 # Investment Return and Volatility Explained

## CAGR is used for measuring investment return and standard deviation for volatility.

Investment return is often expressed as annualized return or CAGR (Compound Annual Growth Rate). Let us explain the concept using an example in which the annual performance of an investment is different each year.

A simple arithmetic average of the three annual returns is 1.3%. However, it is not the same as CAGR. CAGR is the one annual return that when applied to all of the years would result in the same end balance at the end of the investment period. CAGR is 1% in our example. It can be computed using two formulas.

1. CAGR is lower than average return because of standard deviation (σ), a measure of volatility (more on this later). In fact, larger the volatility, the lower the CAGR.
CAGR = Average Return – σ2 / 2

2. CAGR can also be calculated from the compound interest formula. Refer to “Power of Compounding” to see how compound interest works.
CAGR = (End Balance / Beginning Balance)1/Number of Years – 1

CAGR represents ROI (Return on Investment), but so does IRR (Internal Rate of Return). What is the difference? IRR is used when there are cash inflows from the investment such as dividend payment or rental income. When this is not the case, then both will work out to be the same number. IRR is the rate at which all the future cash flows are discounted so that their present values add up to the initial investment amount.

The fluctuations of yearly returns, or volatility, is expressed as standard deviation. The easiest way to calculate it is using the excel function STDEVP. It is 7.4% in our example. If the annual returns (assuming there are enough sample points) approximate a bell curve, then the following principles of probability hold good. The expected annual return in future will be within the following bounds:

• Average Return ± 1σ, about 68% of times
• Average Return ± 2σ, about 95% of times
• Average Return ± 3σ, about 99.7% of times

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