Question

The returns of Company A for the past six months are 12%, 11%, 16%, 8%, 13%,...

  1. The returns of Company A for the past six months are 12%, 11%, 16%, 8%, 13%, and 14%. Calculate the standard deviation of this company’s return.
  1. In your portfolio you have invested 30% and 70% in Stock X and Stock Z, respectively. The standard deviation of X is 12%. The standard deviation of Z is 9%. The correlation between X and Z is 0.50. Calculate the portfolio standard deviation.
  1. For the same problem before, now calculate the portfolio standard deviation if the correlation between X and Z is -0.50.
  1. In your portfolio you have invested 40% and 60% in Stock A and Stock B, respectively. The beta for A is 1.55. The beta for B is 1.24. Calculate the beta of the portfolio.

   Consider the following table.

Company A

Company B

Standard Deviation

7%

8.5%

Mean Return

12%

13%

Beta

1.2

1.45

               Mean risk-free rate is 3%.

  1. Calculate Sharpe Index for both the companies. Which one performed better?
  1. Calculate Treynor Index for both the companies. Which one performed better?
  1. Why is Sarbanes-Oxley Act enacted? Give three examples of changes in Sarbanes Oxley Act.
  1. If a stock has a beta of 1.50. How do you explain it?
  1. What are Poison Pills? Give an example.
  1. Give two major differences between common, bonds and preferred stocks.
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Homework Answers

Answer #1

1. Average Return =(12%+11%+16%+8%+13%+14%)/6 =12.33%
Standard Deviation =(((12%-12.33%)^2+(11%-12.33%)^2+(6%-12.33%)^2+(8%-12.33%)^2+(13%-12.33%)^2+(14%-12.33%)^2)/(6-1))^0.5 =3.58%

2.Standard Deviation at correlation of 0.5 = ((Weight of X* Standard Deviation of X)^2 + (weight of Z * standard Deviation of Z)^2 + 2* Weight of X * Standard Deviation of X * weight of Z * standard Deviation of Z * correlation)^0.5
=((30%*12%)^2+(70%*9%)^2+2*30%*70%*12%*9%*0.50)=8.68%

3. Standard Deviation at correlation of -0.5 = ((Weight of X* Standard Deviation of X)^2 + (weight of Z * standard Deviation of Z)^2 + 2* Weight of X * Standard Deviation of X * weight of Z * standard Deviation of Z * correlation)^0.5
=((30%*12%)^2+(70%*9%)^2-2*30%*70%*12%*9%*0.50)=5.47%

4. Beta of Portfolio =Weight of A*Betaof A+Weight of B*Beta B =40%*1.55+60%*1.24 =1.364

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