. A game of chance offers the following odds and payoffs. Each play of the game

Question

. A game of chance offers the following odds and payoffs. Each play of the game costs $200, so the net profit per play is the payoff less $200.

Profitability Payoff Net Profit
0.2 400 200
0.5 200 0
0.3 100 -100
What are the expected cash payoff and expected rate of return? Calculate the variance and standard deviation of this rate of return.

2. During the boom years of 2006-2010, ace mutual fund manager Diva produced the following percentage rates of return. Rates of return on the market are given for comparison.

2006 2007 2008 2009 2010
Ms. Diva +29.1 +10 +3.1 +20.1 +1.5
DJIA +25.2 +11.8 +8.5 +10.9 +3.5
Calculate the average return and standard deviation of Ms. Diva’s mutual fund. Did she do better or worse than the market by these measures?

Explanation / Answer

1. Mean is 0.2* 200 +.5 *0 +0.3*-100= 10 Variance is (200-10)^2* .2 +(0-10)^2 *.5 +(-100-10)^2 *.3= 10,900 Standard deviation is sqrt (10,900)= 104.40 2. You can do 2 the same way. Too much number crunching for me, though.

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