Portfolio P consists of two stocks, with $50\%$ invested in Stock A and $50\%$ in Stock B$.$ Stock A has a standard deviation of $30\%$ and a beta of $0\mathrm{.}9,$ and Stock B has a standard

deviation of $20\%$ and a beta of $1\mathrm{.}1.$ The correlation between these stocks is $0\mathrm{.}4.$

a$.$ What is the standard deviation of Portfolio P$?$

b$.$ What is the beta of Portfolio P$?$

c$.$ Which stock is riskier to a diversified investor?

An investor has a two$-$stock portfolio with $$30,000$ invested in Stock $x$ and $$45,000$ invested in Stock Y$.$ X$\text{'}$s beta is $0\mathrm{.}50,$ and Y$\text{'}$s beta is $1\mathrm{.}40.$ What is the beta of the investor's

portfolio?

The risk$-$free rate is $4\%,$ and the market risk premium $(r_m-r_{RF})$ is $5\%.$ Stock A has a beta of $1\mathrm{.}3,$ and Stock $B$ has a beta of $0\mathrm{.}7.$

a$.$ What is the required rate of return on each stock?

b$.$ Assuming the investors become less willing to take on risk $($become risk averse$),$ the market price premium rises from $5\%$ to $7\%.$ Assume the risk$-$free rate remains

constant. What effect will this have on the required rates of return on the two stocks?

CAPM, PORTFOLIO RISK, AND RETURNConsider the following information for Stocks A$,$ B$,$ and C$.$ The returns on the three stocks are positively correlated but not perfectly

correlated. $($That is$,$ each correlation coefficient is between $0$ and $1.)$

Fund $G$ has one$-$third of its funds invested in the three stocks. The risk$-$free rate is $5\mathrm{.}5\%,$ and the market is in equilibrium. $($That is$,$ required returns equal expected returns.$)$

a$.$ What is the market risk premium $(r_M-r_{RF})?$

b$.$ What is the beta of Fund G$?$

c$.$ What is the required return of Fund G$?$

d$.$ Would you expect the standard deviation of Fund G to be less than $15\%,$ equal to $15\%,$ or greater than $15\%?$ Explain.