$1.$ Suppose there are two assets, Microsoft and Pepsi, with the following

properties. Microsoft has an expected return of $25\%$ and a standard deviation of

$50\%,$ while Pepsi has an expected return of $5\%$ and a standard deviation of $25\%.$

The correlation is $-0\mathrm{.}30.$

a$.$ Calculate the portfolio expected return and risk $($standard deviation$)$ for the

following portfolios:

a$.(0,1)$: $0\%$ invested in Microsoft and $100\%$ in Pepsi

b$.(0\mathrm{.}2,0\mathrm{.}8)$: $20\%$ invested in Microsoft and $80\%$ in Pepsi

c$.(0\mathrm{.}4,0\mathrm{.}6)$

d$.(0\mathrm{.}6,0\mathrm{.}4)$

e$.(0\mathrm{.}8,0\mathrm{.}2)$

f$.(1,0)$

b$.$ Draw a graph with the different portfolios, i$.$e$.$ their risk and return

combinations $($expected return on the y$-$axis and standard deviation on the

x$-$axis$).$ Which of the above portfolios are on the efficient frontier?

$2.$ Suppose there are two stocks, BMW and Toyota. BMW has a beta of $1\mathrm{.}5$ and a

standard deviation of its returns of $35\%,$ while Toyota has a beta of $0\mathrm{.}6$ and a

standard deviation of its returns of $20\%.$ The excess return of the market portfolio relative to the risk$-$free asset is $15\%$ and the risk$-$free rate is $5\%.$

a$.$ What is the expected return for the stocks?

b$.$ What are the expected return and standard deviation for portfolios that

are equally invested in the stocks and the risk$-$free asset?