# Risk Aversion

The risk aversion theory explains the natural tendency of people to accept an investment with more certain but lower payoff than an investment with uncertain payoff. The concept of risk aversion refers to the behaviors of investors and consumers under some economic or financial uncertainty. The inverse of risk aversion is known as the risk tolerance.
For example we consider that a person is asked to choose between two investments one of which is certain and another is uncertain. Now, in case of the uncertain investment, investor has equal chance of getting either big amount or nothing in return. On the other hand, the certain investment assures the investor of returning certain amount, which is lesser than the return amount of the first scenario.

According to risk aversion theory, the investor is more likely to choose the investment that promises a lower but certain amount of return. The risk taking attitudes of an investor may be various.

An investor may be risk averse when the investor is more likely to accept a certain payoff with less return. The investor can be risk neutral when he or she is not bothered about the less payment and the gamble. The investor is risk seeking when he or she is ready to take some options over gamble if the return is greater than the usual low amount.
According to the theory of utility, u(c) describes the function of utility of consumption where c refers to consumption that is equivalent to money. From the higher curvature of u(c) graph we can say that the risk aversion is higher.

The following mathematical representation is known as the Arrow-Pratt measure of absolute risk-aversion, also known as ARA:

ru(c) = -(u”(c)/ u'(c))

ru(c) is expressed as the coefficient of absolute risk aversion.

The following mathematical representation is known as the Arrow-Pratt measure of relative risk-aversion, also known as RRA:

Ru(c) = cru(c) = -cu”(c)/u'(c)

Ru(c) is referred to as the coefficient of relative risk aversion.

According to modern portfolio theory, the risk aversion refers to the marginal reward that an investor wishes to receive when he or she goes for a new risk amount. In advanced portfolio theory, however, several kinds of risks are considered. The mathematical representation of risk aversion under modern portfolio theory is:

A = dE(r)/d?

An = dE(r)/d n??n

A and An are the symbols used for risk aversion. 