Elton Gruber Essay

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Elton, Gruber, Brown and Goetzmann Modern Portfolio Theory and Investment Analysis, 6th Edition Solutions to Text Problems: Chapter 1 Chapter 1: Problem 1 A. Opportunity Set With one dollar, you can buy 500 red hots and no rock candies (point A), or 100 rock candies and no red hots (point B), or any combination of red hots and rock candies (any point along the opportunity set line AB). [pic] Algebraically, if X = quantity of red hots and Y = quantity of rock candies, then: [pic] That is, the money spent on candies, where red hots sell for 0.2 cents a piece and rock candy sells for 1 cent a piece, cannot exceed 100 cents ($1.00). Solving the above equation for X gives: [pic] which is the equation of a straight line, with an intercept of 500 and a slope of (5. B. Indifference Map Below is one indifference map. The indifference curves up and to the right indicate greater happiness, since these curves indicate more consumption from both candies. Each curve is negatively sloped, indicating a preference of more to less, and each curve is convex, indicating that the rate of exchange of red hots for rock candies decreases as more and more rock candies are consumed. Note that the exact slopes of the indifference curves in the indifference map will depend an the individual’s utility function and may differ among students. [pic] Chapter 1: Problem 2 A. Opportunity Set The individual can consume everything at time 2 and nothing at time 1, which, assuming a riskless lending rate of 10%, gives the maximum time-2 consumption amount: $20 + $20 ( (1 + 0.1) = $42. Instead, the individual can consume everything at time 1 and nothing at time 2, which, assuming a riskless borrowing rate of 10%, gives the maximum time-1 consumption amount: $20 + $20 ( (1 + 0.1) = $38.18

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