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Unformatted text preview: 1 Risk and Return II Portfolio Theory 2 Example MIT 3 4 Another Example 5 Generalizing to a portfolio of n stocks: E(R p ) = w 1 r 1 + w 2 r 2 + w 3 r 3 + ... + w n r n E(R p ) = w i i = 1 n " r i note w i may be negative Portfolio weights sum to 1 Var ( R p ) = # p 2 = w i j = 1 n " i = 1 n " w j # ij In an equal weighted portfolio of n stocks w i = 1/ n " p 2 = 1 n (var ) + n # 1 n (cov ) 6 Limits to diversifcation EFfcient PortFolios 7 Generalizing With many assets, the feasible investment opportunity set is: 8 Adding a risk free asset If the investment opportunity set includes a risk less asset, like T bills, all rational investors will hold the same risky portfolio In combination with an investment in the risk free asset All efFcient portfolios are combinations of the riskfree asset and the tangency portfolio, the market portfolio 9 Combining the EfFcient frontier with risk less borrowing and lending: The Capital Market Line An investor with a positive investment in the risk free asset is lending money, and an investor with a negative investment in the risk free asset is borrowing. The new efFcient frontier is the line that combines an investment in the risk free asset and in M. M, the portfolio at the point of tangency of the efFcient frontier of risky assets to the new frontier is termed the market portfolio . All rational investors hold some combination of M and the risk free asset. 10 EfFcient Portfolios The new efFcient frontier, the Capital Market line , is the locus of all portfolio allocations that are efFcient: They maximize expected return for any given level of standard deviation of return Or, equivalently, They minimize standard deviation of return for any given level of expected return....
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 Fall '09
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