Arbitrage Pricing Theory
ARBITRAGE PRICING THEORY ( APT ) Originally developed by Stephen A. Ross.
The CAPM predicts that security rates of return will be linearly related to a single common factor : ----- the rate of return on the market portfolio. The APT is based on a similar approach but assumes the rate of return on a security to be sensitive to a number of factors.
Market equilibrium is driven by individuals eliminating arbitrage profits across the many factors.
Suppose the actual return on a security can be explained as follows :
Rj = a + b1j F1 + b2j F2 + ej
Where : a = the return when all factors are at zero value. Fn = the value (uncertain) of factor . bnj = the reaction coefficient depicting the change in the security’s return to a one unit change in the factor. ej = an error term ( security specific – unsystematic.)
The expected return on a security would be :
(E) Rj = λ0 + λ1 b1j + λ2 b2j + ……. λ n bnj
Where: λ0 = corresponds to the return on a risk free asset. λ1, λ2 = these represent risk premiums for the type of risk associated with particular factors, e.g. λ1 is the excess return above the risk free rate. Note these risk premiums can also be negative, representing a reduction in risk when the factor is beneficial. bnj = the reaction coefficients.
1. According to APT two securities with the same reaction coefficients ( the ‘ b’ ) should provide the same expected return. This is on the assumption of a perfectly competitive market where the assets are deemed to be riskless.
In equilibrium all portfolios that can be
The CAPM predicts that security rates of return will be linearly related to a single common factor : ----- the rate of return on the market portfolio. The APT is based on a similar approach but assumes the rate of return on a security to be sensitive to a number of factors.
Market equilibrium is driven by individuals eliminating arbitrage profits across the many factors.
Suppose the actual return on a security can be explained as follows :
Rj = a + b1j F1 + b2j F2 + ej
Where : a = the return when all factors are at zero value. Fn = the value (uncertain) of factor . bnj = the reaction coefficient depicting the change in the security’s return to a one unit change in the factor. ej = an error term ( security specific – unsystematic.)
The expected return on a security would be :
(E) Rj = λ0 + λ1 b1j + λ2 b2j + ……. λ n bnj
Where: λ0 = corresponds to the return on a risk free asset. λ1, λ2 = these represent risk premiums for the type of risk associated with particular factors, e.g. λ1 is the excess return above the risk free rate. Note these risk premiums can also be negative, representing a reduction in risk when the factor is beneficial. bnj = the reaction coefficients.
1. According to APT two securities with the same reaction coefficients ( the ‘ b’ ) should provide the same expected return. This is on the assumption of a perfectly competitive market where the assets are deemed to be riskless.
In equilibrium all portfolios that can be