Question

Consider the following information for three stocks, Stocks A, B, and C. The returns on the three stocks are positively correlated, but they are not perfectly correlated. (That is, each of the correlation coefficients is between 0 and 1.)

Stock	Expected Return		Standard Deviation		Beta
A	9.10	%	14	%	0.8
B	10.45		14		1.1
C	12.70		14		1.6

Fund P has one-third of its funds invested in each of the three stocks. The risk-free rate is 5.5%, and the market is in equilibrium. (That is, required returns equal expected returns.) The data has been collected in the Microsoft Excel Online file below.

1. What is the market risk premium (r_M - r_RF)? Round your answer to two decimal places.

   %

2. What is the beta of Fund P? Do not round intermediate calculations. Round your answer to two decimal places.

3. What is the required return of Fund P? Do not round intermediate calculations. Round your answer to two decimal places.

   %

4. Would you expect the standard deviation of Fund P to be less than 14%, equal to 14%, or greater than 14%?

   1. less than 14%
   2. greater than 14%
   3. equal to 14%

Risk-Free Rate, rRF	5.50%
	Stock A		Formula		Stock B		Formula		Stock C
Expected Return	9.10%				10.45%				12.70%
Standard Deviation	14.00%				14.00%				14.00%
Beta	0.80				1.10				1.60
Market Risk Premium, RPM			#N/A				#N/A
% Stock in Fund P	0.333333333				0.333333333				0.333333333
Beta of Fund P			#N/A
Required Return of Fund P			#N/A
Expected Return of Fund P			#N/A

Answer 1

As per CAPM, expected return = risk free rate + beta*market risk premium

Taking stock A

9.10%= 5.5% + 0.8*market risk premium

Market Risk Premium = 4.5%

Stock B

10.45% = 5.5% + 1.1*Market risk premium

Market Risk Premium = 4.5%

Stock C

12.70% = 5.5% + 1.6*Market Risk premium

Market Risk premium = 4.5%

b.Beta of fund P is equal to the weighted average beta

= 0.8*1/3 + 1.1*1/3 + 1.6*1/3

= 1.17 (approx.)

c.Required return on fund P = 5.5% + 1.17*4.5%

= 10.765%

d.The standard deviation of P would be less than 14%, because the returns of the 3 stocks are not perfectly correlated. Risk will be diversified in portfolio and standard deviation will be less than 14%