Annualized Rate
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:
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Where |
Equals |
|
Ra |
Annualized rate of return |
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Rc |
Cumulative rate of return |
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P |
Periodicity (number of time periods in a year:
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|
N |
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:
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.((1 + 0.1025) ^ (365/65) - 1
((1.1025) ^ 5.615385) - 1
0.729705 or 72.97%
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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%
∵ 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
53 / 7.2 * 52 = 390%
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.