Calculating expected returns

Real Rate of Return (RoR) vs. Compound Annual Growth Rate (CAGR)

If the real rate of return is a way to compare the value of an investment from when purchased to a given point of time, the compound annual growth rate is a way of measuring how much the investment has grown on average per year.

This can be useful because it’s a way of comparing investments over annual timespans. This is useful because typically investments are thought of as being held over a given time period and you want to compare which investment is most appropriate or will generate the biggest gains.

The compound annual growth rate does not tell you how much an investment’s value has grown in a given year, but it does give you a basis of comparison. Another assumption of the compound annual growth rate is that any profits from the investment are re-invested.

The formula for the compound annual growth rate is:

CAGR = (present or final value/starting or initial value)^1/n – 1, where n is the number of years.

So let’s look at a stock which you purchased for $50 in 2008 and has now grown to $200 in 2020. The simple rate of return for this stock would be 300%, which sounds impressive. But let’s look at its compound annual rate of return.

CAGR = (200/50)^1/12 – 1
CAGR = 4^.0833 – 1
CAGR= 12.25%

This 12.25% seems more modest than the 300% rate of return, but it’s useful to compare to other annual rates of returns, like from the market as a whole, from treasury bonds, dividend-stocks and more.

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