Question

You believe that the percent change in the 10-year UST note rate, the spread between BBB and AAA bond rates and return on the S&P 500 are the factors in the APT. What is the equation for the expected return for an arbitrary stock j?

Answer 1

Arbitrage pricing theory (APT) is a multi-factor asset pricing model 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. (source - Investopedia )

The following three factors have been identified as explaining a stock's return and its sensitivity to each factor and the risk premium associated with each factor ;-

Risk free rate =Rf

Beta 1 = Sensitivity of stock w.r.t percentage change in US note Rate

Beta 2 = Sensitivity of stock w.r.t the spread between BBB and AAA bond rates

Beta 3 = Sensitivity of stock w.r.t return on the S&P 500

Equation = Rf + Beta1 * (percentage change in US note Rate) + Beta 2 * (the spread between BBB and AAA bond rates) + Beta 3 *( return on the S&P 500)