Annualized Rate of Return

What is the Annualized Rate of Return?

Annualized Rate of Return is a rate of return per year, when the return over a period, shorter or longer than one year is annualized to facilitate comparison amongst annualized return of same or different asset classes.

In simple words, An annualized rate of return is evaluated as an equivalent amount of annual return an investor is entitled to receive over a stipulated period. It is computed based on time-weight, and these are scaled down to a period of twelve months, which allows investors to compare the return on assets over a particular time.

For example, assume that an asset returned 50% in three years, and another asset has returned 85% return in 5 years. With this data alone, it will be hard to figure out which asset gave better returns until we scale these returns and find out which asset delivered a higher rate of return.

Formula

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For eg:
Source: Annualized Rate of Return (wallstreetmojo.com)

When the holding period is more than a year is calculated using the following formula:

Where,

• Ending Value = Value of investment at the end of the period
• Beginning Value = Value of investment at the beginning of the period
• n = Number of years in the period

In the above formula, 1/n can also be substituted with 365/days for a precise calculation. Here “days” will be the number of days the investment is held.

If the investment is held for a period less than a year, the return can be calculated using the following formula:

ARR Formula = (Ending Value / Beginning Value)^365/n – 1

Where

• n = Number of days the investment is held

It is worth noting that Global Investment Performance Standards (GIPS), a global body formulating performance reporting standards, recommend not to annualize performance of period less than one year.

Examples of Annualized Rate of Return

Below are the examples of this concept to understand it in a better manner.

Example #1

Comparing returns for an investment period of more than a year.

Assume two investments with the same beginning value of $100,000 are redeemed in different periods. Investment 1 returned $150,000 in ending value in 3 years while investment 2 returned $185,000 in ending value in 5 years. Total returns for the holding periods were 50%  and 85% for investment one and investment 2.

Solution

Below is given data for calculation of the annualized rate of return

Investment 1

• =($150000/$100000)^(1/3)-1
• =14.5%

Investment 2

• =($185000/$100000)^(1/5)-1
• =13.1%

Absolute comparison of returns will not be helpful here because the holding period is not the same. We need to calculate the rate of return for a meaningful comparison.

Once we have it, we can easily determine that Investment 1 has delivered better returns than Investment 2 on a like-to-like basis comparison of two investments.

Example #2

Comparing Return for the investment period of less than a year.

When the holding period of investment is less than a year, it might not be sensible to compare absolute returns because that does not consider the time taken by these assets to deliver the return.

For example, two investments, Investment 1 and Investment 2, have the same beginning value of $100,000. Investment 1 was kept for 100 days and delivered a 10% return with an ending value of $110,000. Investment 2 reached an ending value of $113,000 in 150 days returning 13% return on investment.

Solution

Below is given data for calculation of the annualized rate of return

Investment 1

• =($110000/$100000)^(365/100)-1
• =41.6%

Investment 2

• =($113000/$100000)^(365/150)-1
• =34.6%

On the face of it, 13% of Investment 2 looks like a better return than 10% of Investment 1. However, we will get different results if we rightly compare the returns of the two investments.

As evident from the calculations above, once we annualize the returns for both these investments, Investment 1 outpaces Investment 2 by a good margin, which was not the case before calculating the annualized return.

In practice, annualize returns for a holding period of less than a year are not considered the right barometer of performance because for several reasons—first, the investment horizonThe Investment HorizonThe term "investment horizon" refers to the amount of time an investor is expected to hold an investment portfolio or a security before selling it. Depending on the need for funds and risk appetite, the investor may invest for a few days or hours to a few years or decades.read more of less than a year too short for an investor to consider seriously. Second, extrapolating returns for a short period means that the investment could have earned a similar return for the entire, which might not hold in most cases. Third, annualized short term returns are, at best, forecasted returns and not real returns.

Conclusion

Annualized Rate of Return comes in handy while comparing and ranking returns. As absolute returns could be misleading, it provides clarity on the return profile of the investments. The biggest advantage is that it tells the investor a compounded annual rate of return, considering that the earnings from the investment were reinvested back at the same rate. It can also be termed as the compounded annual rate of return.

Recommended Articles

This article has been a guide to the Annualized Rate of Return and its meaning. Here we discuss the formula for calculation of the annualized rate of return along with practical examples. You can learn more about from the following articles –

• Calculate the Average Rate of Return
• Calculate ARR
• Rate of Return on Investment
• Calculate Geometric Mean Return
• Annuity vs. Lump Sum