1. Risk aversion depends upon an individual’s relative preference for a certain income over a fair gamble entailing an expected income of the same value as the certain income. An individual is identified as being “risk averse” the certain income is preferred over a fair gamble with an expected income equal to the certain income…
Download file to see previous pages...
Generally, the extent of risk aversion is the degree to which the individual prefers the certain income over the uncertain income. In terms of a utility function, this translates to the distance between the utility generated by the certain income and the utility generated by the gamble which has an expected income equal to the certain income. Obviously, for a concave utility function, the utility of the certain income will lie above the utility of the uncertain income with the same expected value. For a convex utility function this will be reversed. These are 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 both outcomes equally likely to occur. That is, both outcomes X1 and X2 have 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 while a risk neutral person will have a utility function that has a constant 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 individual’s love for risk. Therefore, it can be generally agreed 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 person’s preferences will be designated by a utility function with a constant slope. Now, Mr. D’s Utility function is: Then, and, Since , and thus, Mr. D’s utility function is positively sloped. A positively sloped utility function implies more income is preferred to less by Mr. D. For his attitude 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 parameter 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. D’s attitude towards risk depends on the value of the parameter . If , Mr. D loves
...Download file to see next pagesRead More
Cite this document
(“Risk aversion Assignment Example | Topics and Well Written Essays - 2000 words”, n.d.)
Retrieved from https://studentshare.org/macro-microeconomics/1398038-no-title
(Risk Aversion Assignment Example | Topics and Well Written Essays - 2000 Words)
“Risk Aversion Assignment Example | Topics and Well Written Essays - 2000 Words”, n.d. https://studentshare.org/macro-microeconomics/1398038-no-title.
In investigating these unique phenomena, there arise two key challenges. One is whether the phenomenon exists at all in the first place and two, even if it did, will a radical paradigm shift in behavior be the proposed solution? Psychology therefore becomes a key component when it comes to dissecting and understanding human judgment, behavior and general well-being.
For so many years in the United States, there has been a great difference in average real returns on stocks and average real returns on treasury bills. Market and economic factors related to investment choices and expected returns are engulfed in fair play dilemma of equity premium and risk free rate, with economists developing various models to resolve them.
This is critically important for business growth because it helps break trade barriers, improved competitive advantage, and enhanced globalizations of businesses as well as free flow of capital. An Acquisition or merger occurs when two separate companies working separately decide to operate as one to increase profitability and value (Maksimovic, 2011).
ivalent in relation to an uncertain economic gain is the particular sum of money received by an individual, and is considered equal to the risk or gamble. An individual may implement ways to maximise net benefit, based on the certainty equivalents (Tisdell 1968). The factor of
The risk aversion coefficient points out the extent to which an investor is risk averse. A higher value suggests that the investor will always tend to make less risky investments. A risk aversion coefficient of 1 implies less risk
It becomes hard for them to manage risk effectively without necessarily undergoing the six steps respectively. Risk managers begin by identifying the potential risks that are within and outside the business environment (Outreville, 2014). That is
The economic slowdown in China would affect emerging economies thus warning that global economy would weaken since China has been a major contributor to the recent random economic growth, therefore, the slowdown will affect other emerging economies who rely on China for cheap their imports and grants.
1 Pages(250 words)Assignment
GOT A TRICKY QUESTION? RECEIVE AN ANSWER FROM STUDENTS LIKE YOU!
Let us find you another Assignment on topic Risk aversion for FREE!