Talk:Arbitrage pricing theory

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request for clarification

This is a very nice article, but I'm confused by the sentence that starts "If APT holds, ...". It sounds like an assumption of APT is that risky assests satisfy the equation $E\left(r_j\right)=r_f+b_{j1}R{P}_1+b_{j2}R{P}_2+...+b_{jn}R{P}_n{r}_j=E\left(r_j\right)+b_{j1}{F}_1+b_{j2}{F}_2+...+b_{jn}{F}_n+{ϵ}_j.$ Is this an assumption or a consequence of the theory? For example, does this linear relationship follow from an another assumption such as lognormality of returns or is it a fundamental assumption?

Thanks.

$E\left(r_j\right)=r_f+b_{j1}R{P}_1+b_{j2}R{P}_2+\cdots +b_{jn}R{M}_n$

$r_j=E\left(r_j\right)+b_{j1}{F}_1+b_{j2}{F}_2+\cdots +b_{jn}{F}_n+{ϵ}_j$

where

• $E(r_j)$ is the risky asset's expected return,
• $R{P}_k$ is the risk premium of the factor,
• $r_f$ is the risk-free rate,
• $F_k$ is the macroeconomic factor,
• $b_{jk}$ is the sensitivity of the asset to factor $k$, also called factor loading,
• and ${ϵ}_j$ is the risky asset's idiosyncratic random shock with mean zero.

This doesn't make sense. why does rj's equation include E(rj)? --165.230.46.142 19:45, 5 December 2006 (UTC)

Arbitrage in expectations

Hi All. I propose that the following be re-introduced. Thanks. Fintor (talk) 13:20, 8 March 2010 (UTC)

- The APT describes the mechanism of arbitrage whereby investors will bring an asset which is mispriced, according to the APT model, back into line with its expected price. Note that under true arbitrage, the investor locks-in a guaranteed payoff, whereas under APT arbitrage as described below, the investor locks-in a positive expected payoff. The APT thus assumes "arbitrage in expectations" - i.e. that arbitrage by investors will bring asset prices back into line with the returns expected by the model portfolio theory.

I take it that I can proceed ☺. Fintor (talk) 09:14, 11 March 2010 (UTC)

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