# Question: John Save plans to invest 5 000 in one of

John Save plans to invest $ 5,000 in one of the following instruments:

Bonds of J Ltd., yielding 12% (a1)

Canada Savings Bonds, yielding 8% (a2)

On the basis of his knowledge of current economic conditions and the outlook for the industry of J Ltd., John assesses the prior probability that J Ltd. will go bankrupt as 0.05. If this happens, John will lose both principal and interest and receive no money at the end of the year. If J Ltd. does not go bankrupt, John plans to sell the bonds, plus interest, at the end of one year. John assesses the probability that the Canada Savings Bonds will fail to pay off as zero. John also plans to sell these, plus interest, one year later. John is risk averse and decides to choose the investment that yields the highest expected utility. Assume that John’s utility for an amount of $ x is given by √x, where x is the gross payoff.

Required

a. On the basis of his prior probabilities, which investment should John choose?

b. Rather than choosing on the basis of his prior probabilities, assume that John decides to analyze the current financial statements of J Ltd. These financial statements can look “good” (G) or “bad” (B). After his analysis, John realizes that the statements look good. On the basis of his extensive understanding of financial statement analysis, he knows that the probability that the financial statements would look good given that the firm was actually heading for bankruptcy is 0.10:

Prob(G| S1) 5 0.10

where S1 denotes the state of heading for bankruptcy.

Similarly, John knows that

Prob(G| S2) 5 0.80

where S2 denotes the state of not heading for bankruptcy. Which investment should John now take? Explain why. Use Bayes’ theorem.

Bonds of J Ltd., yielding 12% (a1)

Canada Savings Bonds, yielding 8% (a2)

On the basis of his knowledge of current economic conditions and the outlook for the industry of J Ltd., John assesses the prior probability that J Ltd. will go bankrupt as 0.05. If this happens, John will lose both principal and interest and receive no money at the end of the year. If J Ltd. does not go bankrupt, John plans to sell the bonds, plus interest, at the end of one year. John assesses the probability that the Canada Savings Bonds will fail to pay off as zero. John also plans to sell these, plus interest, one year later. John is risk averse and decides to choose the investment that yields the highest expected utility. Assume that John’s utility for an amount of $ x is given by √x, where x is the gross payoff.

Required

a. On the basis of his prior probabilities, which investment should John choose?

b. Rather than choosing on the basis of his prior probabilities, assume that John decides to analyze the current financial statements of J Ltd. These financial statements can look “good” (G) or “bad” (B). After his analysis, John realizes that the statements look good. On the basis of his extensive understanding of financial statement analysis, he knows that the probability that the financial statements would look good given that the firm was actually heading for bankruptcy is 0.10:

Prob(G| S1) 5 0.10

where S1 denotes the state of heading for bankruptcy.

Similarly, John knows that

Prob(G| S2) 5 0.80

where S2 denotes the state of not heading for bankruptcy. Which investment should John now take? Explain why. Use Bayes’ theorem.

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