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Lecture 10

# Lecture 10 - Portfolio Risk and the Mean-Variance Frontier...

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Lily Qiu, Assistant Professor Economics Department, Brown University EC1710, Lecture 10, Spring 2010, page 1 Portfolio Risk and the Mean-Variance Frontier 0. For stocks, we use their historical characteristics to indicate their future characteristics. We assume that stock returns (rate of returns) are random variables which draw from certain underlying distributions. The past returns are a sample draw from the distribution, and we work with that -> we have no better choice. 1. Portfolio with two securities Assume that you have \$100 to invest, you put \$20 into stock A and \$80 into stock B. The past 3 monthly rate of returns are: A B Portfolio 1, 0.03 0.08 0.2*0.03+0.8*0.08 = 0.07 2, 0.01 0.09 0.2*0.01+0.8*0.09 = 0.074 3, 0.02 0.10 0.2*0.02+0.8*0.10 = 0.084 Mean return(A) = Mean return(B) = When A’s return is 0.03 (3%) and B’s return is 0.08 (8%), what is the portfolio rate of return? Var(A) = σ(A) = Var(B) = σ(B) = Cov(A,B) = Expected rate of return for the portfolio: E( p r ~ ) = E( 2 2 1 1 ~ ~ r w r w ) = 1 w E( 1 ~ r ) + 2 w E( 2 ~ r ) 1 w + 2 w =1 For your portfolio: 1 w = , 2 w =

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Lily Qiu, Assistant Professor Economics Department, Brown University EC1710, Lecture 10, Spring 2010, page 2 For your portfolio: E( p r ~ ) = Variance for the portfolio: σ 2 ( p r ~ ) = n s p p s r E s r 1 2 )) ~ ( ) ( ( Pr
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Lecture 10 - Portfolio Risk and the Mean-Variance Frontier...

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