# Today’s Finance 4335 Class Problem hints…

As promised, the Finance 4335 class problem set and solutions for problems 1-3 on that problem set are linked here:

I strongly encourage everyone to try tackling problems 4-5 prior to Thursday’s class meeting of Finance 4335.  Problem 4 involves finding the expected return and standard deviation for an equally weighted portfolio, whereas problem 5 involves finding the expected return and standard deviation for the least risky combination of assets and b.  The expected return and variance for these portfolios are:

Expected portfolio return: $E({r_p}) = {w_a}E({r_a}) + {w_b}E({r_b})$

Variance of portfolio return: $\sigma _p^2 = w_a^2\sigma _a^2 + w_b^2\sigma _b^2 + 2{w_a}{w_b}{\sigma _{ab}}$

In problem 4, equal weighting implies that ${w_a} = {w_b} = .5$. whereas in problem 5, the least risky combination of assets and can be determined by differentiating the variance equation above with respect to $w_a$, setting the resulting equation to 0, and solving for $w_a$ (see p. 17 of today’s lecture note for the math details); thus the lowest variance combination of assets and can be determined by setting ${w_a} = \displaystyle\frac{{\sigma _b^2 - {\sigma _{ab}}}}{{\sigma _a^2 + \sigma _b^2 - 2{\sigma _{ab}}}}$ and ${w_b} = 1 - {w_a}.$