# ps2sol - P conditional on N ) = Pr( P ) Pr( N ) = : 172 :...

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Financial Economics V 3025 Spring 2006 Rajiv Sethi 5B Lehman Phone: 854 5140 rs328@columbia.edu Problem Set 2 1. If she sells n shares at \$7 each, his balance sheet will be as follows Assets Cash 7 n + 5000 Value of Shares Owed 7 n Net Worth 5 ; 000 so the margin is 5000 = 7 n: If this must exceed 0.5 then n cannot exceed 10000 = 7 = 1428 : 60. Since she can only sell in units of 100, she can short 1400 shares. This increases her cash by 1400 7 = 9800 ; so total cash is now 14800. Let p denote the the price at which she gets a margin call. Then Assets Cash 14800 Value of Shares Owed 1400 p Net Worth 14800 ± 1400 p Solve for p when the margin equals 0.25: 14800 ± 1400 p 1400 p = 0 : 25 So she gets a margin call when p = 8 : 46 : 2. Let P denote the event "wins the presidency" and N the event "wins the nomination". Then Pr( P conditional on N ) = Pr( P and N ) Pr( N ) nomination then Pr( P and N ) = Pr( P ). So the markets predict Pr(Obama P conditional on N ) = Pr( P ) Pr( N ) = 0 : 486 0 : 710 = 0 : 68 Pr(Clinton

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Unformatted text preview: P conditional on N ) = Pr( P ) Pr( N ) = : 172 : 300 = 0 : 57 According to the markets, at that date and time, Obama was more electable. 3. An investor has access to two risky assets P and Q with the following statistical properties: E ( r p ) = 7% ; & p = 6% ; E ( r q ) = 8% ; & q = 8% : The correlation coecient between the two asset returns is zero and the risk-free rate of interest is 5% : (a) The reward-to-variability ratios are 1 3 for asset P and 3 8 for asset Q; so Q has the higher ratio. (b) The expected return of a portfolio consisting of equal weights in the two risky assets is E ( r ) = 1 2 (0 : 07) + 1 2 (0 : 08) = 0 : 075 = 7 : 5% and the standard deviation is & = s 1 4 (0 : 0036) + 1 4 (0 : 0064) = 0 : 05 = 5% (c) No, this is not possible. For every combination of bills and P; there exists a combination of bills and Q that has a higher expected return for the same risk. 2...
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## This note was uploaded on 04/07/2008 for the course ECON v3025 taught by Professor Sethi during the Spring '08 term at Columbia.

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ps2sol - P conditional on N ) = Pr( P ) Pr( N ) = : 172 :...

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