What is an annualized rate?
An annualized rate of return is calculated as the equivalent annual return that an investor receives during a specified period. Global investment performance standards dictate that portfolio or compound returns for periods of less than one year cannot be annualized. this prevents the “projected” performance from occurring in the remainder of the year.
Understand the annualized rate
Annualized returns are returns for a period reduced to a period of 12 months. This scaling process allows investors to objectively compare the returns of any asset over any period.
Calculation using annual data
Calculating the annualized return of an investment or index using annual data uses the following data points:
P = capital or initial investment
G = profit or loss
N = number of years
Ap = annualized rate of return
The generalized formula, which is exponential to account for compound interest over time, is:
Ap = ((p + g) / p) ^ (1 / n) – 1
For example, suppose an investor invested $ 50,000 in a mutual fund and, four years later, the investment is worth $ 75,000. This is a profit of $ 25,000 in four years. thus, the annualized return is:
Ap = (($ 50,000 + $ 25,000) / $ 50,000) ^ (1/4) – 1
In this example, the annualized return is 10.67 percent.
A $ 25,000 profit on a $ 50,000 investment over four years is a 50 percent return. It is inaccurate to say that the annualized return is 12.5 percent, or 50 percent divided by four because this does not take compound interest into account. If you invest the 10.67 percent result in composite over four years, the result is exactly what you expect:
$ 75,000 = $ 50,000 x (1 + 10.67%) ^ 4
It is important not to confuse annualized performance with annual performance. Annualized return is the rate at which an investment grows each year during the period to arrive at the final valuation. In this example, a 10.67 percent return each year for four years increases from $ 50,000 to $ 75,000. But this says nothing about the actual annual returns over the four-year period. returns of 4.5 percent, 13.1 percent, 18.95 percent, and 6.7 percent increase $ 50,000 to approximately $ 75,000. Also, returns of 15 percent, -7.5 percent, 28 percent, and 10.2 percent provide the same result.
Using days in the calculation
Industry standards for most investments dictate the most accurate form of annualized return calculation, which uses days rather than years. the formula is the same, except for the exponent:
Ap = ((p + g) / p) ^ (365 / n) – 1
Suppose from the example above that the fund returned $ 25,000 over a period of 1,275 days. The annualized return is then:
Ap = (($ 50,000 + $ 25,000) / $ 50,000) ^ (365/1275) – 1
The annualized return in this example is 12.31 percent.
