# ECON 1723 Fall 2013 Midterm 1 Solutions - Ec 1723 Midterm 1...

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Ec 1723: Midterm 1 SolutionsOctober 7, 2013Question 1If the value of 45% of Verizon Wireless is priced at \$130 billion, the 55% stakeowned by Verizon has a value of13045%(55%)\$158.9BilSo the stub value of Verizon is135-158.9=-\$23.9BilThere is no arbitrage opportunity in this case because an arbitrage would involveshorting the more expensive Verizon Wireless and going long on Verizon. How-ever, Verizon Wireless is not going to be spun off from Verizon and traded publicly,so it can’t be shorted.Question 2a) Denote the complete portfolio byC, and letwbe the weight it puts on the riskyasset.i) We require that10%=σC=w×20%=w=12ii) This implies that the expected return on the complete portfolio is¯RC=2%+12×8%=6%
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iii) Combining a risky asset with the risk free asset does not change the Sharperatio (think about the CAL). We can verify this:SC=0.06-0.020.1=0.4iv) The optimal standard deviation (shown on the formula sheet) isSRRA=0.1=RRA=0.40.1=4b)i) Letw0be the weight put on the risky asset now to produce a portfolioC0. Werequire¯RC=6%=¯RC0=0%+w0×8%=w0=6%8%=34The standard deviation of the portfolio isσP0=34×20%=15%ii) If RRA remains the same, as the Sharpe ratio of the risky asset has also notchanged, the optimal standard deviation of the complete portfolio and the weightput on the risky asset should be the same as in a). In particular the weight on therisky asset should be less than34.c)i) Letw00be the weight put on the risky asset now to produce a portfolioC00.We require¯RC=6%=¯RC00=2%+w00×6%=w00=4%6%=23The standard deviation of the portfolio isσP00=23×20%=1313%ii) The optimal standard deviation should now beSRRA=0.34=7.5%
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which determines the optimal weight on the risky asset to be7.5%20%=38<23d) Low-return market environments can arise either if the risk free return falls, or ifrisk premia fall. The analysis above suggests that in the first case investors shouldnot change their allocation to risky assets, whereas in the second they should cutback on risk taking. In either case keeping a fixed return target and “reaching foryield" is not optimal.
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