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Question 1 Risk and returns

Here are the past prices for the stock of company A, company B and a stock index that you think represents well the market portfolio M :

t	Security A	Security B	Stock index
0	170,42 $	1 113,65 $	2 775,60 $
1	172,97 $	1 110,37 $	2 792,67 $
2	174,97 $	1 140,99 $	2 803,69 $
3	172,91 $	1 142,32 $	2 743,07 $
4	186,12 $	1 184,46 $	2 822,48 $
5	191,05 $	1 205,50 $	2 800,71 $
6	189,95 $	1 173,31 $	2 834,40 $
7	195,35 $	1 205,92 $	2 873,40 $
8	195,46 $	1 212,57 $	2 874,45 $

*To save you some time, there is an Excel file with this data on the course website. The risk-free rate is 0,20%.

(While the calculations for this question could be done by hand, they would be very time-consuming compared to using Excel.)

1. a) What are the expected returns of A, B, and the stock index?
2. b) What are the standard deviations of A, B, and the stock index
3. c) From your answers in a) and b), can you say that one security is a better investment than the other? Why?
4. d) What are the expected return and the standard deviation of an equally weighted portfolio holding security A and B?
5. e) What are the expected return and the standard deviation of this portfolio:

• 10 000$ invested in security A
• A short sale of 15 000$ of security B
• 10 000$ invested in the stock index
• 5000$ invested in the risk-free security

f) From your answers in d) and e), can you say that one portfolio is a better investment than the other? Why?

Question 2 Systematic risk and returns

Answer the following questions using the same data as Question 1.

1. a) You want to invest in a portfolio that is on the CML. What is the standard deviation of this portfolio if its expected return is the same as security A? What is the weight of the risk-free security in this portfolio?
2. b) You want to invest in a portfolio that is on the CML. What is the expected return of this portfolio if its standard deviation is the same as security B? What is the weight of the risk-free security in this portfolio?
3. c) What should be the expected return on security A according to the CAPM? Is it a good investment according to your expectations (as calculated in Q1a) ?
4. d) What should be the expected return on security B according to the CAPM? Is it a good investment according to your expectations (as calculated in Q1a) ?
5. e) What should be the expected return on the portfolio of Q1d according to the CAPM? Is it a good investment according to your expectations (as calculated in Q1d) ?
6. f) What should be the expected return on the portfolio of Q1e according to the CAPM? Is it a good investment according to your expectations (as calculated in Q1e) ?

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