Consider an economy with two assets, A and B$.$ The expected return vector is $=([0\mathrm{.}08],[0\mathrm{.}03]).$

The agents in the economy are not short$-$selling constrained.

a$)$ We consider a portfolio with fixed portfolio weights. For ${}_{A,B}=1,$ we get ${}_{PF}=0\mathrm{.}28.$

For ${}_{A,B}=-1,$ we get ${}_{PF}=0\mathrm{.}20.$ Determine the correlation coefficient ${}_{A,B},$ which leads

to ${}_{PF}=0\mathrm{.}24$

Additionally, we know ${}_A=0\mathrm{.}1$ and ${}_B=0\mathrm{.}4.$

b$).$ Determine the portfolio weights in the portfolio in a$).$

Independent of your results in a$)$ let the assets A and B be uncorrelated.

c$)$ Determine the maximum expected return ${}_{\text{m}\text{a}\text{x}}$ and the minimum expected return ${}_{\text{m}\text{i}\text{n}}$

for a target volatility of $\frac{?}{\text{b}\text{a}\text{r}}()=0\mathrm{.}2.$

d$)$ Can we achieve all expected returns in the interval ${}_{\text{m}\text{i}\text{n}},{}_{\text{m}\text{a}\text{x}}.$ If yes, show how. If no$,$

provide a counterexample.