Suppose there are $n$ assets which are uncorrelated. (They might be $n$ different "wild cat" oil well prospects.) You may invest in any one, or in any combination of them. The mean rate of return $\bar{r}$ is the same for each asset, but the variances are different. The return on asset $i$ has a variance of $\sigma_{i}^{2}$ for $i=1,2, \ldots, n$.

(a) Show the situation on an $\bar{r}-\sigma$ diagram. Describe the efficient set.

(b) Find the minimum-variance point. Express your result in terms of

\[\bar{\sigma}^{2}=\left(\sum_{i=1}^{n} \frac{1}{\sigma_{i}^{2}}\right)^{-1}\]