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 ,th en E [ R i ]= r f ( E [ R m ] r f )=2 r f E [ R m ] wh ichi singene ra l di f 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 ,whereby construction Cov [ R m 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 investedinthemarketport fo l io ,andacred ito f $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 . 5( E [ R m ] r f ) , so that β P . 5 . Exercise 2 We have the following information: β A =0 . 6 , E [ R A . 05 ,and β A . 8 , E [ R B . 11 .U s ing 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 ] ,asfo l lows ½ β A E [ R m ]+(1 β A ) r f = E [ R A ] β B E [ R m β B ) r f = E [ R B ] so that using the information about expected returns and betas, ½ 0 . 6 E [ R m ]+0 . 4 r f .
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This note was uploaded on 10/15/2008 for the course ECO 362 taught by Professor Harrisonhong during the Fall '08 term at Princeton.

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

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