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Financial Engineering

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FRE 6123 Final Solutions

May 7, 2009

This final was 50% of your grade. Here was the distribution of results:

You can pick up your graded final exam from me on Monday if you want. But perhaps you don’t need to. Here are the solutions.

1. (5 points) Basics
a. (2 points) Under the Capital Asset Pricing Model: A. Every investor holds the risk free asset only, and none of the market portfolio. B. Every investor holds the market portfolio only, and none of the risk free asset. C. Every investor holds a portfolio with a beta of one. D. None of the above. CIRCLE ONE: A B C D

Solution: D. Investors can hold any combination of the riskfree asset and the market portfolio, depending on their particular risk aversion, etc.; so A and B are false. C is false because, for example, an investor holding just the riskfree asset holds a portfolio with a beta of zero. b. (1 point) Asset A has a correlation of 80% with the market, but asset B only has a correlation of 50% with the market. Therefore, asset A has a higher beta to the market than asset B. CIRCLE ONE: TRUE FALSE

Solution: FALSE. The beta is the correlation times the asset volatility divided by the market volatility. If asset A has e.g. half the volatility of asset B, then asset A would have a lower beta. c. (2 points) There are 100 different assets. You plot their means and standard deviations, and painstakingly figure out the efficient frontier. You plot the risk free asset and find the tangency portfolio. Now, you find out there is a 101st asset! Which of the following is closest to the truth? A. You have to redo your efficient frontier if the new asset doesn’t have a 100% or -100% correlation with any of the first 100 assets. B. You have to redo your efficient frontier if the new asset doesn’t have a 100% or -100% correlation with the tangency portfolio. C. You have to redo your efficient frontier if the

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