Reference no: EM132210678

Question - At the beginning of the year, Unocal Corporation announced that 2004 capital expenditures would total $1.93 billion. Planned investments included deep water exploration in the Gulf of Mexico and in the waters off Indonesia, oil and gas development in Thailand, oil development in the Caspian Sea, natural-gas development in China, and developments of the Mad Dog field in the United States and the K2 field in the Gulf of Mexico.

We seek to evaluate Unocal's numerous projects. Because individual project data are not available here, assume that information on the various projects is as given in the table below. Assume further that Unocal's capital budget is capped at $1 billion and that the projects are independent.

Investment alternatives for the energy company

(a) Establish the set of feasible portfolios.

(b) For each portfolio, the expected present worth is the sum of the present-worth values of the individual projects, while the variance is the sum of the variances of the individual projects. (Note that the table gives the standard deviation.) Determine the expected present worth and variance for each feasible portfolio, and generate an efficiency frontier. Which portfolios are dominated?

(c) One way to make a risk averse decision based on the expected return E(PW) and standard deviation σ_PW is to use a utility function known as Freund utility function: U(x) = 1-e^Bx, where x is the return or payoff (PW in this case) and B > 0.

Assuming that the return x is normally distributed with the mean = μ and variance = σ², the expected utility which is used as the final metric to compare alternatives is given by: E(U(x)) =1- e^{-0.5(2Bμ - B^2σ^2)}

With B = 0.01 to determine the expected utility of each portfolio for ranking. Are the results as expected, given the information about the efficiency frontier? How influential is B?