3. Stan Stellar, a risk-neutral decision maker, is trying to decide between sell

Question

3. Stan Stellar, a risk-neutral decision maker, is trying to decide between selling his 1,000 shares of ADZ, Inc., now or holding them until after the earnings are reported in 2 weeks. He knows he can keep them no longer than 2 weeks and believes the price will be either $9, $10, $11 or $12 per share at the end of the 2 weeks. He thinks that the current price of $10 will not change until after the announcement on earnings. His probability assessments for the price in 2 weeks are shown in the following table: Price Per Share$9 $10 $11 $12 Prior Probability 0.24 0.30 0.24 0.22 a) Set up a payoff table for Stan's decision to either sell now or sell later (i.e. in two weeks) including the V column for computation of EVIPL (Hint: transpose the table above for use with your payoff table.) b) Compute the expected values of the decision alternatives and indicate which maximizes EMV. What is the expected value of perfect information (EVPI) for Stan? b) Stan has an opportunity to gather some information on the stock price movement by talking with a friend, Ray Resurch, who follows the company. Ray is generally reliable but not infallible. Moreover, he will only state his opinion as to whether the stock price will go "UP" or "DOWN". Based on his long acquaintance with Ray, Stan assesses the following probabilities. If the price goes down to $9, Ray will forecast down with probability 0.7. If the price stays the same, he will forecast down with probability 0.3. If the price goes up to $11, he will forecast up with probability 0.8; and if the price goes up to $12, he will forecast up with probability 0.9. Based on these conditional probabilities, compute the joint probabilities and the posterior probability distributions for Price Per Share given "UP" and "DOWN" predictions by Ray Resurch. (Hint: the conditional forecast probabilities must sum to 1.0 in each row of the conditional forecast probability table.)

Explanation / Answer

a)

b) Expected value of Selling after 2 weeks = 2160 + 3000 + 2640 + 2640

= 10440

The present value if he sells 1000 shares = 10,000

hence the decision to sell the shares after 2 weeks is a good option.

c) We know,

P(9) = 0.24, p(10) = 0.3, p(11) = 0.24, p(12) = 0.22

Now, p(down/9) = 0.7,

p(down/10) = 0.3

p( up/11) = 0.8

p(up/12) = 0.9

Hence, we calculate

p(up/9) = 1-0.7 = 0.3

p(up/10) =1- 0.3=0.7

p( down/11) = 1-0.8=0.2

p(down/12) =1- 0.9=0.1

Price per share Prior probability Total cost of share Expected Monetary value 9 0.24 9000 2160 10 0.3 10000 3000 11 0.24 11000 2640 12 0.22 12000 2640

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