Ms. S owns a portfolio containing some special securities that she believes will perform well compared to the market as a whole over the next several months However, Ms. S realizes that her portfolio has a high beta relative to the market as a whole and so is exposed to a significant degree of market risk. If the general market declines, her portfolio will also decline, even if her special securities do well. Let P represent the value of Ms. S's portfolio In terms of the present value Po and portfolio return rate Tp for the period from now to time T in the future (write Po as PO, Tp as rP ) Let M be the market as represented by the Standard and Poors 500 stock index. In terms of the present value Mo and market return rate ru for the period from now to time T (2) M (T) = 1 The beta of portfolio P with respect to the market is defined as (3) betap By using the identities var(X + a) = var(X), cov(X a, Y b) = cov(X, Y) var (eX) e'var(X), cov(eX, dY) = cdcov(X, Y) where a, b, c, d are constants, it follows from (1), (2) and (3) that (4)- war(A1(T)) (write 110 as M0, YM as rM ) cov(rp.rM P(T),M betap