15-Diversification I

# B b 008340078107 er b r f er p r f 25 10114925 10108

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• shi1hong
• 25

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b B =0.0834/0.078=1.07 (E[r B ]-r f )/(E[r p ]-r f )=(.25-.10)/(.1*.14+.9*.25-.10)=1.08 So you can still improve the Sharpe ratio of your portfolio by tilting towards stock B.

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Example Suppose you have a portfolio that may or may not contain shares of stock A. You also know Expected return of A Expected return of P Standard deviation of A Standard deviation of P Covariance between A and P You want to know if you should tilt your portfolio towards or away from A to improve your Sharpe ratio
Example 3 E[r A ]=.10, σ A =.40 E[r P ]=.20, σ P =.50 ρ =.35 Risk-free =.05 b A =.35*.4*.5/.5^2=0.28 (E[r A ]-r f )/(E[r p ]-r f )=(.10-.05)/(.20-.05)=0.33 Therefore tilt towards A

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Portfolio Allocation What about the case of many risky assets? The efficient frontier has the same shape Intuition is the same Expected Return Standard Deviation Individual Assets Tangency Portfolio risk free rate Best possible CAL
Multiple Assets Given time series of returns for n stock, you can find the portfolio with maximum Sharpe ratio as follows: Pick arbitrary weights. For the last stock, specify weight as 1-sum of others Find the portfolio return using these arbitrary weights for each date (point to cells with weights) Estimate the expected return and standard deviation Calculate the Sharpe ratio of the portfolio Use solver: maximize Sharpe ratio of portfolio by changing cells containing weights. Change all weights except last, which equals 1-sum of others
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• Fall '10
• BrianBoyer
• Modern portfolio theory, sharpe ratio, Treynor ratio, Tangency Portfolio

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