FINE 441 Midterm Summer 2013 Solutions


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Unformatted text preview: has more systematic risk? For a given stock, Beta of weekly returns, or of monthly returns, is equal to beta of annual returns (there is no scaling since the scaling of the covariance term cancels out with the scaling of the variance term). So B has more systematic risk. /5 9) A portfolio has an alpha of 1% and a Beta of 2. The risk free rate is 3%. The expected return on the market is 9%. What is the average return of the portfolio? CAPM return would be 3% + 2(9%‐3%) = 15%. This portfolio had an alpha of 1%, so the average return was 15% + 1% = 16%. /5 10) Portfolio Q has 100% weight in the market portfolio, 20% in Strategy A, and ‐20% in the risk free asset. Portfolio Q has a lower Sharpe ratio than that of the market portfolio. Discuss what the above implies, if anything, about Strategy A’s alpha. Can’t say anything, it could be negative, zero, or positive. Page 8 of 10 /10 11) Consider a country, Orca, whose stock market, known as the Orca 500, has 2 sectors, Healthcare and Gold Mining. Each sector has a weight of 50% within the Orca 500. Healthcare is not too volatile, but Gold Mining is highly volatile. And since Gold Mining represents a big part (50%) of the Orca 500, this implies that the beta of Gold Mining with respect to the Orca 500 is higher than that of the Healthcare sector. However, the Orca Healthcare sector Beta with respect to a Global Market Portfolio is higher than that of the Orca Gold Mining sector. Now suppose you work at the Orca Pension Plan and you have to construct a mean‐variance optimal portfolio consisting of some weight in the Orca Gold Mining Sector and some weight in the Orca Healthcare sector. a) Assume that because of capital constraints, no foreigners are allowed to own any stocks within Orca and that no residents of Orca a...
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