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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