MATLAB FINANCIAL DERIVATIVES TOOLBOX Manuel d'utilisateur télécharger pdf (Page 115)

114

ReW

and for the case of the three assets in an analytic form:

BCCBACCAABBA

BBAA

swwswwswwswswswmin

222

222222

+++++

s.t.

R)r(Ew)r(Ew)r(Ew

CCBBAA

=++

1=++

CBA

www

Note: If we do not use the first constraint and in the absence of a risk-free

rate we will get the minimum variance portfolio. It is actually advisable to

first get the minimum variance portfolio before we proceed in a real problem.

Then, by changing the level of desire return, we trace points on the efficient

frontier.

To solve this problem, we make two simplifications to the problem. First we

replace everywhere

w with

ww −−1 . Second, we rearrange the

constraint:

R)r(Ew)r(Ew)r(Ew

CCBBAA

=++

0=++− )r(Ew)r(Ew)r(EwR

CCBBAA

and since it equals zero, we multiply it with a constant ? and we get:

0=++− ))r(Ew)r(Ew)r(EwR(?

CCBBAA

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MATLAB FINANCIAL DERIVATIVES TOOLBOX Manuel d'utilisateur Page 115