An analyst has modeled the stock of Crisp Trucking using a two-factor APT model. The risk free rate of return is %, the expected return rate on the first factor (r1) is 12%, and the expected return on the second factor (r2)is 8%. If bi1=0.7, and bi2= 0.9, what is Crisp’s required return?

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An analyst has modeled the stock of Crisp Trucking using a two-factor APT model. The risk free rate of return is %, the expected return rate on the first factor (r1) is 12%, and the expected return on the second factor (r2)is 8%. If bi1=0.7, and bi2= 0.9, what is Crisp’s required return?

The Arbitrage Pricing Theory (APT) suggests that an asset’s required return can be determined by considering several factors such as macroeconomic variables, interest rates, and other market indices. In this case we have two factors: r1 with a weighting of 0.7 and r2 with a weighting of 0.9.

Therefore to calculate Crisp’s required rate of return we need to consider both these weights in addition to their associated expected returns:

Required Return = Risk Free Rate + Beta 1 x (Expected Return – Risk Free Rate) + Beta 2 x (Expected Return – Risk Free Rate)

Substituting our values into this equation gives us:

Required Return = % + 0.7 x (12% – % )+ 0.9 x (8% – % )

Which simplifies to:

Required Return = 10%