Midterm Exam #1 information | Business Risk Management | Le Tour ...

The first midterm exam in Finance 4335 consists of 3 problems that are worth 32 points each; you get 4 points for ?successfully? writing your name on the cover of the exam booklet .? 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.? A particularly important?concept on this exam involves knowing how to calculate risk premiums.? On the formula sheet that I just posted for the midterm exam, I list two ways to do this:

1) the ?exact? method involves calculating E(U(W)), setting U(W_CE) = E(U(W)) and solving for W_CE, and then calculating the risk premium by subtracting W_CE from E(W).

2) the ?approximate? method involves calculating the expected value (E(W)) and variance of wealth and the Arrow-Pratt absolute risk aversion coefficient.? Once you have these data, then you can calculate the risk premium by multiplying 1/2 times the variance times the Arrow-Pratt absolute risk aversion coefficient evaluated at E(W).

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 (DARA), which means that as wealth increases, risk aversion associated with a specific gamble declines.? This?is a particularly important insight,?as it?helps to?explain?a lot of familiar ?real world??behavior; e.g., why?firms go public (recall the ?Risk Analysis Class Problem?, which?illustrates how?an entrepreneur as well as her investors are all better off in an expected utility sense?from going public).? Finally,?DARA implies constant absolute risk aversion (CRRA).

In the meantime, if you have any other questions or concerns related to either the exam or Finance 4335 more generally, feel free to call me at 254-307-1317.

Source: http://risk.garven.com/2012/02/15/midterm-exam-1-information/

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Source: http://letourenglish.jameshouts2010.com/1096/midterm-exam-1-information-business-risk-management/

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