Every person wants to make the best decision but every person may have a different risk attitude and our risk attitude play a major role in our decision making. On the basis of risk attitude, people can be divided into the following three categories:-
- Risk-Averse person:- A person who does not like to take the risk, is known as a risk-averse person.
- Risk lover person:- A person who likes to take the risk to gain a reward is known as a risk lover.
- Risk neutral person:- A person who is indifferent about risk, is known as a risk-neutral person.
How our risk attitude affects our decisions? (Utility of Money/wealth)
At this point, we need to understand the basis of their behavior. We know that in a financial decision, the risk factor is associated with money involved. Hence the basis of risk attitude is the utility of money.
Some people may be shocked by reading about the utility of money, but money does have utility. The value or happiness provided a fixed sum of money to a person is known as the utility of money. We know that every person may have a different money utility function. Following are the different utility function associated with different risk attitude:-
- Risk-Averse person:- The utility curve of a risk-averse person is of concave shape. As wealth rises, the marginal utility of wealth declines. For example, the money utility function of a risk-averse function may be written as: U=√M , where U stands for utility and M stands for wealth.
- Risk lover person:- The utility curve of a risk lover is of convex shape. As the wealth rises the marginal utility of wealth increases for a risk lover. For example, the money utility function of a risk lover can be written as U=M2 , where U stands for utility and M stands for wealth.
- Risk neutral person:- The utility curve of a risk-neutral person rises high as wealth rises to keep the marginal utility as same. As wealth rises the marginal utility of wealth remains the same at all levels of wealth. For example, the money utility function of a risk lover can be written as U=M , where U stands for utility and M stands for wealth.
The goal of all our financial decisions is to maximize the utility of our wealth. Hence every person tries to maximize the utility of wealth as per his own utility function. Now are have framed the formula for decision making as per risk attitude of each person.
A risk-averse person plays gamble but a risk-lover buys an insurance policy.
There should not be any surprise hearing that a risk-averse person play gamble and risk-lover buy insurance policy. This statement can be supported with the help of following example:-
- Risk-averse person:- We know that in the case of a risk-averse person, as the wealth rises the marginal utility of wealth declines. Hence utility function of a risk-averse person can be written as U=√M. Now take the example of a risk-averse person having this utility function. Assume that his initial wealth is Rs. 100. Now a gamble is available to this person wherein he can win Rs. 21 with a probability of 2/3 and losses Rs. 19 with a probability of 1/3. Now let’s see whether the person will accept or reject the gamble, calculation is provided in the table given below:-
Outcome of gamble Amount of wealth after win or loss Utility of the wealth Probabilities Product (A) (B) (C) (D) (C) X (D) Win 100 + 21 = Rs. 121 √121 = 11 2/3 7.33 Loss 100 - 19 = Rs. 81 √81 = 9 1/3 3 Total utility of expected wealth 10.33
As per the above table, if he plays the gamble then expected utility is 10.33. His current wealth is Rs. 100 with utility √100 = 10. Since the utility of current wealth is less that expected utility after gambling. Hence he will accept the gamble, despite the fact that he is a risk-averse person.
- Risk-lover person:- We know that in the case of a risk-lover person, as the wealth rises the marginal utility of wealth increases. Hence utility function of a risk-lover person can be written as U=M2. Now take the example of a risk-lover person having this utility function. Assume that his initial wealth is Rs. 50. Now if an insurance policy of Rs. 100/- with a premium of Rs. 20/- is available to this person wherein the probability of happening the loss is 30%. Now let’s see whether the person will accept or reject the policy, calculation is provided in the table given below:-
Events Amount of wealth after win or loss Utility of the wealth Probabilities Product (A) (B) (C) (D) (C) X (D) Insured event happens 50 + 100- 20= Rs. 130 (130)^2 = 16900 30% 5070 Insured event does not happen 50-20 = 30 (30)^2 = 900 70% 630 Total utility of expected wealth 5700
As per the above table, if this person takes the insurance policy then the expected utility is 5700. His current wealth is Rs. 50 with utility 502 = 2500. Since the utility of current wealth is less than expected utility after insurance policy. Hence he will accept the insurance policy, despite the fact that he is a risk-lover person.
Sometimes a person shows that he is a risk-lover person but his financial decisions discloses his real risk attitude. Hence our risk attitude is a guiding factor in making our financial decisions.