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Arbitrage Pricing Theory


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Mean-Variance Analysis
prior models have their basis in this
Stephen Ross
developed the Arbitrage Pricing Theory of pricing assets in 1976
arbitrage pricing theory
pricing model that uses multiple factors to relate expected returns to risk by assuming that asset returns are linearly related to a set of indexes which are proxy risk factors that influence asset returns
law of one price
A law that says that two identical products at the same venue should sell for the same price.
Utility theory
the APT eliminates this theory that the CAPM has
Equilibrium
APT has a more general description of this than the CAPM
MIM
equation for the APT is more or less the same as the description of this model
What are the three conditions for proving the APT?
portfolio involves zero investment, has no risk, and produces E(R) of zero
Roll and Ross
they consider the underlying causes of the generating process of returns to be an important area of study, but think it should be tested seperately from asset pricing theories; without assumptions (theories) in APT, empir…
Fama and MacBeth
when tested the CAPM, also applied to the APT; tested on basis of econoic theory; result was economic theory does not explain equilibrium returns
Litzenberger and Ramaswamy
found dividend yield as a statistically significant variable
Sharp
Used five firm characteristics to see which had the highest impact and identified some additional criteria beyond Beta with a proxy for the market portfolio; however, recognizes own model as being ad hoc in nature
Barra Model
Second model used to identify firm characteristics; Widely used in industry; Uses 9 firm characteristics: Volatility, momentum, size, liquidity, growth, value, earnings volatility, financial leverage, and industry membership
Chen, Roll, and Ross
Hypothesized and tested a set of economic variables: Inflation, Term Structure, Risk Premia; concluded that there seems to be significan relationship between the hypothesized macroeconomic variables and the statistically identified systematic factors in stock ma…
Burmeister and McElroy
Perform two tests.First Test: Originally used to test the MIM. The no-arbitrage constraint is same as earlier constraints put on CAPM; found: imposing this constraint cannot increase explanatory power; can only decrease it the…
Fama and French
Constructed a model to explain returns and expected returns on both stocks and bonds; Size is measured by the return on a portfolio; Allows them to investigate the time-series and cross-sectional properties of size; Concl…
Sharp-Lintner-Mossin Form of CAPM
The APT solution with multiple factors appropriately priced is fully consistent with this model
Active Management
Involves making bets about some securities and designing the portfolio on a belief that one or more securities are mispriced
Passive Management
Believe mispriced securities can't be identified and try to hold a portfolio that mimics some set of stocks
Long/Short Investment Strategy
Use APT to find which are under/over valued to form portfolios that offer an excess return and have no risk with respect to any factor
Risk-Neutral Strategy
another name for the Long/Short Strategy
Burmeister, Roll, and Ross
examined the risk-neutral strategy assuming the error term could be correctly identified; it indicated the ability of factor-neutral portfolios to lower risk, and if forecasting ability exists, increase returns
APT 3 Propositions
security returns can be described by a factor model
Simple Arbitrage Example
an arbitrage Opportunity arises when an investor can earn riskless profits without making a Net investment
Most Fundamental Concept in Capital Market Theory
the idea that market prices Will adjust to eliminate arbitrage opportunities.
Arbitrage vs. Risk-Return Dominance
-A dominance argument (i.e., CAPM) holds that when equilibrium is violated, many investors would make limited portfolio changes, depending on their A.
Rate of return on portfolio
Well-Diversified Portfolios: Rate of Return on Portfolio
WDP: Portfolio Variance
σ2=ß2pσ2F + σ2(ei)
Betas & Expected Returns Examples
rp = E(rp) + ßpF
3 APT Assumptions for No-Arbitrage
-We have used the no-arbitrage condition to obtain an expected return-beta relationship identical to that of the CAPM, without the restrictive assumptions of the CAPM. As noted, this derivation depends on 3 assumptions:
APT Drawbacks
-Drawback: Factor portfolios are not unique...too many ways to get to a factor portfolio (e.g., spanning argument)
No-Arbitrage
When securities are priced so that there are no risk-free arbitrage opportunities
Market Demand curve
Curve relating the quantity of a good that all consumers in a market will buy to its price (curve shifts right as more enter market)
Consumer Surplus
Difference between what a consumer is willing to pay for a good the the amount actually paid
Theory of the firm
Explanation of how a firm makes cost-minimizing production decisions and how its cost varies with its output
firm
A business organization, such as a corporation, limited liability company or partnership. Firms are typically associated with business organizations that practice law, but the term can be used for a wide variety or business operation units.
