Reference no: EM133254016

Albert Redneck plans to invest his $4,000 in one of the following instruments:

Bonds of Energy Gougers Inc. (EGI), yielding 7%

Canada Savings Bonds, yielding 2.5%

On the basis of his knowledge of current economic conditions and the outlook for the industry of EGI, Albert assesses the prior probability that EGI. will go bankrupt as 4%. If this happens, Albert will lose both principal and interest and will receive no money at the end of the year. If EGI. does not go bankrupt, Albert plans to sell the bonds, plus interest, at the end of one year. The probability that Canada Savings Bonds will fail to pay off is zero. Albert also plans to sell these, plus accrued interest, at the end of one year.

Albert is risk averse, and decides to choose the investment that yields the highest expected utility. Assume that Albert's utility for an amount of $x is given by the square root of x, where x is the gross payoff (i.e. principal plus interest).

REQUIRED:

On the basis of his prior probabilities, which investment should Albert choose? Rather than choosing on the basis of prior probabilities, assume that Albert decides to analyze the current financial statements of EGI. These financial statements can look "good" (G) or "bad" (B). After his analysis, Albert realizes that the statements look good. Albert knows that the probability that the financial statements would look good given that the firm was actually heading for bankruptcy is 0.09, that is:

P(G/Sb) = 0.09

where Sb denotes the state of heading for bankruptcy. Similarly, Albert knows that P(G/Sn) = 0.87 where Sn denotes the state of not heading for bankruptcy.

Advise Albert as to which investment he should now make. Use Bayes theorem.