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

#### 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