University College of the Cayman Islands

FIN301 Financial Management

Tutorial #5 - Risk and Rates of Return - Chapter 5

 

  1. Universal Ltd. is planning to invest in a security that has several possible rates of return.  Given the following probability distribution of returns, what is the expected rate of return on the investment?  Also compute the standard deviation of the returns.  What do the resulting numbers represent?

Probability

Return

0.1

-10%

0.2

5%

0.3

10%

0.4

25%

     

  1. Which of the following investments is clearly preferable? Why

  2. Investment Return Standard Deviation
    A 18% 20%
    B 20% 20%
    C 20% 18%

     

  3. Press Corp. is evaluating a security.  One-year Treasury bills are currently paying 9.1%.  Calculate the investment’s expected return and its standard deviation.  Should Press Corp. invest in this security?

    Probability

    Return

    0.15

    5%

    0.30

    7%

    0.40

    10%

    0.15

    15%

     

  4. Compare and contrast the standard deviation of return and the coefficient of variation of return.  

  5. 5-6

  6. Curtis Manufacturing Inc. has prepared the following information regarding two investments under consideration. Which investment should be accepted?   

    Project A

    Project B

    Probability

    Return

    Probability

    Return

    0.2

    -2%

    0.1

    4%

    0.5

    18%

    0.3

    6%

    0.3

    27%

    0.4

    10%

     

     

    0.2

    15%

       

  7. A financial advisor created an ”index portfolio” from the JSE listed stocks.  Her objective was to “track” the market index with her portfolio. i.e., the returns to both should be about the same. It is clear this was not achieved on a yearly basis, but what conclusions can you draw over the four year life of the fund?  Did she subject her clients to any greater risk than that inherent in the market index? 

    Year

    Fund Return

    Index Return

    1990

    28%

    36%

    1991

    37%

    45%

    1992

    134%

    46%

    1993

    -15%

    57%

     

  8. Sygnal Investment Fund (Synfund) a local investment management firm, presents the following data for its last six (6) months of operation with the claim by one of its financial analysts that the fund did as well as the general stock market index. 

    Month

    Synfund Unit Price

    Market Index

    January

    $13.75

    15,765

    February

    $15.25

    17,545

    March

    $17.85

    18,100

    April

    $16.50

    16,475

    May

    $15.00

    17,840

    June

    $18.05

    19,730

     Do you agree with this claim as indicated by the risk and return of the stock market and the fund?  

     

  9. What is unsystematic risk? What events could affect this type of risk?  

  10. What is systematic risk? What events could affect this type of risk?  

  11. What is the relationship of total risk, firm specific risk and market risk? Why would it be argued that market risk is the only relevant risk?

  12. 5-21 (Although in this particular question, you could have gotten the answer for part c in a different way, try using the standard deviation formula for a 2-asset portfolio using a correlation coefficient of 0.876).

  13. 5-22 (parts a -c only)

  14. 5-19

  15. Compare and contrast the standard deviation and the beta coefficient.

  16. If a security has a beta of 0.85 and the market return is positive. Do you expect the security’s return to be less than the market’s return? Explain your answer  
  17. 5-7
  18. 5-2
  19. 5-8
  20. 5-10
  21. 5-18
  22. You own a portfolio consisting of the following stocks: 

Stock

% of Portfolio

Beta

Expected Return

1

20%

1.00

16%

2

30%

0.85

14%

3

15%

1.20

20%

4

25%

0.60

12%

5

10%

1.60

24%

 The risk free rate of interest is 7%

(a)    Calculate the expected return on the  portfolio.

(b)   Calculate the portfolio beta.

(c)    Given the information above, plot the security market line.

(d) Are any of the stocks under-priced or over-priced?

  1. 5-20