How to Annualize a Percentage Rate of Return

Understanding how investments perform and regularly measuring that performance is the stock and trade of the sophisticated shareholder. Taking into account all of the variables that affect a security, investors carefully watch the rise and fall of values to predict, as best as is possible, future realizations.

One of the metrics that aids in this endeavor is the percentage rate of return or, simply, the rate of return (ROR). This measurement is the net loss or net gain of the investment over a particular stretch of time. This shift is expressed as a percentage of what was paid for the investment to begin with. The annualized rate of return condenses the ROR to reflect a full year.

By subtracting the initial value of a stock, bond or other asset from its current value, and then dividing that difference by the initial value, you get a quotient that must then be multiplied by ​100​. This is the ROR.

Alternative names for this are the growth rate or the return on investment (ROI). For simplicity's sake, then, a stock with a value of ​$25​ that was initially purchased at ​$20​ will show an ROR of ​25​ percent.

​Read More:​ How to Calculate ROI by Period of Time

Before we calculate an annualized rate of return, we should answer a more basic question. Why is this necessary?

Assets are purchased at different times and for differing terms. Comparing them for their profitability can be like comparing apples to oranges unless some way is found for standardizing their earnings. When we annualize a number, we can evaluate it side-by-side with other investments' annualized ROR. This way, investors can rank their securities in terms of profitability. Here is how it is done.

Three factors are needed to formulate the annualized rate of return. The amount for initial investment, the gains or losses realized and the number of years the investment is held thus far. With this, you are provided the annualized performance rate.

Assume an investor placed ​$35,000​ into a mutual fund, for instance, and the fund was valued at ​$55,000​ after four years, representing a ​$20,000​ gain. Dividing the ​$55,000​ by the ​$35,000​ gives a quotient of ​1.57​ which is raised to the ​1/4th​ power, with ​4​ representing the number of years held, and then subtracted from one. This example leaves us with an ROR of ​11.95​ percent.

​Read More:​ How to Calculate a Stock's Realized Annual Return

The number of years is crucial since the annualized rate of return is time-weighted. If the specified time of asset ownership is less than a full year, the calculation is different, employing the cumulative rate of return, i.e. an aggregate number reflecting only the number of months of ownership. This figure is found by subtracting the original price from the current price and dividing the difference by the original price.

From there, the annualized rate is derived by first adding one to the quotient of the cumulative rate divided by ​100​. Raise that sum to the quotient of ​12​ (for months) divided by how many months the asset is owned. Subtract one from that figure and multiply by 100.

The Global Investment Performance Standards (GIPS) are guidelines to which investment professionals voluntarily adhere. Among these ethical rules is one warning against extrapolating annualized rates from securities owned less than a full year. This is put in place to prevent brokers and financial advisors from projecting an asset's value for the remainder of a given year. As always, numerous variables come into play that make briefly held investments harder to measure.