102B-PS_1--W2008 - (b Calculate the variance of the rate of...

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Prof. D. Malueg Problem Set #1 Econ 102B Due in Discussion Section the week of January 14 th . INSTRUCTIONS: Answer all of the questions. Show your work. 1. Sophia faces random income of $1200 with probability 3/4 and $800 with probability 1/4. Sophia’s preferences are represented by the expected utility function on income u ( x ) = x , where x denotes her realized income. (a) Calculate the certainty equivalent of Sophia’s lottery over income. (b) Calculate the associated risk premium. 2. Jack has two investment opportunities. Jack can put all of his investment funds into one opportunity or divide them between the two, in any proportion. The first earns a 20% return with probability 1/2 and a 10% return with probability 1/2. The second opportunity earns a return of 25% with probability 2/3 and a return - 5% with probability 1/3. (a) Calculate the expected returns of each investment.
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Unformatted text preview: (b) Calculate the variance of the rate of return for each investment. (c) Suppose the two rates of return are independent of each other. Jack has $360 to invest in the two alternatives. In order to minimize the overall variance of Jack’s resulting portfolio, how much should be allocated to each opportunity (all $360 has to be invested in these two options). Hint: if X and Y are independent random variables and if a and b are constants, then var( aX + bY ) = a 2 var( X ) + b 2 var( Y ) . 3. Uncle Fester is a practical joker. He carries two quarters (coins) in his pocket. One is a regular quarter but the other has a head on both sides. Fester randomly draws one coin from his pocket, flips it, and it comes up heads. Calculate the probability that the other side of the coin is also heads....
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