fin9 - Factor Models and the Arbitrage Pricing Theory Econ...

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Econ 333 Spring 08 1 Factor Models and the Arbitrage Pricing Theory
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Econ 333 Spring 08 2 Factor Models and the Arbitrage Pricing Theory Our goals: Be able to decompose the variance of an asset into market-related and non market-related components. i.e. common and firm-specific components. Understand why variance decomposition is important for valuing financial assets. Identify the expected return, factor betas, factors, and firm-specific components of an asset from its factor equation. Explain how the principle of diversification relates to firm-specific risk. Be able to compute the factor betas for a portfolio given the factor betas of its component securities. Be able to design a portfolio with a specific configuration of factor betas in order to design portfolios that perfectly hedge an investment’s endowment of factor risk. Make sense of the arbitrage pricing theory (APT) equation.
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Econ 333 Spring 08 3 Factor Models and the Arbitrage Pricing Theory Factor models : Equations specifying that the return of each risky investment is determined by: 1. A relatively small number of common factors (typically proxies for those events in the economy that affect a large number of different investments). 2. A risk component that is unique to the investment or to the firm. In many applications it is possible to ignore firm-specific risks for portfolios of large numbers of assets. The sensitivities of an investment’s return to common factors differ from investment to investment (just like in the CAPM the betas vary from asset to asset): these are factor betas or factor sensitivities . Since there are many common factors and since each investment is affected differently, returns may not be that correlated. In addition to describe how expected changes in various macroeconomic variables affect an investment’s return, factor models also can be used to provide estimates of the expected rate of return of an investment. The APT is applied the same way as the CAPM. The hope is that with APT factors, additional aspects of risk beyond market risk can be taken into account.
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Econ 333 Spring 08 4 A simple factor model and variance decomposition Consider the following Is the uncertain / risky return of asset i Is the uncertain / risky return on the market (tangent) portfolio The residual term is some random extra payoff that can be positive or negative, so that on average it is 0. It is said to be firm or asset-specific (fire in a plant, management,…). Let simplify the analysis by assuming that rf = 0. Then the first equation states that the
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This note was uploaded on 04/01/2008 for the course ECON 3330 taught by Professor Mbiekop during the Spring '08 term at Cornell University (Engineering School).

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fin9 - Factor Models and the Arbitrage Pricing Theory Econ...

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