# F420-5 - Click to edit Master subtitle style BUS-F420...

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Unformatted text preview: Click to edit Master subtitle style BUS-F420 International Diversification January 27, 2011 • Today: – Quick review of Markowitz Portfolio Selection Model – International Diversification: • Background • Risk Factors • Benefits of International Diversification? International Diversification: Background Markowitz Portfolio Selection Model Step 1: Determine the Risk-Return opportunities Markowitz Portfolio Selection Model Step 1: Determine the Risk-Return opportunities • Q: How Do I form the efficient frontier using two risky assets? • A: Vary weights w1 and w2 = (1-w1) and solve for: E(rp)= w1E(r1) + w2E(r2) σp2 = w12σ12 + w22σ22 +2w1w2σ12 The efficient frontier is everything above the portfolio with the minimum variance. Markowitz Portfolio Selection Model Step 1: Determine the Risk-Return opportunities • With two risky assets, the weights for the minimum-variance portfolio are: • Where does this come from? Markowitz Portfolio Selection Model Step 1: Determine the Risk-Return opportunities • Whare are the weights for the min-var portfolio of Apple and ExxonMobil?: • σ22 - σ12 = 2.19%, • σ12 + σ22 -2σ12 = 2.34%, • So, w1 = 2.19 / 2.34 = 0.936 and w2 = 0.064 which gives σP2 = 0.27% covar xom aapl xom 0.28% 0.13% aapl 0.13% 2.32% Markowitz Portfolio Selection Model 1. Pick an E(r), say 5%, for example 1. Minimize (w1, w2, …wn) using constraints: and When there are more than two assets, you could solve by hand, but it’s more practical to use a computer Markowitz Portfolio Selection Model Step 1: Determine the Risk-Return opportunities 3. Do the same variance minimization for a wide range of E(r). Markowitz Portfolio Selection Model Step 2: Find the CAL with the highest Sharpe Ratio Markowitz Portfolio Selection Model Step 3: Find the optimal mix of the risk free asset and P •...
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F420-5 - Click to edit Master subtitle style BUS-F420...

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