An investor is considering two different no-load mutual funds: the Balboa Fund or the Inverness Mutual Fund. The yearly profits of the mutual funds are dependent upon how the market reacts each year. Recently the market has been oscillating around the 14,000 mark from one year end to the next, according to the probabilities given in the following transition matrix:

	13,000	14,000	15,000
13,000	0.4	0.4	0.2
14,000	0.3	0.4	0.3
15,000	0.1	0.4	0.5

Each year that the market moves up (down) 1,000 points, the Balbo Fund has profits (losses) of $20,000, while the Inverness Fund has profits (losses) of $10,000. If the market moves up (down) 2,000 points in a year, the Balboa Fund has profits (losses) of $50,000, while the Inverness Fund has profits (losses) of only $25,000. If the market does not change, there is no profit or loss for either fund.

Suppose that instead of keeping his or her money in the same fund year after, the investor decides each year whether to invest in the Balboa Fund or the Inverness Fund based on the market. For example, one strategy is to invest in the Balboa fund, if the market closed at 13,000 last year and invest in the Inverness fund if the market closed at 14,000 or 15,000. Another strategy is the opposite: invest in the Balboa fund, if the market closed at 14,000 or 15,000 last year and invest in the Inverness fund if the market closed at 13,000.

a)Identify all possible investment strategies.

b)Find the (long-run) expected average annual profit for each for each strategy you identified in part (a).

c)Which investment strategy would you recommend in order to maximize (long-run) expected average profit per year?