$1.$ Calculate the expected return, variance, covariance and correlation coefficient of the following two stocks.

State of the world Good Bad Very Bad

Probability $/0\mathrm{.}7/0\mathrm{.}2/$

Return on stock A $/12\%/4\%/-1\%$

Return on stock B $6\%/8\%/4\%$

$2.$ What would be the variance and standard deviation of a portfolio consisting of only stocks A and B $($as described in question $1),$ when the expected return of the portfolio is $7\%?$

$3.$ A stock with an expected return of $9\%$ has a $$ of $1\mathrm{.}75$ if the risk free rate of return is $3\%$ and the return on the market portfolio is $\_\_\_?($And the CAPM holds.$)$

$4.$

a$.$ What is the variance of nominal returns on a risk free asset such as a treasury bill? Explain.

b$.$ What is the covariance of nominal returns on a risk free asset such as a treasury bill with any risky asset? Explain.

c$.$ Given your answers to a$.$ and b$.,$ what is the expected return, the variance and the standard deviation of a portfolio which consists of treasury bills and shares of stock in ABC Inc. The expected return on ABC Inc. is $13\%,$ the risk free rate of return is $3\mathrm{.}5\%$ and the variance of returns on ABC Inc. has been $0\mathrm{.}36.$ This portfolio is worth $$900,$ $$150$ of which is invested in treasury bills.

i$.$ What are the portfolio weights?

ii$.$ What is the equation for the expected return on a portfolio, when you know the portfolios weights and the expected returns on the component assets?

iii. What is the equation for the expected variance of a portfolio when you know the portfolio weights, the standard deviations and the covariance of the component assets?

iv$.$ Expected return on this portfolio$\_\_\_\_\_\_\_\_\_\_\_\_\_.$

v$.$ Expected variance of this portfolio$\_\_\_\_\_\_\_\_\_\_\_\_.$

vi$.$ Expected standard deviation of this portfolio$\_\_\_\_\_\_\_\_\_\_\_.$

Show your work.