Question

Assume that for $1 you could buy a coin flip that would pay you $2 for heads and nothing for tails. If you are risk averse, should you take the coin flip? What if the coin flip cost you $0.90 instead of $1? What is the lowest price that YOU would take to accept the coin flip and why might this be different for others?

Answer 1

A risk averse individual , he/she would hesitate to agree to a situation with an unknown payoff rather than another situation with a more predictable payoff but lower expected payoff.

In this example, the Expected pay off = 1/2 * $2 + 1/2 * 0 = $ 1 (since 1/2 is the probability of heads or tails)

Since I am paying $ 1 on the opportunity, on average I won't gain or lose anything on the flip. However,as a risk averse person, I would like to take risk only with a payoff and hence will not undertake the coin toss.

If the flip coin costs $ 0.9, then opportunity for profit= $ 1 - $ 0.9 = $ 0.10, hence I would choose this coin toss.

However, not all risk averse person need to accept this offer, and some may not be comfortable with $ 0.10 profit and hence would not undertake the coin toss. The degree of risk aversion varies across individuals.