Risk aversion Assignment Example | Topics and Well Written Essays - 2000 words

Risk aversion - Assignment ExampleGenerally, the extent of peril aversion is the degree to which the individualistic prefers the certain income over the uncertain income. In terms of a value usance, this translates to the distance between the gain generated by the certain income and the public return company generated by the gamble which has an expected income bear on to the certain income. Obviously, for a cupular utility endure, the utility of the certain income leave alone lie above the utility of the uncertain income with the same expected value. For a convex utility function this will be reversed. These ar explained in the diagram below (figure 1). Figure 1 Risk Aversion and the curvature of the utility function In the diagram above, a rational individual is considered whose preferences are represented by the utility function U(.) defined over money incomes X. Suppose the individual has a choice of either playing a lottery with two possible outcomes X1 and X2, where X2 X1. To keep things simple let us further assume that two outcomes reachly likely to occur. That is, both outcomes X1 and X2 nonplus a probability of occurrence = ?. Thus if X1 is realized the individual gets U(X1) and if X2 realizes, the individual derives U(X2). Then, the expected income from the lottery is ?X1+X2 and the expected utility is ? U(X1) +U(X2). Now, observe that whether the utility derived by the individual from a certain income of ?X1+X2 which is equal to U?X1+X2 lies above ? U(X1) +U(X2), the expected utility from the lottery with an expected earning of ?X1+X2, depends upon the curvature of the function. When the utility function is concave, . This shows that the individual prefers a certain income over and above a lottery with an expected income that is equal to certain income. Extending this logic it is simple to show that a risk loving individual will have a convex utility function firearm a risk soggy person will have a utility function that has a const ant slope. Also, greater the distance between U?X1+X2 and ? U(X1) +U(X2), the more risk averse is the individual, since the preference for the certain income is even greater in that case. This implies that the more concave the utility function the greater will be the risk aversion of the individual. Similarly, greater the convexity of the utility function, greater will be the individuals love for risk. Therefore, it can be generally agree upon that a risk-averse person will have a concave utility function while a risk lover will have a convex utility function. A risk neutral persons preferences will be designated by a utility function with a constant slope. Now, Mr. Ds Utility function is Then, and, Since , and thus, Mr. Ds utility function is demonstrablely sloped. A positively sloped utility function implies more income is preferred to less by Mr. D. For his billet towards risk, the curvature (sign of the second order derivative) of the utility function has to be considered. Now , and, Therefore, the utility function is convex if the value of the positive contention and it is concave if the positive parameter . If the utility function is concave, Mr. D is risk averse while if the utility function is convex, then Mr. D is in nature a risk loving person. Therefore, regarding the attitude of Mr. D towards risk, we conclude the following Mr. Ds attitude towards risk depends on the value of the parameter . If , Mr. D loves