equities, bonds, options, and foreign currencies. Looking for the arbi-

trage opportunities ‘‘across the board’’ is technically more challenging

but potentially rewarding.

Some academic research on efficiency of the arbitrage trading

strategies can be found in [9–12] and references therein. Note that

the research methodology in this field is itself a non-trivial problem

[13].

10.5 REFERENCES FOR FURTHER READING

A good introduction into the finance theory, including CAPM, is

given in [1]. For a description of the portfolio theory and investment

science with an increasing level of technical detail, see [5, 14].

10.6 EXERCISES

1. Consider a portfolio with two assets having the following

returns and standard deviations: E[R

1

] ¼ 0: 15, E[R

2

] ¼ 0:1,

s

1

¼ 0:2, s

2

¼ 0:15. The proportion of asset 1 in the portfolio

g ¼ 0:5. Calculate the portfolio return and standard deviation.

The correlation coefficient between assets is (a) 0.5; (b) 0.5.

2. Consider returns of stock A and the market portfolio M in three

years:

A 7% 12% 26%

M 5% 9% 18%

Assuming the risk-free rate is 5%, (a) calculate b of stock A; and

(b) verify if CAPM describes pricing of stock A.

3. Providing the stock returns follow the two-factor APT:

R

i

(t) ¼ a

i

þ b

i1

f

1

þ b

i2

f

2

þ e

i

(t), construct a portfolio with

three stocks (i.e., define w

1

,w

2

, and w

3

¼ 1 w

1

w

2

) that

yields return equal to that of the risk-free asset.

4. Providing the stock returns follow the two-factor simple APT,

derive the values of the risk premiums. Assume the expected

returns of two stocks and the risk-free rate are equal to R

1

,R

2

,

and R

f

, respectively.

120 Portfolio Management

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