Arbitrage pricing theory Flashcards
What is arbitrage pricing theory
Developed by Ross 1976
predicts a return using the relationship between an expected return and macroeconomic factors.
Saw expected return in equilibrium as a linear function of a set of factors capturing systemtic risk, has multi priced factors and the identification of risk factors are not identified. The multi factor model can be used to explain either an individual security or a portfolio
Assumptions
Capital markets are perfectly competitive
Investors always prefer more wealth to less wealth with certainty
The process generating asset returns can be expressed as a linear set of K factors
What doesn’t it assume
Normally distributed security returns
Quadratic utility function
A mean-variance efficient market portfolio
Formula
E(ri) = rf + βi1 * RP1 + βi2 * RP2 + … + βkn * RPn,
What does it state
APT states that the expected risk premium on an asset i depends on the expected risk premium associated with each factor and the stock’s sensitivity to each of the factors.
APT contends there are many factors that are expected to impact the returns to all assets such as inflation, GDP growth, political events or a change in interest rates
The sign in the equation next to beta determines how each asset reacts to the jth common factor, the impact reaction to a factor will differ between assets
Harding / Cho / Chen reading
The likes of Harding (2008) have showed connections between systematic and unsystematic risk and APT factors are the systematic risk that cannot be reduced by the diversification of an investment portfolio
Cho et al 1984 when studying APT model found that multiple factors are required to explain returns
Conversely, Chen (1983) compared the APT model to the CAPM using 180 stocks and 5 factors. He concluded that the CAPM was misspecified and that the missing price information was picked up by the APT.
What does it assume
APT assumes markets sometimes misprice securities, before the market eventually corrects and securities move back to fair value. Using APT, arbitrageurs hope to take advantage of any deviations from fair market value.
Limitations
However, this is not a risk-free operation in the classic sense of arbitrage, because investors are assuming that the model is correct and making directional trades—rather than locking in risk-free profits.
The main limitation of APT is that the theory does not suggest factors for a particular stock or asset. One stock could be more sensitive to one factor than another, and investors must be able to see the risk sources and sensitivities.
Also it is a far more complex theory that CAPM due to the multiple factors.
