# APT Description: Page 430 CFAI Portfolio Concepts

Does anyone know what the book is doing in these step? I thought we would have substituted the two factors we just solved for into the 3rd equation but they’ve completly lost me on this step.

"Substituting this expression for the risk-free rate into the equation for E(Rk), we find, after simplication, that x1 = 0.04 - x2, Using x1 = 0.04 - x2, to eliminate x1, in the equation for E(Rj),

10 = Rf + 0.5x

Using x1, = 0.04 - x2 to eliminate x1, in the equation for E(Rj),

.058 = Rf - 0.2x"

Wait, what?

Aren’t they saying we substitue x1 (calculated above as .04 - x2) into 0.11 = Rf + 1.3x1 + 1.1? Where is .058 = Rf - 0.2x coming from?!

bump… someone brave enough to answer?

When you solved "λ1 "= .04 - λ2, you then substitute this for λ1 in the E(RL) equation as follows: .11 = Rf + 1.3(.04 - λ2) + 1.1λ2 .11 = Rf + 0.052 - 1.3λ2 + 1.1λ2 0.058 = Rf - 0.2λ2 Rf = 0.058 + 0.2λ2

thanks! I should have just revisited this example with fresher eyes.