The term daily return indicates the daily rate of growth of an investment. Since the majority of investments are reported as annual returns, it is important to convert your daily returns to annualized rates of return. To accomplish this, you need to go beyond simple mathematical calculations to determine compound growth. Just multiplying your daily return by 365 will not enable you to accurately annualize daily returns for all investments.
Formula for Calculating the ARR
You can compute the annualized rate of return (ARR) on an investment by performing the following formulated steps:
1. Convert to a decimal number. Convert the daily return percentage to a decimal number by dividing this percentage by 100. For instance, if your investment returns 0.02 percent each day, dividing it by 100 will give your the decimal number of 0.0002.
2. Add the number 1. When you add the numeral "1" to the number calculated in Step 1, the resulting number will be 1.0002.
3. Raise to the power of 365. Next, raise the figure 1.0002 to the power of 365, which will give you the number 1.0757.
4. Subtract 1 from 1.0757. By subtracting 1 from the number 1.0757, you will have the annual return as a decimal number of 0.0757.
5. Multiply by 100. Convert the decimal number into a percentage form by multiplying 0.0757 by 100. This will determine that the annual return on your investment is 7.57 percent. You can annualize daily returns for additional investments in this same way.
Read more: Cumulative Return vs. Annualized Return
Annualize Daily Returns for Investments: Business Day System
Some investments that you own or would like to purchase may use a business day system. For these investments, you first need to determine the cumulative investment value at the beginning of the month you choose to use for your analysis. For an investment that you own, you can find the value of your account as printed on the latest statement from your broker.
For any investment that you want to purchase, you can locate daily data or month-to-date return reports on the investment company's website. Next, following the same procedure, locate the investment's end-of-month value.
Read More: How to Calculate Daily Stock Return
Total Monthly Return and Average Daily Rate of Return
Next, subtract the figure representing the end-of-month value from the beginning value figure. The resulting number equals the investment's total monthly return. To determine your average daily rate of return, divide the monthly average return by the number of days you want to examine. Next, convert this figure to a decimal number by dividing the average daily rate by 100, and then add the number 1 to the decimal number.
Number of Days You Receive Returns During the Year
For investments using a business day system, find the number of days during the year that you receive returns. Typically, there are 250 days each year in the business day system. This number includes the number of regular business days in any 12-month time period, excluding 10 federal holidays.
Of course, for investments that do not use a business day system, you will make your calculations using 365 days for the year. Consult your investment broker to ensure which daily return system your investment uses.
Take the decimal figure that resulted when you divided your average daily rate by 100 and added 1 above. This is the figure that you will raise to a power that corresponds to the number of days during the year when returns are posted for an investment.
Using either an online or offline scientific calculator, select the key that designates the letter "x" raised to the power of "y." For "x," enter the decimal figure, and for "y," use the number of days in your annual return system. Then, subtract the number 1 from the resulting figure. Next, multiply the resulting number by 100 to determine your annualized daily rate of return.
How to Calculate Multi-Year Returns on Investments
The figure representing a multi-year return on an investment reveals the total profit over several years' time. For example, if your profits equal $12,000, $13,000 and $15,000 over three consecutive years, the multi-year profit total equals $40,000. If your initial investment was $100,000, divide $40,000 by $100,000. Then multiply this figure by 100 to determine your multi-year return of 40 percent.
Adam Luehrs is a writer during the day and a voracious reader at night. He focuses mostly on finance writing and has a passion for real estate, credit card deals, and investing.