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

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern