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Diversifiable risk The standard deviation of portfolio A is 8%, the covariance between A and the market portfolio is 0.008, and the standard deviation of the market portfolio is 6%. Find the diversifiable risk of P. I have tried using the single index model, but am unsure which part of the model is diversifiable risk.

$\beta = \frac{0.008}{(0.06)^2} = 2.222$

Unsystematic risk of a portfolio can be calculated as follows:

$$\sigma_\lambda-\rho_{\lambda,m}\sigma_\lambda=\sigma_\lambda(1-\rho_{\lambda,m})$$

where $\sigma_\lambda$ is the volatility of the stock $\lambda$ and $\rho_{\lambda,m}$ is the correlation between this portfolio and the market.

Written differently this is the same as:

$$\sigma_\lambda-\beta_\lambda\sigma_m$$

which means that the unsystematic risk of a portfolio is its volatility minus its beta scaled by the market volatility.

Diversifiable Risk (Unsystematic Risk)$ = Max(0.08 - 2.22*.06,0) = 0 $

If covariance were to be $0.0008$, then $\beta = 0.222$ and subsequently

Diversifiable Risk $= 0.08-.222*.06 = 0.0667$

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