Capital Market Theory and Pure Securities

The derived price of pure security p1 is $\frac{7}{10.5} = \frac{2}{3}$.

The derived price of pure security p2 is $\frac{3}{30} = \frac{1}{10}$.

Capital market completeness refers to a market where all risks can be fully hedged and all future states can be traded.

<p>A payment of $\frac{3}{2}$ is required for a promise of a payoff of 1 in state 1.</p> Signup and view all the answers

<p>Pure securities are financial instruments that provide a payoff in a specific state of the world without any default risk.</p> Signup and view all the answers

<p>Analytical purposes and simple description of uncertainty.</p> Signup and view all the answers

<p>Supply must equal demand for every security.</p> Signup and view all the answers

<p>It states that any two securities with equal state-contingent payoffs must have the same market price.</p> Signup and view all the answers

<p>It leads to buying low-priced securities and selling high-priced ones, disrupting supply and demand.</p> Signup and view all the answers

<p>It suggests that two portfolios with identical state-contingent payoff vectors should have equal prices.</p> Signup and view all the answers

<p>Sell the expensive portfolio and buy the cheap one.</p> Signup and view all the answers

<p>They are determined by the combination of various pure securities.</p> Signup and view all the answers

<p>The price of a market security reflects the determinants of its underlying pure securities.</p> Signup and view all the answers

<p>A complete capital market has an equal number of unique linearly independent securities and future states of nature.</p> Signup and view all the answers

<p>Pure securities are defined as having an end-of-period payoff of 1 in a given state and 0 in all other states.</p> Signup and view all the answers

<p>State probabilities are equivalent to the probabilities of the associated end-of-period security payoffs.</p> Signup and view all the answers

<p>The state preference model assumes a perfect capital market.</p> Signup and view all the answers

<p>Economic uncertainty denotes the unknown future states of nature that affect investment outcomes.</p> Signup and view all the answers

<p>In a perfect and complete market, any security can be priced using existing securities due to their linear independence.</p> Signup and view all the answers

<p>A one-period model signifies that all investments and their outcomes are evaluated over a single time frame.</p> Signup and view all the answers

<p>The probability of a state of nature aids investors in assessing potential outcomes and making informed choices.</p> Signup and view all the answers

<p>Time preferences for consumption, expectations of state-probabilities, and risk attitude towards wealth variability.</p> Signup and view all the answers

<p>The price of a riskless portfolio, pf, is calculated as $pf = \frac{\sum ps}{1 + r_f}$ where ps represents the price of pure securities.</p> Signup and view all the answers

<p>A riskless security refers to a portfolio of one pure security for each state that guarantees a certain payoff.</p> Signup and view all the answers

<p>Individuals may have different beliefs, experiences, and information that shape their expectations about state probabilities.</p> Signup and view all the answers

<p>The risk-free rate reflects the time value of money and productivity of capital, influencing the pricing of securities.</p> Signup and view all the answers

<p>Time preferences for consumption determine how much value is placed on future payoffs versus current consumption, impacting security prices.</p> Signup and view all the answers

<p>The expected end-of-period payoff for a pure security is expressed as $\sum \pi_s \times payoff_s$ for all states s.</p> Signup and view all the answers

<p>$\pi_1, \pi_2$ represent the probabilities associated with different states that influence the expected payoff from a pure security.</p> Signup and view all the answers

<p>The price of a pure security is given by $p_s = heta_s \pi_s$, where $ heta_s$ is the price of an expected dollar payoff if state s occurs.</p> Signup and view all the answers

<p>Individuals with risk aversion will find a state with lower end-of-period wealth (LW) more attractive than a state with higher wealth (HW), leading to $p_{LW} &gt; p_{HW}$.</p> Signup and view all the answers

<p>The formula $E[U(W)] = \sum_{s} \pi_s U(Q_s)$ incorporates the probabilities of each state and the utility derived from the end-of-period wealth associated with pure securities.</p> Signup and view all the answers

<p>$\theta_s$ represents the price of an expected dollar payoff if a particular state s occurs.</p> Signup and view all the answers

<p>Individuals tend to make investment decisions based on the variability of their end-of-period wealth, exemplifying their risk aversion.</p> Signup and view all the answers

<p>Due to risk aversion, the expected payoff in state LW is valued higher, resulting in $p_{LW} = \pi^* \theta_{LW} &gt; p_{HW} = \pi^* \theta_{HW}$.</p> Signup and view all the answers

<p>The state preference model explains how individuals make optimal portfolio decisions by considering their preferences and aversion to risk associated with different states.</p> Signup and view all the answers

<p>Market prices adjust based on the perceived risk associated with state-variation in end-of-period wealth, favoring securities aligned with lower risk states.</p> Signup and view all the answers

<p>The objective function is to maximize $u(C) + \sum_{s} \pi_s U(Q_s)$ subject to the wealth constraint.</p> Signup and view all the answers

<p>The wealth constraint is represented as $\sum_{s} p_s Q_s + C = W_0$.</p> Signup and view all the answers

<p>The Fisher separation principle states that in a perfect capital market, actions maximizing share price also maximize shareholder utility.</p> Signup and view all the answers

<p>The components are maximizing the expected utility of current shareholders and increasing the firm's share price.</p> Signup and view all the answers

<p>It represents the output produced by firm j as a function of its initial investment Ij and the state of nature s.</p> Signup and view all the answers

<p>The Lagrange method helps solve for the optimal allocation of consumption and investment given the wealth constraint.</p> Signup and view all the answers

<p>The capital market must be perfectly competitive, frictionless, and complete.</p> Signup and view all the answers

<p>Issuing securities allows firms to gather the necessary capital required for investments while also sharing ownership with investors.</p> Signup and view all the answers