Investors attribute all securities’ systematic risks to one single factor.
Suppose portfolios A and B are well-diversified. We know A B
β 0.3 0.9
E(r) 8% 16%
(a) For a portfolio P = 0.2◦A + 0.8◦B, what is the expected return E(rP) of the portfolio? What is its beta βP? (b) What is σP, the volatility of the portfolio P? Assume that the volatility of the single factor is 20%. 3 (c) If A and B are fairly priced, what is the risk-free interest rate? [Hint: risk-free asset has zero beta and zero idiosyncratic volatility.] [ (d) Suppose that there is a portfolio D with βD = 1.2. What is E(rD) under the Arbitrage Pricing Theory
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