Compute the expected return $\mu_V$ and standard deviation $\sigma_V$ of a portfolio consisting of three securities with weights $\omega_1=40\%$, $\omega_2=-20\%$, $\omega_3=80\%$, given that the securities have expected reuturns $\mu_1=8\%$, $\mu_2=10\%$, $\mu_3=6\%$, standard deviations $\sigma_1=0.15$, $\sigma_2=0.05$, $\sigma_3=0.12$, and correlations $\rho_{12}=0.3$, $\rho_{23}=0$, $\rho_{31}=-0.2$.

I know how to compute the expected return of the portfolio, I got $\mu_V=0.06$, but I don't know how to calculate the standard deviation of a portfolio? What is the formula I need to use given the information? Do I need to find the variances given the standard deviations?

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    $\begingroup$ @BobJansen So this is basic? $\endgroup$ – BCLC Feb 23 '16 at 18:39

You can calculate variance of a portfolio/basket by taking direct weighed averages of the components and then adding the relevant correlation terms * weights for each pair.

Can take sqrt of the expression obtained to have Standard deviation.

Exact formula for calculation goes like this :

(source: benetzkorn.com)

  • $\begingroup$ The site that had your image went down. Could you please find a way to replace the image? $\endgroup$ – Mithical Mar 8 '17 at 12:46

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