Production function
Function showing the highest output that a firm can produce for every specified combo of inputs
Law of diminishing marginal return
As a firm increases input, holding all other inputs and technology constant, the corresponding increases in output will become smaller eventually (marginal product of that input will diminish eventually)
Marginal product
Additional output produced as an input in increased by 1 unit, keeping other inputs constant
Average product
Output per unit of particular input
Marginal product of labor
-When the marginal product of labor is greater than the avg. product, the avg. product of labor increases
Labor productivity
Can increase if there are improvements in technology, even though any given production process exhibits diminishing returns of labor
Returns to scale
Rate at which output increases as all inputs are increased by equal proportions
Constant returns to scale
Output might increase by exactly 100% if inputs are increased by 100%
Decreasing returns to scale
Output might increase by less than 100% if inputs are increased by 100%
Increasing returns to scale
Output might increase by more than 100% if inputs are increased by 100%
Total cost
Total economic cost of production, consisting of fixed and variable costs
Fixed cost
Cost that does not vary with the level of output and that can be eliminated only by shutting down
Variable cost
Cost that varies as output varies
ATC
Firm's total cost divided by the units of output produced
AFC
Fixed costs divided by units of outputs produced
AVC
Variable cost divided by the units of output produced
Marginal Cost curve
Crosses AVC and ATC curves at their minimum points
Costs in LR
0 fixed costs
Optimal Output
Firms should consider- its cost function, how much it can sell at a given price, the market structure(perfectly competitive, monopoly, oligopoly), the number of firms competing, how …
Profit maximization
Whether to increase quantity produced by 1 unit, the firm will have to compare the additional revenue and the additional production cost generated by the additional unit of production
Marginal Revenue
Change in revenue resulting in a 1-unit increase in output
Marginal Cost
Change in cost resulting from a 1-unit increase in output
Profit Maximization Rule
Keep increasing Q as long as the additional revenue you obtain is greater than the additional costs obtained
P=MR=MC
Perfectly competitive firm
Shut down rule
Firm may produce in the short run if price is greater than AVC
Short Run
Everything above the AVC on the MC curve is the short run supply curve
P=MC
Only in perfect competition
Long Run competitive equilibrium
All firms in an industry are maximizing profit, no firm has an incentive to enter or exit, and price is such that quantity supplied equals quantity demanded
Welfare
Well-being of groups such as consumers and producers
Consumer Surplus Area
Area below the demand curve and above the price up to quantity being produced
Producer Surplus
Gain from participating in a market- The difference between amount for which good sells and minimum amount necessary for seller to produce good
Producer Surplus Area
Area above supply curve and below the price up to quantity being produced
Price Ceiling
Price is held below the market price. There is a welfare loss. Protects consumers. Plug amount into supply curve to find Q. Then plug that Q into demand curve to find new P
Price Floors
By law, the price cannot be lower than a certain price. Protects producers
Sales Tax
Tax of a certain amount of money per unit sold
Pb
The price paid by buyers--> Pb=Ps+t
Ps
The price that sellers receiver
Property of Welfare
Maximized under perfect competition- Perfectly competitive market is efficient
Market Power
Ability of a seller of buyer to affect the price of a good
Monopoly
Market with only 1 seller. Price-setter. MR=MC(Q*)
Natural Monopoy
Market has a natural monopoly if one firm can produce total market output at lower cost than could several other firms
Monopolistic Competition
Market in which firms can enter freely, each producing its own brand or version of a differentiated product
Oligopoly
Market in which only a few firms compete with one another, and entry by new firms is impeded
Cartel
Market in which some or all firms explicitly collude, coordinating prices and output levels to maximize joint profits
Equilibrium in SR
Profit maximization rule: MR=MC which determines Q*
Equilibrium in LR
Profits attract new firms which cause the demand curve to shift downward
Positive theories
Try to describe the world
Normative theories
Are used to prescribe policies for both governments and businesses
Microeconomics
The branch of economics that studies the behavior of individuals such as consumers workers and firms
Macroeconomics
Concentrates on the study of economic aggregates such as the gross national product the unemployment rate and the money supply
Market
A virtual place (sometimes physical) where there are trades.
Perfectly competitive market
a market with many buyers and sellers in which no individual buyer or seller has a significant impact on the price
Market price
The single price that will usually prevail in competitive markets
Noncompetitive market
a market in which individual firms can affect the market price. sellers may sometimes charge different prices
Nominal prices
The raw or observed price data with no adjustments for inflation. sometimes called current dollar prices
Real prices
Prices that are adjusted according to an index of the overall Level of prices. They are sometimes called "constant dollar" prices because the price index attempts to hold constant the value of the dollar overt…
Positive analysis
Deals with explanation and prediction
Normative analysis
Deals with what ought to be
Positive versus normative analysis: which comes first
Positive analysis must come before normative analysis
Limits of microeconomics
Can only point out the costs and benefits of the potential action or actions; it cannot tell us what the best policy is. That is up to each person or society to decide.
inflation
Real interest rate r accounts for the _______ effect.
Constant dollars
Real terms
[new-original]/original
Percentage change formula
Real price formula
[CPIoriginal/CPInew]*nominal price new