FINE 441 Midterm Summer 2013 Solutions

# Specificallywritedownanoptimizationproblem

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Unformatted text preview: that the expected value of the market at t = 1 remains unchanged at \$110. b) Based on the above, what is the new expected return on the market at t = 0 after the volatility shock? % % . → % c) Based on the above, what is the new market value at t = 0? 110/1.15 = 95.65 Page 6 of 10 /10 6) You are given the following information: ‐ The borrowing rate is 4% ‐ The lending rate is 2% ‐ Stock A has an expected return of 10% and a standard deviation of 40% ‐ Stock B has an expected return of 12% and a standard deviation of 50% ‐ Stock C has an expected return of 14% and a standard deviation of 60% ‐ The correlation between each pair of assets is 0 ‐ Elmo has mean variance preferences ‐ Elmo has a very low level of risk aversion and his optimal allocation to the risk free asset will be negative ‐ Elmo has a target standard deviation of 75% a) Explain how you would figure out the optimal weights in A, B, and C for the risky component of Elmo’s overall portfolio. Specifically, write down an optimization problem, including the relevant constraint(s). Note that wA, wB, and wC are the only variables that should appear in your maximization function as well as in your constraint(s). Everything else must be numbers. Need to find the right tangency portfolio. Maximize the Sharpe ratio with the borrowing rate in the formula: % , , % . % . % . : b) Suppose the variance of the risky portfolio you found in part a was 0.0805. What does this imply about Elmo’s optimal allocation to the risk free asset? % √. wT = 2.64 wf = ‐1.64 Page 7 of 10 /5 7) The standard deviation of Stock A’s weekly returns is 10%. The standard deviation of Stock B’s monthly returns is 15%. Which stock, A or B, is more volatile? %√ . % . % %√ So A is more volatile. /5 8) The Beta of Stock A’s weekly returns is 1.2. The Beta of Stock B’s monthly returns is 1.3. Which stock, A or B,...
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## This note was uploaded on 02/11/2014 for the course FINE 441 taught by Professor Ruslangoyenko during the Fall '08 term at McGill.

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