Homework SourseYou have 2000 and are interested in trading commodities You
You have $2000 and are interested in trading commodities. You notice that tin currently sells for $2 per ounce. Suppose that after one week, tin will sell for either $1/oz or $4/oz (think bitcoins!). The chance of it dropping to $1 is 75% and the chance it rises to $4 is 25%.
You can choose the goal of maximizing how much money you have at the end of the week, or maximizing how much tin you have at the end of the week.
Suppose you decide to maximize the expected amount of money you have at the end of the week. Which of the following choices is the best choice and what is the expected amount of money that you will have at the end of the week?
| A.Do not immediately buy, but wait and use your money to buy after one week; $1750 expected value | |
| B.Use all your money now and buy 1000 oz of tin, then sell after one week; $1750 expected value | |
| C.Do not immediately buy, but wait and use your money to buy after one week; $1625 expected value | |
| D.Use all your money now and buy 1000 oz of tin, then sell after one week; $1250 expected value |
Solution
Currently we can buy 1000 oz of tin at $2000.
If we buy 1000 oz of tin and sell after one week then expected value is: 1000*0.75 + 4000*0.25
= 750 + 1000 = 1750
Thus expected value is $1750, if we use all money now and sell after one week.
If we wait now and buy after one week then 2000 oz of tins can be purchased at probability 0.75 or 500 oz can be baugth at probability 0.75.
Thus, expected value = 2000*0.75 + 500*0.25 = 1500 + 125 = 1625.
Expected value is higher in the first case. i.e. Use all your money now and buy 1000 oz of tin, then sell after one week.
Hence we would select the choice B.
Use all your money now and buy 1000 oz of tin, then sell after one week; and $1750 is the expected value.
