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1 1 . Assume that our pal John ( see PS # 2 ) is still fixated on the stock of X Co .

"11. Assume that our pal John (see PS #2) is still fixated on the stock of X Co. John follows the financial news and notes that when X reports a positive earnings surprise, the X stock price goes up; when X reports a negative earnings surprise, the X stock price declines. In the past, positive surprises have been rare, occurring only twice in 10 years. John estimates (e.g., from studying past earnings announcement results) that if there is good earnings news this year, 10 shares of X will be worth $4k. If X reports poor earnings this year, 10 shares will be worth only $500. X Co. stock is currently $100/share, and John is considering investing his hard-earned bucks in 10 shares of X.
#b. Assume the information in (a.) above applies. Now, John has been watching lots of T.V.; way too much, actually. He notes that when the Federal Reserve Open Market Committee meets each month, if the Chairman is smiling, the economy does well; if the Chairman is frowning, the economy does poorly. In the past, when X Co. earnings surprise has been positive, the Chairman had smiled 60% of the time. When X Co. earnings surprise has been negative, the Chairman had frowned 70% of the time. Guess what? X Co. is soon to report annual earnings, and Chairman Bernanke just smiled. Is
the stock a good buy at $100/share, according to Johns model? How much would John be willing to pay?
[Hint: first, realize that this is a Bayes problem, about updating your beliefs due to new information. The probability that the Chairman smiles, given that earnings surprise is good, is .6(e.g., p(Cs|Sg)=.6). Also, p(Cf|Sb)=.7. But this is backwards! We already know the Chairman is smiling; now we want to know the probability that surprise will be good, right? Or, p(Sg|Cs)=? Once you calculate the probabilities of surprise being good/bad based on the Chairman smiling, then you can calculate expected utility from buying the stock. Second, you need to know how to work backwards from utility to price. Assume a payoff of $36 gives utility of 6(square root function). A payoff of $16 gives utility of 4. So, a fair gamble (p =.5) paying $16 or $36 has an expected utility of 5. What amount for certain gives the same utility? $25, right? So when you realize you are about to spend $1k on a gamble that pays off either $4k or $500, do the following: use Bayes Theorem to calculate the appropriate probabilities; calculate the expected utility of the gamble; then calculate the dollar amount for certain that gives this same utility (the certainty equivalent). This is, basically, how investors with their own beliefs about a companys prospects (hopefully using valuation theory like Ohlsons models) set stock prices, based on their information.]"

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