_Portfolio Analyses_ Practice Problems Solution

_Portfolio Analyses_ Practice Problems Solution - FINA 3104...

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1 FINA 3104 Practice Problems Fall 2011 Portfolio Analyses and the Markowitz Portfolio Selection Model 1. True or False (Briefly Explain) (a) The efficient frontier includes the set of all possible optimal complete portfolios. The optimal complete portfolio is picked from the efficient frontier using indifference curves. Solution: FALSE. The efficient frontier includes the set of all possible optimal risky portfolios only. The optimal risky portfolio is at the tangent point where the Capital Allocation Line (CAL) touches the efficient frontier. The optimal complete portfolio is picked from the CAL using indifference curves. (Note: The statement is TRUE if there is no riskfree asset. In that case, the optimal complete portfolio is the optimal risky portfolio, which is picked from the efficient frontier.) (b) As long as the correlation between Security X and the original portfolio is not 1, adding X to the portfolio can lower the portfolio standard deviation. Solution: TRUE. This is the benefit of diversification. As long as Security X does not perfectly co-move with the original portfolio, including it in the portfolio can help diversify the portfolio idiosyncratic risk. 2. Diversification In an economy, every stock has the same expected return E(r) of 15%, the same standard deviation of 60%, and the correlation between any two stocks is 0.5. (a) Find the expected return E(r p ) and standard deviation p for an equally-weighted portfolio of 25 stocks. Solution: E(r p ) = 25 ( E(r) /25) = E(r) = 15% p = [ 2 / n + ( n -1)/ n *  2 ] 1/2 = [(  2 /25 + (25-1)/25 (0.5)(0.6) 2 ] 1/2 = 43.27% (b) How many stocks should be held in an equally-weighted portfolio such that the standard deviation p is less than 43%?
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2 Solution: Find n so that p <= 43% (0.43) 2 <= (  2 / n + ( n -1)/ n (0.5)(0.6) 2 ] 0.1849 n <= 0.36 + (0.36)(0.5) n – 0.18 n >= 36.73 Therefore, at least 37 stocks should be held. (c) What is the systemic risk for this economy?
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_Portfolio Analyses_ Practice Problems Solution - FINA 3104...

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