Compute the risk measured by the standard deviations $\sigma K_1, \sigma K_2, \sigma K_3$, does this have to do with weights?

Question

Compute the risk measured by the standard deviations $\sigma K_1, \sigma K_2, \sigma K_3$ for each of the investment projects, where the returns $K_1, K_2$, and $K_3$ depend on the market scenario:

$$ \begin{matrix} Scenario & Probability & Return K_1 & Return K_2 & Return K_3 \\ \omega_1 & 0.3 & 12\% & 11\% & 2\% \\ \omega_2 & 0.7 & 12\% & 15\% & 22\% \\ \end{matrix} $$

I am not sure what this question is asking me to do, I think it has something to do with weights?

Answer 1

This is very basic question. You just need to compute the standard deviation of three projects $K_1$, $K_2$ and $K_3$.

$$\text{Standard deviation}= \sqrt{E[(X-\mu)^2]}$$

For the first project $K_1$:

Expected return ($\mu_{K_1}$) = $.3*.12 + .7*.12 = .12$

Standard Deviation ($\sigma K_1$) = $\sqrt{.3*(.12-.12)^2+.7*(.12-.12)^2}=0 $

For the second project $K_2$:

Expected return ($\mu_{K_2}$) = $.3*.11 + .7*.15 = .138$

Standard Deviation ($\sigma K_1$) = $\sqrt{.3*(.11-.138)^2+.7*(.15-.138)^2}=0.018330=1.83\% $

You may follow the same procedure for the third project.