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
where T is the number of periods in the sample.
b. arithmetic average (r)—the best estimate of next period’s return
c. average real return. The real return is defined using a compound formula as
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
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
where Cov (rA, rM) is the covariance between the asset and ...