Midterm Exam #1 information - Business Risk Management

The first midterm exam in Finance 4335 consists of 3 required problems.? Be sure to show your work as well as provide a complete answer for each problem; i.e., in addition to producing numerical results, also explain your results in plain English.

All three problems involve applications of expected utility.? I use only two types of utility functions in these problems; specifically, logarithmic (i.e., U(W) = ln W) and square root (i.e., U(W) = W^.5).??A particularly important?concept on this exam involves knowing how to ?back into? the certainty equivalent of wealth (W_CE) once you have calculated expected utility.? Hopefully this is a very familiar concept by now; once you have calculated E(U(W)), you set U(W_CE) = E(U(W)) and solve for W_CE.??Of course, once?you know W_CE, then you also know the risk premium since the risk premium?is equal to?E(W) ??W_CE.? Other important concepts to think about include the following:

1. A utility function is risk averse/risk neutral/risk loving if marginal utility decreases/stays constant/increases as wealth increases; therefore, utility functions such as U(W) = ln W and?U(W) = W^.5?are risk averse?because of diminishing marginal utility.??To see this,?note?that marginal utility in both cases is positive (which implies ?greed?); for U(W) = ln W, marginal utility is U?(W) = 1/W?> 0 and for U(W) = W^.5, marginal utility is U?(W) = .5W^-.5?> 0.? Furthermore, the rate of change in marginal utility in both cases is negative (which implies ?fear?); for U?(W) = 1/W,?U?(W) =?-1/W² < 0, and for U?(W) = .5W^-.5, U?(W) = -.25W^-1.5?< 0.
2. The Arrow-Pratt absolute risk aversion coefficients for U(W) = ln W and?U(W) = W^.5 are 1/W and .5/W respectively.? Therefore, a person with utility U(W) = W^.5 is less risk averse than a person with utility U(W) = ln W.? Furthermore, both utility functions imply decreasing absolute risk aversion, which means that as wealth increases, risk aversion associated with a specific gamble declines.

The formula sheet for the exam is available at http://fin4335.garven.com/fall2012/formulas_part1.pdf.? It will also be included as the last page of your exam booklet.

Source: http://risk.garven.com/2012/10/01/midterm-exam-1-information-2/

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