Question

Historical Returns: Expected and Required Rates of Return You have observed the following returns over time:...

Historical Returns: Expected and Required Rates of Return

You have observed the following returns over time:

Year Stock X Stock Y Market
2009 14% 15% 13%
2010 20 7 9
2011 -15 -8 -12
2012 4 2 2
2013 24 13 18

Assume that the risk-free rate is 4% and the market risk premium is 6%. Do not round intermediate calculations.

  1. What is the beta of Stock X? Round your answer to two decimal places.

  2. What is the beta of Stock Y? Round your answer to two decimal places.

  3. What is the required rate of return on Stock X? Round your answer to one decimal place.
    %
  4. What is the required rate of return on Stock Y? Round your answer to one decimal place.
    %
  5. 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.
    %

Homework Answers

Answer #1
Stock X
Year Year Stock Deviation=Return-Expected return Deviation^2
2009 1 14.00% 4.600% 0.212%
2010 2 20.00% 10.600% 1.124%
2011 3 -15.00% -24.400% 5.954%
2012 4 4.00% -5.400% 0.292%
2013 5 24.00% 14.600% 2.132%
Total 47.00% Total 9.712%
Expected return= 47%/5
So the expected return is 9.4%
Variance in return 9.712%/5
Variance in return 1.9424%
Standard deviation '1.9424%^(0.5)
Standard deviation 13.94%
Stock Y
Year Year Stock Deviation=Return-Expected return Deviation^2
2009 1 15.00% 9.200% 0.846%
2010 2 7.00% 1.200% 0.014%
2011 3 -8.00% -13.800% 1.904%
2012 4 2.00% -3.800% 0.144%
2013 5 13.00% 7.200% 0.518%
Total 29.00% Total 3.428%
Expected return= 29%/5
So the expected return is 5.8%
Variance in return 3.428%/5
Variance in return 0.6856%
Standard deviation '0.6856%^(0.5)
Standard deviation 8.28%
Market
Year Year Stock Deviation=Return-Expected return Deviation^2
2009 1 13.00% 7.000% 0.490%
2010 2 9.00% 3.000% 0.090%
2011 3 -12.00% -18.000% 3.240%
2012 4 2.00% -4.000% 0.160%
2013 5 18.00% 12.000% 1.440%
Total 30.00% Total 5.420%
Expected return= 30%/5
So the expected return is 6%
Variance in return 5.42%/5
Variance in return 1.0840%
Standard deviation '1.084%^(0.5)
Standard deviation 10.41%

