Question

Excel Online Structured Activity: Evaluating risk and return

Stock X has a 9.5% expected return, a beta coefficient of 0.8, and a 30% standard deviation of expected returns. Stock Y has a 12.0% expected return, a beta coefficient of 1.1, and a 30.0% 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.

Evaluating risk and return
Expected return of Stock X	9.50%
Beta coefficient of Stock X	0.80
Standard deviation of Stock X returns	30.00%
Expected return of Stock Y	12.00%
Beta coefficient of Stock Y	1.10
Standard deviation of Stock Y returns	30.00%
Risk-free rate (rRF)	6.00%
Market risk premium (RPM)	5.00%
Dollars of Stock X in portfolio	$7,500.00
Dollars of Stock Y in portfolio	$5,500.00
			Formulas
Coefficient of Variation for Stock X			#N/A
Coefficient of Variation for Stock Y			#N/A
Riskier stock to a diviersified investor			#N/A
Required return for Stock X			#N/A
Required return for Stock Y			#N/A
Stock more attractive to a diversified investor			#N/A
"Required return of portfolio containing Stocks X and Y in amounts above"			#N/A
New market risk premium	6.00%
With new market risk premium, stock with larger increase in required return			#N/A
Check:
New required return, Stock X			#N/A
Change in required return, Stock X			#N/A
New required return, Stock Y			#N/A
Change in required return, Stock Y			#N/A
Stock with greater change in required return			#N/A

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 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.
   2. 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.
   3. 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.
   4. 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.
   5. 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.
   
   _____IIIIIIIVV

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 $7,500 invested in Stock X and $5,500 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?

   _________Stock XStock Y

Answer 1

Answer

a) CVx = 0.0316 or 3.16%

      CVy = 0.025 or 2.50%

Particulars	Standard Deviation	Expected Return	Coefficient Of Variation
	a	b	a/b
Stock X	30%	9.5%	3.16%
Stock Y	30%	12%	2.5%

b) Statement I,II,III,IV are incorrect only Statement V is Correct.

I. The statement is incorrect as both the stocks have same standard deviation both the stocks are equally risky in terms of standard deviation.

II. The statement is incorrect . Stock with higher Beta is more volatile hence riskier as compared to stock with low beta . Thus stock X is less riskier than stock Y .

III. The statement is incorrect as stock with higher standard deviation is riskier than stock stock with lower standard deviation. As both the stocks have same standard deviation both the stocks are equally risky in terms of standard deviation.

IV. The statement is incorrect Stock with higher Beta is more volatile hence riskier as compared to stock with low beta . Stock Y is more risky as compared to stock X.

V. The statement is Correct Stock with higher Beta is more volatile hence riskier as compared to stock with low beta . Stock Y is more risky as compared to stock X.

c) Required Rate of Return.

Re = Rf +(Rm-Rf)B

rX = 6 + (5)0.80 = 10%

rY = 6 + (5)1.1 = 11.5 %

d)

Expected Return of Stock X is 9.5% where as investor requires 10% therefore as there is a short return of 0.5% stock X is less attractive

Expected Return of Stock Y is 12% where as investor requires 11.5% therefore as there is a excess return of 0.5% stock Y is more attractive

e)There are two answers for this question. Alternate Solution 1 is more logical however in few publications Alternate solution 2 is used.

Answer (workings given below)

Required Rate of Return in Alternate Solution 1 = 10.85%

Required Rate of Return in Alternate Solution 2 = 10.94%

Alternate Solution 1 :

i) Computation of Weights of Stock in Portfolio.

Weight of Stock X = 5500 / (5500 + 7500) = 0.4231

Weight of Stock Y = 7500 (5500+ 7500) = 0.5769

ii) Computation of Portfolio Beta

Particulars	Weight	Beta	Weighted Average Beta
	A	b	a*b
Stock X	0.4231	0.8	0.34
Stock Y	0.5769	1.1	0.63
Total			0.97

iii) Required Return = Rf + (Rm-Rf)Beta

                                     = 6 + 5(0.97)

                                    = 10.85%

Alternate Solution 2 :

i) Computation of Weights of Stock in Portfolio.

Weight of Stock X = 5500 / (5500 + 7500) = 0.4231

Weight of Stock Y = 7500 (5500+ 7500) = 0.5769

Particulars	Weight	Expected Return	Weighted Average Beta
	a	B	a*b
Stock X	0.4231	9.5	4.02
Stock Y	0.5769	12	6.92
Total			10.94

f)

If market risk Premium increases to 6 % then

Re = Rf +(Rm-Rf)B

rX = 6 + (6)0.80 = 10.8%

rY = 6 + (6)1.1 = 12.6 %

Required rate of Return of Stock X has increased from 10% to 10.8% i.e by 0.8 %

Whereas of Stock Y has increased from 11.5% to 12.6% i.e. by 1.1%

As stock Y has higher Beta it will have larger increase in its required return.