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PS3Solutions_09

# PS3Solutions_09 - Solution to Problem Set 3 Investments...

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Solution to Problem Set 3 Investments Prof. Pierre-Olivier Weill 1. (a) The return on the risk free asset is given as 8%. The standard deviation of that return is 0 by definition, since the asset is risk free. (b) Expected return is given by: E ( R p ) = w M E ( R M ) + w f E ( R f ) = ( . 5)( . 16) + ( . 5)( . 08) = . 12 Because the standard deviation of the return on the risk free asset is 0, the standard deviation of the portfolio is: σ p = w M σ M = ( . 5)( . 10) = . 05 = 5% (c) The standard deviation of return will be equal to: σ p = w M σ M = (1 . 25)( . 10) = 0 . 125 = 12 . 5% Expected return will be equal to: E ( R p ) = w M E ( R M ) + (1 - w M ) R f = 1 . 25( . 16) + ( - . 25)( . 08) = . 18 This result can also be obtained using: E ( R p ) = R f + E ( R M ) - R f σ M σ p = . 08 + . 16 - . 08 . 10 . 125 = . 18 (d) From above we have: σ p = w M σ M for the risk of the portfolio. The question asks for w M and w f that produces σ p = 2 σ M . Substituting 2 σ p for σ M into the equation gives: 2 σ M = w M σ M This implies w M = 2 1

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We also know that w f = 1 - w M = 1 - 2 = - 1 This says the following in words: To produce a portfolio that is twice as
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PS3Solutions_09 - Solution to Problem Set 3 Investments...

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