# Problem set 3: A finance simulation

For Krieger's and Greenshtein's sections, this assignment will be passed out on Tuesday (Oct 12) and due Thursday (Oct 14). For Foster's sections, it will be passed out on Wednesday (Oct 13) and due the following Wednesday (Oct 20). So if you missed class when it is passed out, try to find someone else in the class and join their group--or find a 6 sided dice and do it on your own. You will have trouble following class if you haven't done the assignment before coming to class.

For this assignment, it will be best if you work together in groups of 2 or 3. You have the option of doing this assignment alone, but I think it's best if you do it as a group. Each group with more than one person gets THREE dice. If you are doing it alone, you get one and will have to pretend. Please type up a one or two page summary of what you find. Print a copy to turn in and print a copy for yourself. You will need to bring your copy to class for discussion purposes.

For this homework exercise, you will use three dice to simulate the uncertainty in financial markets. There are three basic instruments in this simplified market, each associated with a single die.

Color Die Annual Return Variability (SD)
green 7.5% 20%
Red 71% 130%
White 0% 5%

1. Before starting the simulation, which of the three investments looks most appealing to you? Does the group agree (have a consensus) or is it not so clear? Explain your choice briefly.
2. The rest of this assignment deals with a small simulation of these three financial instruments represented by the dice described above. For each "year" of the game, you will roll all three dice, and use the outcomes to determine what has happened to the value of each investment. Each of the three investments starts off with an initial value of \$1000. Run the game out for 25 years. Which investment wins? Is it the same one that you picked in Question 1? Try to explain any differences or surprises.
3. The following table shows how the rolls of the dice affect the values of the three investments.

 Roll Green Red White 1 0.8 0.06 0.9 2 0.9 0.2 1 3 1.05 1 1 4 1.1 3 1 5 1.2 3 1 6 1.4 3 1.1

For example, suppose that on the first roll of all three dice, you obtain

(Green 2) (Red 5) (White 3)

Then the values of the investments after the first year become

 Green: \$1000 * 0.9 = \$900 Red: \$1000 * 3 = \$3000 White: \$1000 * 1 = \$1000

For the next roll, the values are compounded from these. Suppose that on the second roll of all three dice, you obtain

(Green 4) (Red 2) (White 6)

then the values of the three investments after two years are

 Green: \$900 * 1.1 = \$990 Red: \$3000 * .2 = \$600 White: \$1000 * 1.1 = \$1100

4. The final part of this assignment considers the performance of a hybrid investment, one which mixes the outcomes of "Red"; and "White". To compute the value of this investment, roll both the red and white dice for each round. It’s easiest to describe what to do with an example. Before doing any simulating, what do you think of this hybrid?

5. Again, simulate the hybrid. What happens? How does it compare to the previous instruments?

For the first round, using the same dice rolls as above (Green 2), (Red 5) and (White 3), the value of this "Pink"; investment is

 Pink: \$1000 * (3 + 1)/2 = \$2000

and compounded in the second round which had (Green 4), (Red 2), and (White 6)
 Pink: \$2000 * (0.2 + 1.1)/2 = \$1300