Lynn Miller has recently come into enough money to consider seriously the various types of investments that are available to her. After studying the various forms of investments, Lynn has decided that only three types suit her needs. These are money funds, stocks, and bonds. The choice of an investment depends on the prime rate since the return on the investment will be a function of this interest rate. The interest rate is quite volatile and could go up or down so Lynn is considering hiring National Forecasting Service to provide her with a forecast of the interest rates before she makes the investment decision.
If Lynn doesn't hire the forecasting service and just makes a choice, the following payoffs are expected.
|
Rates go up
|
Rates go down
|
|
Money fund
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$115
|
$108
|
|
Stocks
|
$60
|
$125
|
|
Bonds
|
$75
|
$140
|
Without any further information, the probability of rates going up is estimated as 0.60, the probability of rates going down is estimated as 0.40.
If Lynn does hire the forecasting service a cost of $5 must be taken off of the expected payoffs.
Past records show that the service predicts rates will go up 70% of the time, and predicts rates will go down 30% of the time.
If the service predicts that rates will go up, the probability that they actually go up is 90%.
If the service predicts that rates will go down, the probability that they actually go up is 5%.
Draw a decision tree for this problem, solve the tree and make a recommendation for Lynn.