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03rec8 - 15.407 Recitation MIT Sloan School of Management...

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15.407 Recitation November 19, 2003
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MIT Sloan School of Management Portfolio Choice: Things to cover today: 1. Risk and return of a portfolio 2. Effects of diversification 3. How to choose an optimal portfolio 4. Problems of Portfolio Choice
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Algebra review: Suppose you have a portfolio of n stocks, and weights { w 1 , w 2 , ...w n } on each stock. For stock i , expected return is r i , variance (squared volatility) is σ 2 i , and covariance with stock j be σ ij . Denote the mean and volatility of the portfolio return be r p and σ p , then r p = n k =1 w k r k σ 2 p = Cov ( n k =1 w k r k , n l =1 w l r l ) = n k =1 n l =1 w k w l Cov ( r k , r l ) = n k =1 w 2 k σ 2 k + k = l w k w l σ ij
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Assumptions - Portfolio Choice: Given a fixed expected return, you prefer to have lower volatility to your portfolio Diversification: Diversification is good in general. Suppose there are two stocks, with the same return but different variance, should you invest everything in the one with lower variance? No. Let σ 1 = 20% , σ 2 = 30% , ρ 12 = 0 . 5 Invest everything in the stock 1, volatility = 20% Invest 90% in 1 and 10% in 2, volatility = 19.6723% Suppose that stock 1 has higher return and lower variance. Is it still beneficial to invest in stock 2?
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