Consider an economy with $3$ securities: A$,$ B$,$ C and one risk$-$free asset. The

composition of the tangency portfolio is $w^A=20\%,w^B=50\%$ and $w^C=30\%.$ The

correlation between each pair of securities is zero. The expected return of the

tangency portfolio is $12\%$ and its standard deviation is $16\%.$ The risk$-$free interest rate

is $4\%.$

What is the composition and the expected rate of return of an efficient portfolio

with standard deviation $20\%?$

Consider a portfolio with expected rate of return $3\%$ and standard deviation $8\%.$ Is

it efficient? Explain.

Consider a portfolio that contains security A$,$ security B and the risk$-$free asset but

not security $C.$ Is such a portfolio efficient? Explain.

What is the standard deviation of security $A$ if its expected rate of return is $15\%?$