# Elton Question 13.1,Video,Apply the CAPM in calculating the expected return on an asset-

#### Branislav

##### Member
Subscriber
Dear David,
Sorry if missed something, but why do you think that RF should be stated in the question? It could be derived from the equations?
Maybe irrelevant but I am afraid I am missing something methodologically important.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @Branislav That's is Elton's Question 13.1 and, you are correct, they do not provide the riskfree rate. It is not necessary: we have two equations and we can solve for two variables, in this case, we can solve for both the market risk premium (MRP) and the risk-free rate. I'm not sure why I included the risk-free rate, but you do appear to be correct, I don't think you are missing anything!

#### JamesVU2000

##### Member
A stock has a beta of 0.75 and an expected return of 13%. The risk-free rate is 4%. Calculate the market
risk premium and the expected return on the market portfolio.
According to CAPM: 0.13 = 0.04 + 0.75[E(RM) − RF].
Therefore, the market risk premium is equal to: [E(RM) − RF] = 0.12 = 12%.
The expected return on the market is calculated as: [E(RM) − 0.04] = 0.12, or E(RM) = 0.16 = 16%.

If anyone could help me with the algebra I would appreciate it. not urgent for David or Nicole to answer

#### Detective

##### Active Member
A stock has a beta of 0.75 and an expected return of 13%. The risk-free rate is 4%. Calculate the market
risk premium and the expected return on the market portfolio.
According to CAPM: 0.13 = 0.04 + 0.75[E(RM) − RF].
Therefore, the market risk premium is equal to: [E(RM) − RF] = 0.12 = 12%.
The expected return on the market is calculated as: [E(RM) − 0.04] = 0.12, or E(RM) = 0.16 = 16%.

If anyone could help me with the algebra I would appreciate it. not urgent for David or Nicole to answer

If you agree with CAPM...

ER_i = RF + BETA_i(E(RM) - RF))

Plugging in givens:

13% = 4% + 0.75(E(RM) - 4%)
(13% - 4%) = 0.75(E(RM) - 4%)
9% = 0.75(E(RM) - 4%)
9%/0.75 = E(RM) - 4%
12% = E(RM) - 4% --> Note: this is E(RM) - RF = Market Risk Premium
16% = E(RM)

The expected return on market portfolio is 16%, and risk premium is E(RM) - RF = 16% - 4% = 12%.

#### JamesVU2000

##### Member
thank you for the help

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