1. Imagine that your mother-in-law owns a Cadillac dealership and that one evening you were sitting with her on the deck, smoking cheap cigars and drinking expensive scotch when she mentioned that she was having a tough time figuring out how many cars to order next quarter. After asking her a few questions, it became clear that she has three options
a) She can place a small order. If she does this, she will sell all the cars at list price and make a profit of $100,000.
b) She can place a large order. If she does this, her profits will depend on market conditions. If demand is strong, she will earn $120,000. If demand is weak, she will have to discount and so will earn $60,000.
c) Before ordering she can hire a consultant will forecast demand conditions. Once she gets the forecast she can proceed with her decision as place a big order or a small order.
Mom belongs to a dealer's association and the members have kept careful records of how the forecaster has performed. The following table the data. Read this just like a joint distribution-e.g., there is a 5% chance that there will be forecast of low demand and actual demand is low.
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Actual Outcome
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|
|
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Low Demand
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High Demand
|
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Consultant's Forecast
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Low
|
.05
|
.45
|
|
High
|
.45
|
.05
|
Should mom hire the forecasting firm and if so, how much should she pay? Draw a carefully labeled the decision tree to support your answer.
2. You have three days to find a job. Every morning you will get up, put on your grown-up clothes and go for an interview. Since you look great in your suit you will always get an offer, the only question is what salary you will earn. There is a 1/3 chance that the job will pay $120, a 1/3 chance that it will pay $100 and a 1/3 chance that it will pay $50. You must decide on the spot whether to take the offer and if you accept, you cannot look for another job. If you reject, you go home and get up the next morning and do the same thing. You need to formulate some decision rules. Some of these are obvious
• On day 3 you will accept whatever is offered.
• If you are ever offered the $120 job, you will accept (you could never do better by waiting).
• On day 1 and day 2 if you are offered the $50 job, you will reject (you can always get that job and so you should keep looking).
The only hard question is whether you will accept a $100 offer on day 1 and/or whether you would accept a $100 offer on day 2. Model this by drawing a decision tree (assume that you are risk neutral and so care only about expected values.
3. You are a trader in gasoline. You trading position will suffer if gas prices increase. The attached spreadsheet gives the conventional gasoline price (Gulf coast, regular) for the past year. It also gives the daily percentage change. Calculate the 1% value at risk for price increases. (That is give a number,"x", for which you can say that there is a 1% probability that we would see price increases more than x%.) Use both the historical and parametric method.
Attachment:- Data.xlsx