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Let's assume that vector $(R_1, R_2, R_3)$ has multivariate normal distribution $N(\mu, \Sigma)$ where $\mu = (2, 6, 4)$ and

$$\Sigma^{-1} = \begin{bmatrix} 2 & 2 & 2\\ 2 & 4 & 4 \\ 2 & 4 & 8 \end{bmatrix}$$

risk free rate equals to 0.5. I want to calculate expected value of return of portfolio with weigths $\hat{w} = (\frac 1 4, \frac 1 4, \frac 1 4, \frac 1 4)$ using CAPM model.

I'm reading the theory behind CAPM model, but I have no idea how it can be used to calculate expected value of this portfolio. Could you please give me a small hint in which direction should I follow?

Could you please also explain to me why it's not as usually calculated as: $$\mu_w = w_1\mu_1 + w_2\mu_2+w_3\mu_3+w_4\mu_4 =$$

$$ = \frac{1}{4} \cdot 0.5 + \frac {1}{4} \cdot 2 + \frac 1 4 \cdot 6 + \frac 1 4 \cdot 4$$ ?

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