amount of money earned (or that would be earned) by an investment or portfolio over one year.

Annualized returns are calculated to represent what an investor would earn if the holding period returns compounded over a year.

How to calculate annualized return

The 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 held at different times for potentially different durations.

To calculate the holding period return as a percentage, subtract the asset’s current value from the purchase price, add 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, and sold the stock for $110 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.

If the investor made the 15% return in 6-months, the annualized return would be higher than 15% because there are two 6-month periods in a year.

The effective annual return is calculated using the following formula:

So, a 1% holding period return earned in one month would have an effective annual return equal to 12.68%.

The holding period, m, is one month. Since there are 12 months in a year, the exponent in the annualized return calculation is 12. 

Notice the effective annual return is greater than 12% (simply taking 1% and multiplying it by 12) because each period’s 1% return compounds on top of the previous period’s starting balance.

For illustration, if you decrease the holding period from one month to one week, the effective annual return compounds significantly.

Calculating annualized returns allows traders to compare “apples to apples” to assess portfolio performance across timeframes. 

See evaluating portfolio performance for more performance calculations insights.