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Understanding Expected Value, Risk, and Uncertainty
The expected value of a risk is equal to the sum of each probability times the potential
You can model uncertainty on the basis of willingness to risk loss or gain. Individuals or
institutions can be classified as risk-neutral, risk-inclined, or risk-averse.
In studying uncertainty, you always have to
begin with the expected value of an
outcome: the expected value of any outcome
is the sum of the odds of each outcome times
the value of that outcome.
Assume that in a coin toss, you could win a $2
bet on heads. The expected value of the
gamble is found by the formula on the left.
That value is $1. The expected value is the
average outcome if you played this exact
game repeatedly.
You want to now ask how much someone (or
some institution) would be willing to pay to
play this game. A risk-neutral person would
pay only $1, the expected value; a riskinclined person would pay more than $1; a
risk-averse individual would pay less than
The analysis of risk behavior has applications
in financial markets, insurance, and sales.