In this appendix, we summarize the probability concepts we rely on throughout this book. We present them in the context of discrete probability distributions, for example:
We first look at three useful properties of expected values:
|Property 1:||The expected value of a constant is that constant. In particular, we shall make considerable use of the notion throughout the book of a risk-free rate of return rf; thus, E(rf) = rf.|
|Property 2:||The expected value of a constant times a random variable is the constant times the expected value of that random variable. In particular, if xi is the proportion of a portfolio invested in security i and ri is its return, then E(xiri) = xiE (ri).|
|Property 3:||The expected value of a sum equals the sum of the expected values. In particular, suppose a portfolio consists of two securities, 1 and 2; then E(rp) = E(x1r1) + E(x2r2) = x1E(r1) + x2E(r2). This property is quite general and applies also to sums of functions of random variables.|
We next look at measures of dispersion for random variables, defining first the variance,
Since the term E(r) inside the braces can be treated as a constant,
We then define standard ...