Instructions: $(1)$ Do not show the calculation process. Provide your final answers only. $(2)$ Use four decimal places for your calculations. Show your answers by rounding the calculation results to two decimal places if the answers are in dollars. For example, if your calculation results in $$100\mathrm{.}1265,$ show your answer as $$100\mathrm{.}13.$ If you need to show your answers as a percent, take four decimal places from your calculation and convert them into a percent. For example, if your calculation results in $0\mathrm{.}4567,$ show $45\mathrm{.}67\%,$ not $45\mathrm{.}7\%$ or $46\%.$ To set your Texas Instrument BA II PLUS calculator at $4$ decimal places, press $[2$ND$]$ FORMAT $4[$ENTER$].$ Please follow the instructions for homework assignments on the syllabus.

Questions

Use the following scenario for stocks X and Y to answer questions $17.$

$$

Bear Market

Normal Market

Bull Market

Probability

$0\mathrm{.}4$

$$

$0\mathrm{.}4$

$$

$0\mathrm{.}2$

$$

Stock X

$10\%$

$$

$10\%$

$$

$20\%$

$$

Stock Y

$20\%$

$$

$10\%$

$$

$-10\%$

$$

Additional information for your computational convenience:

$$ Variance of returns on stock X $=0\mathrm{.}0144$

$$ Expected return on stock Y $=10\%$

$$ Variance of returns on stock Y $=0\mathrm{.}0120$

$$ Standard deviation of returns on stock Y $=0\mathrm{.}1095$

$$ Covariance between the returns on stocks X and Y $=-0\mathrm{.}0120$

$1.$What is the expected return for stock X$?$

$2.($a$)$ What is the coefficient of variation $($CV$)$ for stock X$?($b$)$ Which stock is riskier based on the CVs$?$ Why? Justify your answer.

$3.$Compute the correlation coefficient between returns on stocks X and Y$.$

$4.$Identify the direction of interrelationship based on the correlation coefficient. $$

$5.$Based on the correlation coefficient, how strongly are the returns on the two stocks related? Choose one from below.

$$A$)$Very strongly positive

$$B$)$Very weakly positive

$$C$)$Very strongly negative$$

$$D$)$Ver weakly negative

$$E$)$You cannot tell the strength of interrelationship by the correlation coefficient.

$6.$Assume that of your $$10,000$ portfolio, you invest $$4,000$ in stock X and $$6,000$ in stock Y$.$ What is the expected rate of return on your portfolio?

$7.$What is the standard deviation of returns on your portfolio? $$

Use the following information to answer questions $810.$

Assume that as a professional portfolio manager, you manage a risky portfolio with an expected rate of return of $11\mathrm{.}5\%$ and a standard deviation of $20\%.$ The T$-$bill rate is $5\%.$ Suppose your client prefers to invest in your portfolio a proportion $($y$)$ that maximizes the expected return on the complete portfolio subject to the constraint that the complete portfolio$$s standard deviation will not exceed $12\%.$

$8.$What is the investment proportion y$?$

$9.$What is the expected rate of return on the complete portfolio? $$

$10.$ What is the Sharpe ratio of your client$$s overall portfolio? $$