# Diversified wager

You may do this in a group of two students as long as you both participate and you work together.

There are two competing funds in which you can invest \$100, Fund A and Fund B. Each fund flips its own coin. If the coin comes up heads, you earn 60% on your investment, and if it comes up tails, you lose 40%. While each fund behaves the same way, they are independent.

For Thursday, you should first flip 60 coins, one for each of 30 days for each of the two funds. You'll generate a table such as:

 Fund A Fund B 1 2 3 4 ... 30 H H T H ... T T T T H ... H
Now, make a table showing how much money you would make in each of the following three scenarios:
1. Fund A: Suppose you invested all \$100 in fund A. How much would you end up with?
2. Fund B: Suppose you invested all \$100 in fund B. How much would you end up with?
3. Diversified: Suppose that every day, you split your money evenly between fund A and fund B. Then how much would you end up with?

For the example above,

1. Fund A: On day 1 you'd win and have \$100*1.6 = \$160. After two days, you'd have \$160*1.6 = \$256. After three days, \$256*.6 = \$153.60. And so forth.
2. Fund B: On the first 3 days, you'd lose. But on day 4 you'd win.
3. Diversified: On day 1 you put \$50 into A and \$50 into B. You win on A, ending up with \$50*1.6 = \$80. You lose on B, leaving \$50 * .6 = \$30. So, after one day you have \$110.

On day 2, you put \$55 into A and \$55 into B. It's important that you keep splitting all your money evenly between the two funds each day. Again, Fund A wins and Fund B loses. So fund A has \$55*1.6 = \$88, and fund B has \$55*.6 = \$33, and in total you have \$88+\$33=\$121.

Here are my results after four days using the coin flips in the above table:
 Fund A Fund B Diversified day 0 day 1 day 2 day 3 day 4 ... \$100.00 \$160.00 \$256.00 \$153.60 \$245.76 ... \$100.00 \$ 60.00 \$ 36.00 \$ 21.60 \$ 34.56 ... \$100.00 \$110.00 \$121.00 \$ 72.60 \$116.16 ...
You might want to draw your table vertically so you have room for 30 entries.