Dear Tutor,

I am confused about the following question.

additional information: the value of the portfolio on 7/26/2000 is 34533799.

1. In CAPM model, B reflects the covariance of the return of a stock/portfolio with some benchmark return, for example, the market index. Once we know the B of a portfolio, we can calculate the A of the portfolio with respect to the market index. Here, A is defined as "the increase in the value of the portfolio with one unit increase in the market index" (An alternative way of interpreting the concept of A in this context is, if NASDAQ 100 increases by $1, by how much PSC's portfolio is expected to increase?). Here we derive a formula that expresses A of a portfolio (with respect to the market) as a function of its market B. Derivation: Let Ao denote the value of the portfolio at time 0, and Ar denote the value of the portfolio at time T. Then AT = Ao X R where R is the return on the portfolio. Regressing the portfolio return on that of the Nasdaq, R = a + RNasdaqB + where RNasdaq is the return on the market index (in the case, it is the NASDAQ 100 inder). Assuming zero dividend yield on the NASDAQ 100 inder, we have RNasdaq = 3, where ST denote the NASDAQ 100 index at time T. Therefore we have: AT = Aox( at - Bte) = Ao x (a+ =) + s Ao x B X ST. 6 The above equation implies that if ST (The NASDAQ 100 index) increase by $1, then AT (PSC's portfolio) is expected to increase by 58 Ao x B. Therefore PSC's A is : A = Ao So X B (1) 2. Assume PSC's portfolio B with respect to NASDAQ 100 is 1.785. Suppose today is July 26, 2000, PSC decides to short the NASDAQ 100 index to hedge the market risk. What is the total (dollar) amount of short positions that PSC should take in the NASDAQ 100 index? (You'll need to check Exhibit 2 in the case to find the value of PSC's portfolio on July 26, 2000.)