Mixed portfolio Suppose that Ms Lynch can make up her portfolio using a risk-free asset that offers a surefire rate of return of 15% and a risky asset with an expected rate of return of 25% with standard deviation 5. If she chooses a portfolio with an expected rate of return of 20% then the standard deviation of her return on this portfolio will be: a)2.5% b)5% c)5.5% d)1.25% e)None of the above Calculations should be very simple, but i have no idea how to solve this question.

You have two random variables $X_1$ and $X_2$, which represent the returns of the risk-free asset and the risky asset, respectively. You're given this information: $$ \operatorname{E}(X_1) = 15,\ \operatorname{E}(X_2) = 25,\ \operatorname{Var}(X_1) = 0,\ \operatorname{Var}(X_2) = 25. $$

Your job is to find a linear combination $X = c_1X_1 + c_2X_2$ of assets with mean $\operatorname{E}(x) = 20$ and then compute its variance. So first, you need to find the $c_i$s (that's just a little bit of algebra). Then you need to either look up or derive[1] the formula for the variance of a linear combination of random variables (it involves the covariance matrix) and then use what you know about $X_1$ and $X_2$.

[1] From $\operatorname{Var}(X) = \operatorname{E}(X^2) - \operatorname{E}(X)^2$