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Looking at your code, you seem to be mixing the risk minimization formulation of the mean-variance problem with the risk aversion formulation. Both formulations include the "budget" constraint, that the sum of the weights equal 1, and can require that each of the weights be greater than zero, the "long-only" inequality constraints. In the risk minimization ...


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As regards the free sources, the best place where you can find material about credit risk management is defaultrisk.com; it is a website where are collected (almost) all academic (and not) articles and working paper, references and researchers. Moreover, as regards the forums, I think you should try visiting Credit Risk Group at Linkedin; it is a very ...


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FinAnalytica Inc www.finanalytica.com has a multi-asset class commercial implementation including fitted classical tempered stable distributions and fitted skewed t-distributions (for lower frequency data) in its software named Cognity. You should talk to those guys. Their backtests do all the talking...risk forecasts from left tail all the way through to ...


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This problem is from the exercise for Chapter 2 of Kerry Back's Asset Pricing Book. The setup of the problem is rather simple. You want to \begin{equation*} \begin{aligned} & \underset{\phi}{\text{maximize}} & & \phi'\mu + \frac{1}{2} \alpha \phi' \Sigma \phi\\ & \text{subject to} & & 1'\phi = w_0 \end{aligned} \end{equation*} The ...


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This is my experience (I am heading the Risk Analytics team for an investment bank in the City): We only ever bought the Optimization and Statistics toolboxes. You are better off writing any extra functionality yourself. Most of the stuff is simple, and writing it yourself improves your understanding and highlights potential pitfalls. Having said that, we ...


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These are identical definitions of ES. It's just a matter of expressing losses as negatives or positives. First definition Notice the integral bounds are $a$ and $1$: losses are positive; this is so-called Loss(+)/Profit(-). Here alpha might be 95%, as in 95% confidence VaR or ES. Second definition Losses are negative, and the corresponding quantile is ...


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Conversion to a butterfly can mitigate or even eliminate all risk taken by opening a initial debit spread or long option position. This is possible only if the underlying moved in your favor after your initial position is open. To convert to a butterfly you simply sell and buy enough options (for a credit) that together with your initial position forms a ...



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