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Unformatted text preview: 10−1 , and plot the optimal values
of pT x versus η . Also make an area plot of the optimal portfolios x versus η .
¯
Hint: The Matlab functions erfc and erfcinv can be used to evaluate
x
√
2
e−t /2 dt
Φ(x) = (1/ 2π )
−∞ and its inverse: √
1
Φ(u) = erfc(−u/ 2).
2
Since you will have to solve this problem for a large number of values of η , you may ﬁnd the
command cvx_quiet(true) helpful. (c) Monte Carlo simulation. Let x be the optimal portfolio found in part (b), with η = 0.05.
This portfolio maximizes the expected return, subject to the probability of a loss being no
more than 5%. Generate 10000 samples of p, and plot a histogram of the returns. Find the
empirical mean of the return samples, and calculate the percentage of samples for which a loss
occurs.
Hint: You can generate samples of the price change vector using
p=pbar+sqrtm(Sigma)*randn(4,1);
13.3 Simple portfolio optimization. We consider a portfolio optimization problem as described on pages
155 and 185–186 of Convex Optimization, with...
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 Fall '13
 F.Borrelli
 The Aeneid

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