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Asset Pricing > Lecture 4 > Flashcards

Lecture 4 Flashcards

1
Q

What is the ‘General’ Fundamental Theorem of Finance

A

If there exists an equilibrium, then we have no abritrage which would mean that there exist strictly positive risk neutral probabilities & martingale pricing

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2
Q

What is the setting of an Arrow-Debrau Model

A

The Arrow-Debrau model has two time period and S different states of the world, representing the different ways in which exogenous uncertainty might be resolved between period 0 and 1 The key idea is that of a contingent commodity: a commodity whose delivery is conditional on the realized state of the world

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3
Q

What does an Arrow Debreu Model suggests (outcome)

A

The Arrow–Debreu model suggests that under certain economic assumptions (convex preferences and perfect competition) there must be a set of prices p and allocations such that aggregate supplies will equal aggregate demands for every commodity in the economy.

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4
Q

What three assumptions have to be satisfied for an Arrow Debreu Equilibrium

A

Budget Constraint Consumers choose their optimal consumption bundle Markets clear

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5
Q

When is trade happening in the AD model

A

In the Arrow-Debreu model of general equilibrium, all commodities are traded at once, no matter when they are consumed, or under what state of nature Retrading at t=1 is not necessary for the Arrow-Debreu equilibrium Even if spot markets for all the L commodities were operating at t=1 and in each state, trade in these markets would not occur

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6
Q

What is an asset market model

A

In an asset markets model consumers face a multiplicity of budget constraints, at different times and under different states of nature In asset markets equilibrium retrading at t=1 is important and agents have to correctly anticipate today the price that will prevail tomorrow-Rational Expectations

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7
Q

Assuming there are L goods and S states at time period 1. How many markets are there for the AD model and for the Asset market model

A

For the Asset Market: L*(S+1) For the AD : 2*L + S

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8
Q

What is Walras Law

A

There exists a price vector for which the excess demand is equal to zero

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9
Q

What is a Financial Equilibrium

A

It is therefore a solution to the specified problem wherein every agent i maximizes his utility subject to his budget constraints , and the goods and security markets clear. Under very general conditions, an FE exists. We should interpret observed prices as equilibrium prices.

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10
Q

What is the no arbitrage property and what is the intuition

A

No arbitrage property: If utilities are strictly increasing then in a financial equilibrium there is no arbitrage Intuition: With strictly increasing utility function the budget constraints are binding. If there was an arbitrage opportunity an agent could increase his utility without affecting his budget constraints in a negative way (remember the definition of arbitrage). Thus the budget constraints would not be binding anymore which is a contradiction. The price will adjust until equilibrium is reached

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11
Q

How do we price redundant securities in a financial equilibrium

A

They will be never traded in a FE and they will be priced via the arbitrage condition

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12
Q

How does pareto efficiency have anything to do with marginal rates of substitution

A

Sufficient condition of Pareto Optimality: The marginal rates of substitution (MRS) across states of the world are equal for all agents

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13
Q

Which 4 properties do Financial Equilibria have

A
  1. No arbitrage property: If utilities are strictly increasing then in a financial equilibrium there is no arbitratge 2. Redundant Securities: Redundant securities will never be traded in a Financial Equilibrium 3. When markets are complete, FE is Pareto Optimal 4. When markets are incomplete, FE is constrained Pareto Optimal (for one good, i.e. L=1)
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14
Q

What are the fundamentals of the lucas model

A

A representative agent GE model with one commodity Objective: derive the equilibrium prices of these J assets at every point in time Agent’s decision problem: How much holding to sell and how much to keep and collect the payoffs (dividends) in the following period

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15
Q

How much trade is going on in the Lucas Model

A

A representative agent will not find a counterparty to trade with since everyone demands or supplies the same –> No trade The representative agent consumes his endowment today and the dividends from the assets in the future

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16
Q

How do we call the ratio of the marginal utilities of consumption

A

Marginal intertemporal rate of substitution between today and state s tomorrow It is also called the pricing kernel or the stochastic discount factor The price of an asset depends not only on how high or low its payoffs are, but also on how “valuable” are these payoffs in the states that they occur, which is measured by the MRS for that state

17
Q

The price of an arrow securitiy is … when the income is lower

A

The lower the income in state s, the higher the price of the insurance contract (Arrow Security) for that state

18
Q

What is Breeden’s Formula

A

The Breeden formula decomposes the price into two components 1. The expected income, discounted by the riskless rate 2. A premium for risk

19
Q

What is the equity premium puzzle

A

GE theories of asset pricing cannot account for the differences in the U.S. historical data between real return to treasury bonds ( 1% per year) and the real return from a broad stock market index ( 7% per year)

