what is the arbitrage pricing theory apt 
arbitrage pricing theory apt is a multi factor asset pricing model it s based on the idea that an asset s returns can be predicted using the linear relationship between the asset s expected return and a number of macroeconomic variables that capture systematic risk it is a useful tool for analyzing portfolios from a value investing perspective in order to identify securities that may be temporarily mispriced the formula for the arbitrage pricing theory model ise r i e r z e i e r z nwhere e r i expected return on the assetrz risk free rate of return n sensitivity of the asset price to macroeconomicfactor nei risk premium associated with factor i begin aligned text e r text i e r z e i e r z times beta n textbf where text e r text i text expected return on the asset r z text risk free rate of return beta n text sensitivity of the asset price to macroeconomic text factor textit n ei text risk premium associated with factor textit i end aligned e r i e r z e i e r z n where e r i expected return on the assetrz risk free rate of return n sensitivity of the asset price to macroeconomicfactor nei risk premium associated with factor i the beta coefficients in the apt model are estimated by using linear regression in general historical securities returns are regressed on the factor to estimate its beta 