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Quantitative Portfolio Management Course – ESCP EUROPE, Année universitaire 2014/15

E U R 0 P E
Année universitaire 2014-201 5
Exercise 1:
Consider a perfect market with two risky assets characterized by the following statistical
parameters:
E1= 0.1 (712 = 0.04
and
E2 = 0.2 022 = 0.16
1°) Determine the co-ordinates in the standard deviation/ mean plane of the risky portfolios with
W1 = 0; 0.2; 0.4; 0.6; 0.8; l in the four following correlation cases:
3) 101,2 = +1
b) 101,2 = 0
C) 101,2 = ‘0-5
d) 101,2 = ‘1
2°) Determine the minimum variance portfolio composition and its co-ordinates in the standard
deviation/ mean plane in the four previous correlation cases.
3°) Represent graphically the feasible sets in the mean-standard deviation plane.
Exercise 2:
1°) Consider a perfect market with two risky stocks, characterized by the following statistical
parameters:
E1 = 0.05 of = 0.01
and 2
E2 =0.15 02 =0.l6
Knowing that the correlation coefficient between the two risky assets is equal to ,01,2 = -0.5
a) Determine the co-ordinates in the standard deviation/ mean plane of the risky portfolios with
w1 = 0; 0.25; 0.5; 0.75; 1.
b) Determine the minimum variance portfolio composition and its co-ordinates in standard
deviation/ mean plane. What is the covariance between the equally weighted portfolio and the
minimum variance portfolio? What do your remark.

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