Question

Stock X has a 10.0% expected return, a beta coefficient of 0.9, and a 35% standard deviation of expected returns. Stock Y has a 12.0% expected return, a beta coefficient of 1.1, and a 25.0% standard deviation. The risk-free rate is 6%, and the market risk premium is 5%. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the questions below.

1. Calculate each stock's coefficient of variation. Round your answers to two decimal places. Do not round intermediate calculations.

   CV_x =

   CV_y =

2. Which stock is riskier for a diversified investor?

   1. For diversified investors the relevant risk is measured by beta. Therefore, the stock with the lower beta is more risky. Stock X has the lower beta so it is more risky than Stock Y.
   2. For diversified investors the relevant risk is measured by standard deviation of expected returns. Therefore, the stock with the lower standard deviation of expected returns is more risky. Stock Y has the lower standard deviation so it is more risky than Stock X.
   3. For diversified investors the relevant risk is measured by beta. Therefore, the stock with the higher beta is less risky. Stock Y has the higher beta so it is less risky than Stock X.
   4. For diversified investors the relevant risk is measured by beta. Therefore, the stock with the higher beta is more risky. Stock Y has the higher beta so it is more risky than Stock X.
   5. For diversified investors the relevant risk is measured by standard deviation of expected returns. Therefore, the stock with the higher standard deviation of expected returns is more risky. Stock X has the higher standard deviation so it is more risky than Stock Y.
   
   

3. Calculate each stock's required rate of return. Round your answers to two decimal places.

   r_x = %

   r_y = %

4. On the basis of the two stocks' expected and required returns, which stock would be more attractive to a diversified investor?

   _________Stock XStock Y

5. Calculate the required return of a portfolio that has $3,500 invested in Stock X and $2,500 invested in Stock Y. Do not round intermediate calculations. Round your answer to two decimal places.

   r_p = %

6. If the market risk premium increased to 6%, which of the two stocks would have the larger increase in its required return?

Answer 1

	Given,
	Stock	Expected return	Beta coefficient	Standard deviation
	X	10%	0.9	35%
	Y	12%	1.1	25%
	Risk free rate (Rf)	6%
	Market risk premium (Rm-Rf)	5%
a)	Coefficeient of variation= (SD/Expected return)*100
	CVx= (35/10)*100	350%
	Cvy= (25/12)*100	208.33%
b)	We know that for diversified invetor, firm specific risk i.e standard deviation is eliminated and investor only faces non-diversifiable risk or the market risk. As beta is measure of stock volatility in relation to market so a stock with high beta would be considered riskier. Going by this explaination we can conclude that option 1, 2, 3 and 5 are wrong. Correct answer: Option 4
c)	As per CAPM,
	Required rate of return= Rf+(Rm-Rf)*Beta
	Rx= 6+5*0.9= 10.50%
	Ry= 6+5*1.1= 11.50%
d)	Calculation of alpha
	Alpha= Expected return- Required return
	Alpha of Stock X= 10-10.50= -0.50
	Alpha of Stock Y= 12-11.50= 0.50
	Positive alpha indicates stock is underpriced whereas a negative alpha indicates the stock is overpriced
	Therefore, Stock Y would be more attractive to diversified investor as it is underpriced.
e)	Investment in X= $3500
	Investment in Y= $2500
	Total investment= $6000
	Weight of X= 3500/6000= 0.5833
	Weight of Y= 2500/6000= 0.4167
	Required return= Weighted average
	0.5833*10.50+0.4167*11.50
	10.92%
	Expected return= Weighted average
	0.5833*10+0.4167*12
	10.83%
f)	If the market risk premium increased to 6%, Stock Y would have larger increase in its required return as it has higher Beta in comparison to Stock X.