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$$s overall portfolio? $$