Understanding your investments means keeping an eye on a lot of different spinning plates, but none are as important as the math surrounding your returns, including knowing how to annualize daily returns. It's a very simple process once you understand the components of the equation and how to apply it to your own portfolio.
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Converting returns
How to convert returns
Converting returns isn't difficult, especially when you're going from a daily return to an annual return. Before you start, you'll need to know just one piece of information: How much is your daily return on your investment? Once you know that, you can follow these steps to calculate your annual returns.
Start by converting your return percentage to a decimal. Do this by dividing the return percentage by 100, or slide your decimal two places to the left. Example: 0.02% becomes 0.0002. This is now your Daily Return.
The equation for converting Daily Returns (DR) to Annual Returns (AR) is as follows:
AR = ((DR + 1)^365 – 1) x 100
Returns
Returns are the difference between the initial price of an asset and the dollar value that has been generated after ownership has ended.
When you do this math, it's important to understand that you're raising your DR + 1 by 365 because that's how many return periods you have in your year. If there were fewer, like, say, you only saw returns quarterly, you'd use 4, or if it was only figured based on business days, you'd use 250.
Here's an example of this in real life. Let's say your investment has given you a daily return of .05% this year. That would mean your equation would look like this:
AR = (0.0005 + 1)^365 - 1) x 100 = 20.02%
So your annual return would be 20.02%, which is pretty fantastic for a great number of investments.
Converting returns to annual
Converting other returns to annual
Of course, as stated above, you can also convert other types of returns to annual using the same formula. If you have quarterly returns, for example, you'd simply swap out the 365 for 4 since your periodicity is now quarterly (four times a year) instead of daily (365 times a year). This applies to any type of period that's less than a year.
| Periodicity | Formula | Example |
| Daily | AR = (DR + 1)^365 – 1) x 100 | AR = ((0.0002 + 1)^365 – 1) x 100 = 7.57% |
| Weekly | AR = (DR + 1)^52 – 1) x 100 | AR = ((0.0002 + 1)^52 – 1) x 100 = 1.05% |
| Monthly | AR = (DR + 1)^12 – 1) x 100 | AR = ((0.0002 + 1)^12 – 1) x 100 = 0.24% |
| Quarterly | AR = (DR + 1)^4 – 1) x 100 | AR = ((0.0002 + 1)^4 – 1) x 100 = 0.08% |
Related investing topics
Equation
Converting returns can be simple
Although it can be intimidating to convert your daily, weekly, or monthly returns to annual returns, it's really pretty simple. The same equation can be used regardless of the number of times your investment returns in a year; just simply swap out the 365 (the periodicity) in the basic equation to reflect the number of returns you actually have in your year.
Again, that equation is: AR = (DR + 1)^365 – 1) x 100.
FAQs
Converting Returns FAQs
How do you calculate total return from daily return?
You can calculate a total return over multiple years using the daily return (DR) formula, as well. You'll just need to add an extra step. First, figure out the annualized return (AR) for each year that you're including in your total return using this formula: AR = ((DR + 1)^365 – 1) x 100.
Next, take the AR and put it into a similar equation in the same way, along with first converting the annual return to a decimal.
AR = (((1 + AR1) x (1 + AR2) x (1 + AR3)... x(1+ARn))^(1/n) – 1) x 100
AR1 is your first year's annual return, AR2 is your second's, and so forth until you've got all the years included. The value of n is the total number of years, so you'll raise the lot of your returns by 1/n and minus 1 to get the decimal value of your return rate, then multiply by 100 to convert it to a percentage.
How do you annualize the daily interest rate?
There are two formulas you can use to annualize daily interest rates, either by calculating the annual percentage rate (APR) or the annual percentage yield (APY), depending on your goal.
Calculating the APR based on daily interest is simple: Multiply the periodic rate by the number of periods in the year, in this case, 365. So, if the rate was 0.02%, your equation would be:
APR = 0.0002 x 365 x 100 = 7.3%
It's similar but more complicated for APY:
APY = (1 + periodic rate)^ number of periods) – 1
In our example, that would be:
APY = (((1 + 0.0002)^365)) – 1) x 100 = 7.57%
What is the formula for calculating annual return?
Your annual return can be calculated by taking the gain or loss in your investment, and dividing it by your initial investment value, then multiplying by 100.
For example, if your initial investment was $125, but after a year, it was worth $150, it would look like this:
Annual Return = (($150 – $125) / $125) x 100 = 20%
How do you convert monthly return to annualized return?
If your investment has monthly returns instead of daily returns, you can use the same equation but change the number for periodicity from 365 to 12. The formula then becomes:
AR = (DR + 1)^12 – 1) x 100
How do you convert monthly return to annualized return?
You can convert other types of returns to annual using the same formula. If you have monthly returns, for example, you'd simply swap out the 365 for 12 since your periodicity is now monthly (12 times a year) instead of daily (365 times a year). This applies to any type of period that's less than a year.
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