Annualized Rate

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Annualized rate is a rate of return for a given period that is less than 1 year, but it is computed as if the rate were for a full year. It is essentially an estimated rate of annual return that is extrapolated mathematically. The annualized rate is calculated by multiplying the change in rate of return in one month by 12 (or one quarter by four) to get the rate for the year. Annualized rate of return is computed on a time-weighted basis.

For example, if one month's rate of return is 0.21% and the next month's is 0.29%, the change in the rate of return from one month to the next is 0.08% (0.29-0.21). The annualized rate of return is equal to 0.08% x 12 =0.96%. But the more accurate way is to calculate geometric average rate of return.

Annualized rate of return (geometric average) is calculated as follows:

Annualized rate




Annualized rate of return


Cumulative rate of return


Periodicity (number of time periods in a year:
4 for quarterly data, 12 for monthly data, 365 for days)


Number of time periods in observed diapason

How to Calculate Annualized Rate of Return

I set up the Prudent Portfolio with $10,000 nearly 65 days ago. As of this morning it had an account balance of $11,025, with a total gain of $ 1,025. If that were the gain for the year, it would be a 10.25% return for the year. But, it's not. It's the return for 65 days. So, how do you annualize that number to get a rate of return for a year? That's simple enough. Here's the formula:

((1 + Rate of Return) ^ (365/65)) - 1

365 - days in whole year

The Rate of Return is 10.25% or 0.1025

So, the formula looks like this:

((1 + 0.1025) ^ (365/65) - 1

((1.1025) ^ 5.615385) - 1

0.729705 or 72.97%

So you can now have the annualized rate of return on your investment. It may become smaller as the year passes because this high rate cannot necessarily be maintained unless a very detailed market analysis is made in conjunction with timely sale and purchase of stocks.
Quote Guest, 14 October, 2013
Method is right, calculation is wrong. 1.1025 should be raised to tit.he power 5.615385 not multiplied by it.
Quote Guest, 25 April, 2014

effective annual yield= (1+holding period yield)^(365/days in the period)-1

EAY= (1+0.1025)^(365/65)-1=0.729705=72.97%

In the example above EAY is 72.97%
Quote Vit. A., 28 April, 2014
Thanks! The calculations have been corrected, the author will be killed ;)
Quote Guest, 1 January, 2015
Simplified: (Holding Period Ratio ^ (365 / Days Held))  -  1

∵ Holding Period Yield = (Ending Number / Beginning Number) - 1
∴ 1 + Holding Period Yield [IMG] 1 + (Ending Number / Beginning Number) - 1

And since parentheses and division have a higher order of operation precedence in mathematics, the ratio of Ending Number to Beginning Number gets calculated first. Thus, the ones cancel out as one minus one is zero.

In a spreadsheet: (End/Begin)^(365/days held)-1
Quote Guest, 28 March, 2016
So is this effective annual yield or Annualised yield and what is the annualised yield is it plain 10.25% multiplied by 5.6???
Quote Guest, 21 November, 2018
What you are doing here is assuming a compounding rate and interval of exactly 65 days.
Quote Steve, 25 September, 2019
I'm trying to calculate 54% return over 7.2 weeks to get APR% - anyone?
Quote Cornelius J. van Dyk, 4 May, 2020
54% / 7.2 weeks * 52 weeks = APR
53 / 7.2 * 52 = 390%
Quote Guest, 17 August, 2020
Second quarter YTD ROCE is 9.37%. How to apply the formula for annualising
Quote Guest, 5 February, 2021
I don't think that investment companies typically annualize returns for periods shorter than 1 year. If they did the computation as you describe, it could be taken by some as projecting that the 65-day return *would* continue for the rest of the year, and of course they cannot do this. It might get them in hot water.

However, it is common to annualize total returns of longer than one year (e.g., 2, 3, 5, or 10 years). This gives you a (geometric) average annual return over that period.

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