Calculation of BETA

Beta Security= Co-variance with Market/Market Variance
Year Market deviation X deviation Market D * Stock X deviation Y deviation Market D * Stock Y deviation
2011 7.00% 4.60% 0.32% 9.20% 0.64%
2012 3.00% 10.60% 0.32% 1.20% 0.04%
2013 -18.00% -24.40% 4.39% -13.80% 2.48%
2014 -4.00% -5.40% 0.22% -3.80% 0.15%
2015 12.00% 14.60% 1.75% 7.20% 0.86%
Total 7.00% Total 4.18%
Stock X Stock Y
Co-variance with market= 7%/(5-1) 4.18%/(5-1)
Co-variance with market= 1.75% 1.05%
BETA= 1.75%/1.084% 1.05%/1.084%
BETA=                                                            1.61         0.97
Required return Risk-free rate + Beta * Market premium
Stock X Stock Y
Required return 4%+1.61*6% 4%+0.97*6%
Required return 13.66% 9.82%
Portfolio return
Stock X Stock Y Total
Required return 13.66% 9.82%
Weight 80% 20%
Required return*weight 10.92800% 1.96400% 12.89%
So required return on portfolio will be 12.89%
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Historical Returns: Expected and Required Rates of Return You have observed the following returns over time:...
Historical Returns: Expected and Required Rates of Return You have observed the following returns over time: Year Stock X Stock Y Market 2009 16% 14% 13% 2010 19 6 9 2011 -15 -2 -13 2012 2 1 1 2013 23 11 18 Assume that the risk-free rate is 3% and the market risk premium is 6%. Do not round intermediate calculations. What is the beta of Stock X? Round your answer to two decimal places. What is the beta of...
Historical Returns: Expected and Required Rates of Return You have observed the following returns over time:...
Historical Returns: Expected and Required Rates of Return You have observed the following returns over time: Year Stock X Stock Y Market 2011 15% 14% 10% 2012 19 6 12 2013 -17 -3 -12 2014 3 2 3 2015 19 12 17 Assume that the risk-free rate is 6% and the market risk premium is 6%. Do not round intermediate calculations. What is the beta of Stock X? Round your answer to two decimal places. What is the beta of...
Historical Returns: Expected and Required Rates of Return You have observed the following returns over time:...
Historical Returns: Expected and Required Rates of Return You have observed the following returns over time: Year Stock X Stock Y Market 2012 16% 15% 12% 2013 21 6 11 2014 -16 -6 -11 2015 3 3 1 2016 22 12 13 Assume that the risk-free rate is 4% and the market risk premium is 7%. Do not round intermediate calculations. What is the beta of Stock X? Round your answer to two decimal places. What is the beta of...
Problem 2-14 Historical Returns: Expected and Required Rates of Return You have observed the following returns...
Problem 2-14 Historical Returns: Expected and Required Rates of Return You have observed the following returns over time: Year Stock X Stock Y Market 2011 16% 12% 13% 2012 19 7 10 2013 -15 -2 -14 2014 4 1 1 2015 24 9 17 Assume that the risk-free rate is 4% and the market risk premium is 7%. Do not round intermediate calculations. What is the beta of Stock X? Round your answer to two decimal places.    What is...
Historical Returns: Expected and Required Rates of Return You have observed the following returns over time:...
Historical Returns: Expected and Required Rates of Return You have observed the following returns over time: Year Stock X Stock Y Market 2012 16% 12% 14% 2013 18 6 8 2014 -16 -4 -14 2015 5 2 3 2016 21 11 16 Assume that the risk-free rate is 6% and the market risk premium is 6%. Do not round intermediate calculations. What is the beta of Stock X? Round your answer to two decimal places. What is the beta of...
Historical Returns: Expected and Required Rates of Return You have observed the following returns over time:...
Historical Returns: Expected and Required Rates of Return You have observed the following returns over time: Year Stock X Stock Y Market 2012 16% 14% 14% 2013 21 7 11 2014 -14 -3 -10 2015 5 2 1 2016 21 9 17 Assume that the risk-free rate is 3% and the market risk premium is 6%. Do not round intermediate calculations. What is the beta of Stock X? Round your answer to two decimal places. What is the beta of...
Problem 6-14 Historical Returns: Expected and Required Rates of Return You have observed the following returns...
Problem 6-14 Historical Returns: Expected and Required Rates of Return You have observed the following returns over time: Year Stock X Stock Y Market 2012 15% 12% 12% 2013 18 8 9 2014 -14 -3 -14 2015 4 1 1 2016 20 12 18 Assume that the risk-free rate is 3% and the market risk premium is 7%. Do not round intermediate calculations. What is the beta of Stock X? Round your answer to two decimal places. What is the...
eBook Problem 6-14 Historical Returns: Expected and Required Rates of Return You have observed the following...
eBook Problem 6-14 Historical Returns: Expected and Required Rates of Return You have observed the following returns over time: Year Stock X Stock Y Market 2012 14% 11% 11% 2013 17 7 11 2014 -13 -2 -11 2015 4 2 1 2016 21 8 15 Assume that the risk-free rate is 3% and the market risk premium is 6%. Do not round intermediate calculations. What is the beta of Stock X? Round your answer to two decimal places. What is...
Required Rate of Return Stock R has a beta of 1.9, Stock S has a beta...
Required Rate of Return Stock R has a beta of 1.9, Stock S has a beta of 0.65, the expected rate of return on an average stock is 12%, and the risk-free rate is 4%. By how much does the required return on the riskier stock exceed that on the less risky stock? Round your answer to two decimal places. Historical Returns: Expected and Required Rates of Return You have observed the following returns over time: Year Stock X Stock...
Problem 6-13 Historical Realized Rates of Return Stocks A and B have the following historical returns:...
Problem 6-13 Historical Realized Rates of Return Stocks A and B have the following historical returns: Year 2012 -24.70% -14.40% 2013 22.75 23.00 2014 11.75 37.10 2015 -2.50 -6.10 2016 31.50 -0.80 Assume that someone held a portfolio consisting of 50% of Stock A and 50% of Stock B. What would have been the realized rate of return on the portfolio in each year? What would have been the average return on the portfolio during this period? Round your answers...