Question

You play a game that has the following payoffs: (25 pts)

35% probability of winning $1,000

35% probability of losing $1,500

30% probability of winning $550

Use the information above to answer the following questions:

a) What is the expected value of playing the game? (5 pts)

b) Would a risk neutral person play this game? Why or why not? (5 pts)

c) What level of risk tolerance (e.g. risk seeking, risk averse, risk neutral) must a person have to play this game? (5 pts)

d) How much in dollars, would a risk-averse and a risk neutral person need to be paid to play the game. Explain. (5 pts)

e) Which party has a positive risk premium for this game – the game's sponsor or the game's player? Explain. (5 pts)

Answer 1

a) The expected value of playing the game = Summation of (Probability*Expected payoff)

The expected value of playing the game = 0.35*1000 + 0.35*(-1500) + 0.30*550

The expected value of playing the game = -$10

b) A risk-neutral person would not play this game. This is because the expected payoff of this strategy is negative and a risk-neutral person would not like taking a bit excess risk.

c) A risk-seeking person should play this game. This is because since the expected payoff is negative, there is a finite risk associated with the game which only a risk-seeking person is expected to take

d) A risk-neutral person would need $10 for him to play the game as this would make the expected payoff=0 and would make the game neutral risky. A risk-averse person would need 0.35*(-1500) = $525 for him to play as this would weed out the negative payoff associated with the game.

e) The game's sponsor has a positive risk premium since the expected payoff for the player is negative. The game is a zero-sum game and hence the game sponser is compensated for the risk he/she is willing to take.