Question

Problem 6-14
Historical Returns: Expected and Required Rates of Return

You have observed the following returns over time:

6. Problem 6-14 eBook Problem 6-14 Historical Returns: Expected and Required Rates of Return You have observed the following returns over time: Year Market Stock X 14% 21 -14 Stock Y 2012 2013 2014 2015 2016 12% 12% -14 2 15 -4 23 10 Assume that the risk-free rate is 3% and the market risk premium is 6%. Do not round intermediate calculations a. What is the beta of Stock X? Round your answer to two decimal places b. What is the beta of Stock Y? Round your answer to two decimal places c. What is the required rate of return on Stock X? Round your answer to one decimal place d. What is the required rate of return on Stock Y? Round your answer to one decimal place e, what is the required rate of return on a portfolio consisting of 80% of Stock X and 20% of Stock Y? Round your answer to one decimal place

Answer 1

(a) and (b)

Stock Y Market Stock X Year 12 12 2012 2013 2014 2015 2016 14 21 14 14 4 7 Mean Return 8 Standard Deviation 9 Covariance with Market 10 Beta 23 9.4 13.63 133.36 1.26 10 4.8 5.84 56.32 0.53 15 4.6 10.27

Year Stock X Stock Y Market 2 2012 3 2013 4 2014 5 2015 6 2016 7 Mean Return 14 12 12 21 14 14 10 15 -SUM(D2:D6)/5 23 -SUM(B2:B6)/5 8 Standard Deviation 9 Co ia ith Market 10 Beta :((((B2-B7)べ2)HIB 3-57시2)-(B4-B7)시 2)HIB5-B7)시 2)HIB6-87)시 2)))/5)시 1,2) ((B2-87) (D207 -(B9/(SDS8)시 2)) dll(C2-C7)시2)HIC B6-7)(D6-07))/5-(C2C7) (D2D7) 2) C4-C7) (0407) 2)HIC C5C7) (D5D가 2/51 C6 (B3B7) D3D7 B4B7) (0407) BS-B7) (D5-07 C3C7) (D307 7) D D7)/5 IC9/ISDS8)(2))

(c) Risk-Free Rate = Rf = 3 % and Market Risk Premium (MRP) = 6 %

Expected Return = Rf + Beta of X x MRP = 3 + 1.26 x 6 = 10.56 %

(d) Risk-Free Rate = Rf = 3 % and Market Risk Premium (MRP) = 6 %

Expected Return = Rf + Beta of Y x MRP = 3 + 0.53 x 6 = 6.18 %

(e) Portfolio Weight of X = 80 % or 0.8 and Portfolio Weight of Y = 20 % or 0.2

Required Return on Portfolio = 0.8 x 10.56 + 0.2 x 6.18 = 9.684 %