Rearranging the CAPM to solve for Beta... problem w/ algebra

CFA Level I
#1

Hi,

Having trouble algebraically rearranging formulas with letter terms, can you please show me the steps to get from

Er = rf + B * (rm - rf)

to

B = (Er - rf) / (rm - rf)

Thnx!

#2

The CAPM states E[r] = rf + Beta*(E[Rm]-rf)

1.Subtract both sides by rf to get : E[r]-rf=Beta*(E[Rm]-rf)

2.Divide left hand side by (E[Rm]-rf) to get : Beta = (E[r]-rf) / (E[Rm]-rf) = Excess Return / Market Risk Premium

If you are having trouble doing these manipulations, I urge you to consult some basic math books or websites because you will be needing them in other areas aswell in the CFA exams.

#3

This is really quite basic algebra, if you are struggling with this then I really think you are going to have trouble with the CFA program as a whole.

#4

Thanks for the answer Alladin and for the advice. I have taken out my old college algebra book and tried several online resources to brush up on my algebra. It’s just when it comes to rearranging equations with mainly letter terms that I have problems around the rules. I tried ten different ways of rearranging this equation but couldn’t come up with the answer you so simply gave. All I can do is keep trying… if you come accross some source I can use for practicing equations using only letter terms please forward.

Warm regards,

Rob

#5

Hey rob, apart from your old math books you could also make use of khanacademy. Sometimes it is easier to just listen and see how it is done and there is no better than khan!

http://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities

#6

Thanks Alladin that will be very helpful. I am happy to report that I am doing much better on rearanging formulas now that I’ve had some help!

Best,

Rob