APPENDIX: DESCRIPTION OF THE STATISTICAL TOOLS

There are three measures of returns that will be used throughout the book:

a. compound (geometric) average (R)—the best measure of the long-term return on an asset or portfolio. If rj is the return in any given period, the compound average is defined by

Unnumbered Display Equation

where T is the number of periods in the sample.

b. arithmetic average (r)—the best estimate of next period’s return

Unnumbered Display Equation

c. average real return. The real return is defined using a compound formula as

Unnumbered Display Equation

where π is the compound average inflation rate.13

There are two measures of risk which will be used extensively in later chapters.

a. Standard deviation (σ)—measures the total variability of the asset or the portfolio. It is the square root of the variance, σ2, defined as

Unnumbered Display Equation

b. Beta (β)—measures the systematic risk of an asset relative to a market benchmark. If rA is the return on asset A and rM is the return on the market benchmark, then

Unnumbered Display Equation

where Cov (rA, rM) is the covariance between the asset and ...

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