# Risk aversion

To illustrate the concept of risk aversion in the context of options, imagine a fair coin will be tossed a year from now. If the coin comes up heads, you will receive $1 million. If the coin comes up tails, you receive nothing. Note that the coin toss is a kind of option. The expected value of the payment you will receive in one year is $500,000, which is half of $1 million. If the discount rate is 11% per year, the present value of the expected payment in one year is $450,450, which is $500,000 divided by 1.11. The amount $450,450 is the fair value of the right to receive either $1,000,000 or zero in one year depending on the outcome of the coin toss. That is, it is the fair value of the option. A risk-neutral entity is indifferent between $450,450 and the option. A risk-averse individual strictly prefers a sure payment today of $450,450 to the right to receive either $1,000,000 or zero in one year depending on the outcome of the coin toss. In other words, a risk-averse individual would willingly exchange the option for a cash payment of less than $450,450.

Individuals typically are risk-averse. Entities such as corporations that pool the financial interests of many shareholders are typically thought to be nearly risk-neutral. Thus, it is entirely consistent that the cost of the option to the corporation, which the Financial Accounting Standards Board labels the option's fair value, exceeds the cash payment the employee would willingly accept in exchange for the option.