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 May5 comment What is the main reasons to use Miltersen & Schartz (1998) model for commodity futures options Note that it is a very widely cited paper, not a crazy model coming from nowhere Apr3 comment What are some different methods for calculating hedge ratios for multiple leg spreads? Do you mean "hedge ratio"? Apr3 comment Why is delta-hedging of ATM options near expiry difficult to do? Why is this closed? There is a scientific explanation to this question, as the delta of ATM options close to expiry becomes binary. Apr3 comment What are some different methods for calculating hedge ratios for multiple leg spreads? which "ratios" do you mean? Aug14 comment portfolio optimisation with VaR (or CVaR) constraints Thank you very much, this is very insightful Aug14 comment portfolio optimisation with VaR (or CVaR) constraints it seems that even though CVXOPT is open source, it only contains interfaces to the solvers in MOSEK, which is not open source. Aug14 comment portfolio optimisation with VaR (or CVaR) constraints Thanks for your input, makes sense. What about $r_{ij}$ ? The return of asset $i$ in simulation $j$ ? Do you really have to simulate them or can you take simply the past ones? i would like to avoid modelling the returns, as it could create errors (bad tail correlation estimation etc.) Now if you need 10,000 of them I understand you have to simulate. But is it not dangerous? Aug14 comment portfolio optimisation with VaR (or CVaR) constraints If I am not wrong these $m$ are the Monte Carlo simulations that @David Nehme is mentioning in his answer. I guess $m$ has to be high enough. 1000? 2000? Do you have an idea? Aug13 comment portfolio optimisation with VaR (or CVaR) constraints The second link seems very interesting, thanks. I have read carefully the paper. however, I truggle to understand how they replace the expectancy that is in formula (9) page 8, with a sum over $j$. What are these $r_{ij}$ and what is $m$? Apart from that, the solution is quite elegant... Can be solved with a very standard optimizer. Aug13 comment portfolio optimisation with VaR (or CVaR) constraints +Alexey, do you have this ebook "Portfolio Optimization with R/Rmetrics"? On the google preview at page 333 it seems that I read that quadratic constraints are treated in the other ebook "Advanced Portfolio Optimization with R/Rmetrics" If you have the book, can you confirm if there are such examples? books.google.com.sg/… Aug13 comment How to normalize different instruments by volatility? not sure what your discussion on quants really brings to Freewind's question. Sounds like a useless digression. Aug10 comment portfolio optimisation with VaR (or CVaR) constraints indeed. I need quadratic constraints. The objective function is linear but the VaR constraint is definitely quadratic. Will have a look at your link. Thanks Aug10 comment portfolio optimisation with VaR (or CVaR) constraints @BobJansen I have several VaR constraints on several groups of assets in my portfolio. I cannot manually adjust every day the expected returns of all my assets to ensure the VaR constraints. Ideally I would have to model the constraint in the optimization problem. Apr18 comment Why is the first principal component a proxy for the market portfolio, and what other proxies exist? Thank you for enhancing your answer, I appreciate reading it a lot. Apr18 comment Why is the first principal component a proxy for the market portfolio, and what other proxies exist? When you say "Why is this the market factor? If you examine the weights (factor loadings) of the first eigenvector in a histogram you will find they are generally all of the same sign whereas this is not the case for any of the subsequent eigenvectors", I am not convinced by this argument. I agree that the among all PCA components, the first one is the most representative of the market, but maybe there is another set of weights that is better than this one. Feb10 comment How to compute performance attribution between daily rebalanced strategies? interesting idea Feb10 comment Why is the first principal component a proxy for the market portfolio, and what other proxies exist? I still think it is very accurate to say that "PCA is maximizing the variance". PCA weights can be found by formulating the problem as a max of the variance under constaint Feb1 comment How to hedge against lack of volatility some trading strategies perform better when there is high volatility. Hence hedging against low volatility can makes sense. Jan11 comment Has high frequency trading (HFT) been a net benefit or cost to society? It definitely has been a benefit for exhanges, that have made millions in trading fees Jan3 comment Why a self-financing replicating portfolio should always exist? in theory, yes, but then you need to readjust your position dynamically intraday and very often the cost and slippage of this replication will be so high that in practice it doesn't work.