State Preference Model and Capital Markets

The end-of-period payoffs for security X are $2$ in a bust and $10$ in a boom, while for security Y, they are $5$ in a bust and $4$ in a boom.

Security X costs $3 in the capital market today.

The equations are $3 = 2p1 + 10p2$ for security X and $4 = 5p1 + 4p2$ for security Y.

<p>There are two states of nature considered: bust and boom.</p> Signup and view all the answers

<p>The quantities used to replicate the payoff in security X are $QX ,1 = 2$ and $QX ,2 = 10$.</p> Signup and view all the answers

<p>The main assumption is that it operates in a perfect capital market with uncertainty about future states of nature.</p> Signup and view all the answers

<p>A complete capital market exists when the number of unique linearly independent securities equals the total number of alternative future states of nature.</p> Signup and view all the answers

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

<p>State-contingent payoffs are determined by the probabilities of various states, which reflect the economic uncertainty in the market.</p> Signup and view all the answers

<p>Economic uncertainty is captured by various states of nature, influencing investor preferences and the pricing of securities.</p> Signup and view all the answers

<p>Market completeness is crucial because it ensures that all possible risks can be traded, allowing for accurate pricing of securities.</p> Signup and view all the answers

<p>One-period models simplify the analysis by focusing on a single decision-making timeframe, reducing the complexities of future uncertainties.</p> Signup and view all the answers

<p>The state preference model allows for the pricing of securities based on the existing market conditions and the probability-weighted outcomes of different states.</p> Signup and view all the answers

<p>Pure securities are financial instruments that provide a payoff of 1 in a specific future state and can be combined to replicate market securities.</p> Signup and view all the answers

<p>A market security's payoff can be expressed as a linear combination of the payoffs from pure securities corresponding to different states.</p> Signup and view all the answers

<p>The price of a market security is given by $p_j = \sum_{s} p_s Q_{js}$, where $Q_{js}$ is the number of pure securities used.</p> Signup and view all the answers

<p>A perfect and complete market allows for the construction of pure securities for every state using existing market securities.</p> Signup and view all the answers

<p>The number of pure securities determines the magnitude of their contribution to the overall payoff of a market security in a specific state.</p> Signup and view all the answers

<p>An example structure could be a market security with a payoff of $4$ in state 1, $2$ in state 2, and $7$ in state 3.</p> Signup and view all the answers

<p>Pure securities allow investors to construct optimal portfolios that align closely with their risk preferences and expected payoffs.</p> Signup and view all the answers

<p>A system of equations is solved to determine the prices of pure securities based on the payoffs and their combinations.</p> Signup and view all the answers

<p>To maximize the expected utility of end-of-period wealth.</p> Signup and view all the answers

<p>It represents the expected utility of wealth based on various probable end-of-period outcomes.</p> Signup and view all the answers

<p>Investment decisions are made by comparing the expected utility of end-of-period wealth across different probability distributions.</p> Signup and view all the answers

<p>Securities allow firms to fund investments in real assets and enable individuals to claim ownership of these assets.</p> Signup and view all the answers

<p>Equilibrium occurs when demand equals supply, resulting in a consistent set of security prices.</p> Signup and view all the answers

<p>Investing in securities inherently involves taking on risk and uncertainty.</p> Signup and view all the answers

<p>It involves making informed investment choices based on the expected utility for individuals and firms given security prices.</p> Signup and view all the answers

<p>Expected utility is the weighted average of utilities across all uncertain alternatives, reflecting both probability and outcome.</p> Signup and view all the answers

<ol> <li>Time preferences for consumption and productivity of capital, 2. Expectations of state-probabilities, 3. Risk attitude towards variability in end-of-period wealth.</li> </ol> Signup and view all the answers

<p>A riskless portfolio is constructed as a combination of one pure security for each state.</p> Signup and view all the answers

<p>The price of a riskless claim is given by $pf = ps / (1 + rf)$, reflecting the time value of money and the productivity of capital.</p> Signup and view all the answers

<p>State probabilities represent individuals' beliefs about future market occurrences and affect the expected payoffs of securities.</p> Signup and view all the answers

<p>When individuals have homogeneous expectations, expected end-of-period payoffs can be calculated uniformly across investors.</p> Signup and view all the answers

<p>Time preferences indicate how much individuals value present consumption over future consumption, influencing their investment choices.</p> Signup and view all the answers

<p>An investor's risk attitude determines their willingness to accept variability in potential outcomes, influencing their portfolio choices.</p> Signup and view all the answers

<p>The formula illustrates the concept of discounting future payoffs to present values taking into account the risk-free rate.</p> Signup and view all the answers

<p>The objective is to maximize the utility function, which is expressed as $u(C) + \sum_{s} \pi_s U(Q_s)$.</p> Signup and view all the answers

<p>The Lagrange method is used to solve the optimization problem subject to the wealth constraint, represented as $\sum_{s} p_s Q_s + C = W_0$.</p> Signup and view all the answers

<p>A firm aims to maximize the expected utility of its current shareholders.</p> Signup and view all the answers

<p>Under certainty, the Fisher separation principle states that actions maximizing firm share prices also maximize shareholders' wealth and utility.</p> Signup and view all the answers

<p>It holds true in a capital market that is perfectly competitive, frictionless, and complete.</p> Signup and view all the answers

<p>Firms are characterized by their production functions, expressed as $Q_{sj} = \phi_j(I_j, s)$, where $I_j$ is the initial investment.</p> Signup and view all the answers

<p>The wealth constraint ensures that the total consumption and investment do not exceed initial wealth $W_0$.</p> Signup and view all the answers

<p>Maximizing the price of shares implies maximizing the expected utility of current shareholders.</p> Signup and view all the answers