1. You are forced to gamble on a coin flip with a fair coin (Prob (Head) = .5) but an unfair payoff. A head yields $10 a tail costs $20. Calculate the expected value and variance of your payoff.

2. You are going to play two games, the X game and the Y game. The X game is played first and if you win, you receive $2 and if you lose, you pay $2. The Y game is played next and has the same payoffs. The table below gives the probability of each of the four possible outcomes (for example, the probability of winning both games and making $4 is 5%).

X GameWin Lose

Y GameWin .05 .45Lose .45 .05

a. The probability of winning game X is ________.

The probability of winning game Y is ______

b. The expected value of the X game is ________

The expected value of the Y game __________

c. The covariance between the payoff of the X game and the Y game is ________

3. Suppose you own a house that is worth $200,000 and that there is a .01 probability that the house will be destroyed. Rather than accept that risk you choose to buy an insurance policy that is offered for sale at a price of $1,000. What does this mean about your attitude towards risk? (Explain using the concept of certain equivalence.)

4. A mutual fund salesman is trying to get your business and tells you that his fund has had a higher risk and lower standard deviation of returns than the average of similar funds. Is this conclusive proof that his is better. Briefly explain (one or two sentences is fine.)