MATLAB FINANCIAL DERIVATIVES TOOLBOX Manuel d'utilisateur télécharger pdf (Page 118)

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change slightly the

n function so that its calling syntax

becomes:

“[MinPoints] =

t(fun, x, r, V, R)”

with r to be the column vector of the assets’ expected returns, V the

assets’ variance-covariance matrix and R the desire expected return.

Similar changes in order to pass the additional arguments should be

done also to NumerDers.m (the new should be named as:

t) and NumerHessian.m (the new should be named as:

t). Because the portfolio optimization problem is

actually the minimization of a quadratic function, the Newton descent

algorithm can find its solution with a single iteration. So, alleviate

also the rule of thumb according to which the elements of the Hessian

matrix except the ones of the main diagonal are set to zero. Use the

origin (0, 0, 0) as an initial point.

• Add a risk free asset with expected return 1%, find and plot the

efficient frontier. Create a new m-file with the name:

portFunRiskFree.m that includes the new expression of f after the

inclusion of risk-free rate (hint: find which components are zero-

valued and ignore them). Create a third figure that combines the two

previous ones. If you are familiar with investment theory, you can

view various interesting components (e.g. two fund separation

theorem, capital market line, etc).

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MATLAB FINANCIAL DERIVATIVES TOOLBOX Manuel d'utilisateur Page 118