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Finance
the beta of Spock's portfolio is (.5)(.7)+(.5)(1.1) = 0.9
The beta of Kirk's portfolio is (.9)(1) + (.1)(0) = 0.9
The risk of these two portfolios is the same. Both have the same beta, which implies that they are equally risky, even though their composition is quite different.
Essentially, all securities should be priced at their fair market value, under the efficient market hypothesis. Investors should be completely ration. However, there are two possibilities to explain underpricing of assets. The first is that the investors are not entirely rational. There is certainly enough evidence to support the idea that investors behave irrationally, and the science on the subject is far from certain. So there is at least the possibility of irrational behavior leading to underpricing. Another possible explanation is that the markets are not strong form efficient. This would mean that, if the markets were weak form efficient, that they are functionally efficient but only based on having some information. There is information that exists about the company but which has not yet been priced into the stock. In this situation, the stock could be underpriced.
C. If a two-stock...
So for example, a portfolio which is 50/50 and one security has a beta of 0.8 and the other has a beta of 1.2. In this scenario, the beta of the total portfolio would be (.5)(1.2) + (.5)(.08) = 1.0. The fully-diversified portfolio has a beta of 1.0. Diversifiable risk is only related to the idiosyncratic risk of the firms involved. Systematic risk is not diversifiable so its presence is accepted in a diversified portfolio.
D. 1. The bond yield to maturity is 9.98%. The cost of debt is the ytm -- (1-tax) = 5 x (1-.4) = 5.988%
2. The cost of preferred is D/P = 10/110 = 9.09%
3. The cost of the equity can be calculated using a number of different techniques, including the capital asset pricing model or the dividend discount growth model. Using CAPM, the cost of equity is (7) + (1.2)(6) = 14.2%
Using the dividend discount model it would be P = D/r-g, where 50 = 4.19 / r-.05. So 50r -- 2.5 = 4.19, or 50r = 6.69, gives a rate of 13.38%.
The bond yield plus risk premium approach gives a cost of equity of 5.988 + 4 = 9.988%. Taking the average of these three is…
References
Bond yield to maturity calculator. Retrieved December 11, 2013 from http://www.miniwebtool.com/bond-yield-to-maturity-calculator/?current_bond_price=1153.72&bond_par_value=1000&bond_coupon_rate=12&years=15
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