Principles of Finance Lecture 5: Utility Theory

The end-of-period wealth for investment 1 would be $2010.

The expected utility for investment 2 is approximately 7.601.

The Pratt-Arrow risk premium for investment 1 is $0.

<p>The expected wealth for investment 2 is $1750.</p> Signup and view all the answers

<p>The Pratt-Arrow risk premium focuses on utility while the Markowitz risk premium considers mean and variance.</p> Signup and view all the answers

<p>The variance of end-of-period wealth is used to measure the risk associated with investment outcomes.</p> Signup and view all the answers

<p>Stochastic dominance refers to a situation where one investment is preferred over another under uncertainty.</p> Signup and view all the answers

<p>The normality assumption simplifies decision-making by allowing the use of mean and variance for investment analysis.</p> Signup and view all the answers

<p>The formula is $π = \frac{σ_{Z}^2}{2}U''(W) - U(W)$.</p> Signup and view all the answers

<p>ARA is defined as $ARA = -\frac{U''(W)}{U'(W)}$.</p> Signup and view all the answers

<p>RRA measures the level of risk aversion relative to wealth, defined as $RRA = -\frac{U''(W)}{W U'(W)}$.</p> Signup and view all the answers

<p>Both ARA and RRA are constant in $W$ for power utility functions.</p> Signup and view all the answers

<p>ARA decreases and RRA is constant as $W$ increases.</p> Signup and view all the answers

<p>It represents the expected wealth at the end of a period, considering the risk profile of the investor.</p> Signup and view all the answers

<p>Utility functions are specific to individuals but changes in marginal utility can be compared across them.</p> Signup and view all the answers

<p>Uncertainty requires investors to assess risk, influencing their choice based on expected utility.</p> Signup and view all the answers

<p>The local risk premium affects how investors value risky assets and their willingness to take on risk.</p> Signup and view all the answers

<p>A risk-averse investor dislikes risk and seeks compensation for taking it.</p> Signup and view all the answers

<p>Uncertainty of returns compels investors to evaluate potential risks versus returns in their decisions.</p> Signup and view all the answers

<p>A risk-neutral investor makes decisions solely based on expected end-of-period wealth, ignoring risk.</p> Signup and view all the answers

<p>A risk lover enjoys taking risks and seeks compensation for avoiding risk.</p> Signup and view all the answers

<p>The expected utility can be expressed as $E[U(W)] = \sum_{i} p_i U(W_i)$, where $p_i$ is the probability of wealth $W_i$.</p> Signup and view all the answers

<p>An investor's initial wealth and their risk profile significantly influence the decision to invest.</p> Signup and view all the answers

<p>Risk attitude determines how an individual evaluates potential decisions amidst uncertainty, influencing their choices.</p> Signup and view all the answers

<p>A risk-averse investor prefers to avoid risk and will often choose a guaranteed outcome over uncertain potential gains.</p> Signup and view all the answers

<p>Certainty equivalent wealth refers to the guaranteed amount of wealth an investor would accept instead of taking a risk with uncertain outcomes.</p> Signup and view all the answers

<p>A risk-loving investor has a convex utility function, indicating they derive higher utility from risky choices compared to certain outcomes.</p> Signup and view all the answers

<p>For a risk-neutral investor, the expected utility equals the utility of the expected wealth, as their utility function is linear.</p> Signup and view all the answers

<p>The risk premium represents the difference between the expected wealth and the certainty equivalent wealth.</p> Signup and view all the answers

<p>It means that, on average, both investment options provide the same amount of wealth at the end of the period, but not necessarily the same level of utility.</p> Signup and view all the answers

<p>Risk-averse investors typically find that the expected utility of a certain outcome is greater than the utility of expected wealth, indicating they value certainty more.</p> Signup and view all the answers

<p>Attitudes towards risk can significantly affect investment choices, with risk-averse investors favoring safer options, while risk-tolerant investors may seek higher returns through riskier investments.</p> Signup and view all the answers

<p>The mean and variance.</p> Signup and view all the answers

<p>It is defined as $E(R) = rac{E(W_f) - W_0}{W_0}$.</p> Signup and view all the answers

<p>Returns, $R$, can be expressed as $R = rac{W_f - W_0}{W_0}$, where $W_f$ is the end-of-period wealth.</p> Signup and view all the answers

<p>It represents the variability or risk of asset returns.</p> Signup and view all the answers

<p>It means that returns follow a normal distribution characterized by mean $R̄$ and variance $ heta_R^2$.</p> Signup and view all the answers

<p>It implies that investors make decisions based on expected return and risk, ignoring other factors.</p> Signup and view all the answers

<p>The variance of returns is calculated as $ heta_R^2 = E[(R - E(R))^2]$.</p> Signup and view all the answers

<p>It represents the initial wealth at the beginning of the investment period.</p> Signup and view all the answers

<p>The mean represents the average expected wealth at the end of the investment horizon.</p> Signup and view all the answers

<p>It can be expressed as $ heta_W^2 = E[W_f^2] - (E[W_f])^2$.</p> Signup and view all the answers

<p>Absolute risk aversion and relative risk aversion.</p> Signup and view all the answers

<p>They would likely avoid the investment due to risk aversion, preferring safer options.</p> Signup and view all the answers

<p>It suggests that individuals choose investments to maximize their expected utility, often leading to risk aversion.</p> Signup and view all the answers

<p>CE is calculated as CE = E(W + Z) - π(W, Z), where π is the risk premium.</p> Signup and view all the answers

<p>The risk premium represents the amount above the expected value of a gamble that an investor requires to accept the risk.</p> Signup and view all the answers

<p>An actuarially neutral gamble has an expected value of zero, meaning it neither adds nor subtracts from expected wealth.</p> Signup and view all the answers

<p>It indicates decreasing marginal utility, implying that as wealth increases, the additional satisfaction from each extra dollar decreases.</p> Signup and view all the answers

<p>Taylor series expansion approximates the utility of wealth by taking into account the variance and higher moments of the utility function.</p> Signup and view all the answers

<p>The expected value is zero, as the outcomes balance each other out.</p> Signup and view all the answers

<p>Higher levels of risk aversion lead to more conservative investment choices, favoring lower-risk options.</p> Signup and view all the answers