20
Q

Tell me a bit about the Lucas Model Framework

A
  1. Identical agents: Representative agent economy 2. The representative agent has an endowment of (quantity) 1 of the asset 3. The asset pays out a dividend dt at each period t 4. Its price is pt at period t 5. The representative agent decides how much to sell at each period. This is his decision variable and is denoted by xt 6. His consumption at each period t will be the given by the dividend on the proportion of the asset he hasn’t sold yet, plus his earnings from asset sales at that period
21
Q

What is the essential part of the Crochain Book about empirical matters

A

There is nothing essential. It is Bla Bla

22
Q

What is the usual constraint in the lucas model

A

c_t = d_t * (1 - \sum_{j=0}^{t-1} x_j) + p_t * x_t Assume that the representative agent is at time 0 (t=0). His decision variable is x0, the amount of the asset that he will sell in period 0. This affects both consumption at time 0, c0, and consumption in every subsequent period, ct

23
Q

What is the equilibrium in the lucas model

A

In each period t every agent will want to sell/buy xt of the asset But the total sum of the buy/sell orders should be zero If N is the number of agent then N xt = 0 ) xt = 0 In equilibrium ct = dt

24
Q

What does the Arrow Debreu model suggest

A

The Arrow–Debreu model suggests that under certain economic

assumptions (convex preferences and perfect competition) there

must be a set of prices p and allocations such that aggregate supplies

will equal aggregate demands for every commodity in the economy.

25
Q

What is the setting in an Arrow Debreu Model

A

All commodities are traded at once, no matter when they are consumed, or under what state of nature

All consumer face only budget constraint

26
Q

What is the distinguishing difference between the asset market model and the arrow debreau model

A

The distinguishing feature of the asset market model is that consumers face a multiplicity of budget constraints, at different times and under different states of nature

27
Q

What is the setting of an asset market model

A

Consumers face a multiplicity of budget constraints, at different times under different states of nature

To transfer wealth among budget constraints

In asset market equilibrium retrading at t=1 is important and agents have to correctly anticipate today the price that will prevail tomorrow-Rational Expectations

28
Q

Construct the efficient frontier for the general case (return r_1, r_2) standard deviation \sigma_1 \sigma_2 with perfect positive correlation

A
29
Q

What is the two fund separation theorem

A

All optimal portfolios would consist of combinations of the risk-free asset and the tangency portfolio T

The optimal portfolio of risky asset can be identified independent of the knowledge of individual risk preferences

If every agent’s risk tolerance is linear with common slope, then date1-consumption plans at any Pareto optimal allocation lie in the span of the risk-free payoff and the aggregate endowment

30
Q
A
31
Q

How do you derive the SML - Important to know

A
32
Q

What is the first puzzle and what are potential Solutions

A

Puzzle:

The term structure is upward sloping although spot interest rates have been historically stable

Solutions:

RRLP

  1. Risk premium
  2. Representative agent with transaction technology
  3. Preferred Habitat
  4. Liquidity
33
Q

What is the second puzzle and what are potential solutions

A

Puzzle:

The term structure has been flattening in recent years

Solutions:

BIILDR

  1. Better anchored inflation
  2. Increased preference for long-term bonds
  3. Increased demand from growing countries with high saving rates
  4. Lower supply of long term bonds due to changes in environment
  5. Demographical changes
  6. Reduction in the volatility of real activity
34
Q

Topic: Value at Risk

The loss level is a function of two parameters

Which ones?

A

The time horizon

The confidence level

35
Q

What are the advantages of VaR

A

It captures an important aspect of risk in a single number

It is easy to understand

It asks the simple question: “How bad can things get”

36
Q

How do you arrive at the 10-day 99%VaR from a 1-day 99%VaR

And when does this hold

A

\sqrt{10} x 1-day VaR

This equality holds true when portfolio changes on successive days and come from independent identically distributed normal distributions

37
Q

What are relevant frictions you learned in that course

A
  1. Market incompleteness
  2. Liquidity
  3. Default
  4. Information
38
Q

Define: Ex-Ante; Interm; Ex-Post

When is an Allocation Pareto Optimal

What is Ex-Ante Pareto Optimality; Interim Pareto Optimality; Ex-Post Pareto Optimality

Does any of these PO implies one of the other?

A

Ex-Ante: The state of nature is drawn but not observed

Interim-Stage: Agents receive private signals

Ex-Post: The stage of nature is revealed

An allocation is Pareto Optimal if there is no other allocation that increases the expected utility of one agent without lowering the expected utility of another agent

Ex-Ante PO implies interim PO, which in turn implies ex-post PO

39
Q

Start with eler equations for the risk free asset and risky asset and use breedens formula to end up with the CAPM equation

Good luck!

A

Asset Pricing (8 decks)

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