ps5 - ECO 362 November 6 2007 PROBLEM SET 5 FINANCIAL...

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ECO 362 November 6, 2007 PROBLEM SET 5 FINANCIAL INVESTMENTS Professor: Burt Malkiel Exercise 1 (a) FALSE. if β i = 1 , then E [ R i ] = r f ( E [ R m ] r f ) = 2 r f E [ R m ] which is in general di ff erent from zero (unless r f = 1 2 E [ R m ] ). (b) FALSE. One can represent the return on asset i as R i = (1 β i ) r f + β i R m + ε i , where by construction Cov [ R m , ε i ] = 0 . Hence, the volatility of stock i is V [ R i ] = β 2 V [ R m ] + V [ ε ] Therefore, for a given market portfolio, and hence a given V [ R m ] , an increase in volatility may be due to an increase in β or an increase in V [ ε ] . However, the CAPM only prices the risk associated to β i.e. the systematic risk. (c) TRUE. Consider the portfolio P : $1 . 5 invested in the market portfolio, and a credit of $ 0 . 5 from the cash account (it is assumed that one can lend and borrow at the same rate). Then, R P = 0 . 5 r f + 1 . 5 R m . Substracting r f to both sides, we get R P r f = 1 . 5( R m r f ) . Finally, taking expectations, E [ R P ] = r f + 1 . 5( E [ R m ] r f ) , so that β P = 1 . 5 . Exercise 2 We have the following information: β A = 0 . 6 , E [ R A ] = 0 . 05 , and β A = 1 . 8 , E [ R B ] = 0 . 11 . Using the usual CAPM formula, E [ R i ] r f = β i ( E [ R m ] r f ) , we can write a system of two equations and two unknowns, r f and E [ R m ] , as follows ½ β A E [ R m ] + (1 β A ) r f = E [ R A ] β B E [ R m ] + (1 β B ) r f = E [ R B ] so that using the information about expected returns and betas, ½ 0 . 6 E [ R
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