I want to solve the following problem as an exercise to test my understanding of the capm material:

Assume that CAPM is valid. The market portfolio consists of 3 stocks such that $i = A, B, C$ with respective weights $0.12$, $0.19$ and $0.69$. The stocks’ expected returns, $E(R_i)$ are $16.2$%, $24.6$% and $22.8$%, while the market portfolio’s standard deviation $\sigma_m = 15.2$% and $r_f = 4$%. We are also given $\sigma_{A, B} = 187$, $\sigma_{A, C} = 145$, $\sigma_{B, C} = 104$.


(i) Estimate the $\beta$ for all stocks. (ii) Calculate the variances $\sigma^{2}_{A}$, $\sigma^{2}_{B}$ and $\sigma^{2}_{C}$.

For (i) I used the formula expected return = risk free rate + $\beta \cdot$ market return premium which for stock A would be $0.162 = 0.04 + 0.152 \cdot \beta \iff \beta = \frac{0.122}{0.152} = 0.8026$. However, I am not sure if I am doing this the correct way and whether the market return premium is the same as the market portfolio's standard deviation (highly probably not).

Any hints are appreciated. Also for solving (ii).


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