<t>Assuming that portfolios must be fully invested (all exposures add to one) and short positions (exposures smaller than zero) and leverage on asset level (individual exposures larger than one) are possible, we know that linear combinations of mean-variance efficient portfolios are again mean-varia...

<t>Thank you for confirming this.It seems to be the case that the resulting tri-criteria frontier plotted in mean-variance space is not concave throughout anymore. The consequence is that certain corner solutions will dominate for a wide range of (volatility-) risk aversions. See example below which...

<t>The "traditional" portfolio construction problem is...max U(w,L1) = r_p + L1*v_p...with U = goal (or utility) function, r_p = w'*r_a = portfolio return, w = vector of portfolio constituent weights, r_a = portfolio asset returns, v_p = portfolio risk (in the most basic case, this is portfolio vari...

<t>The solution to the classical mean-variance optimization problem allowing short positions is...w = lambda * MINV(V) * mu...with w being a vector containing asset weights, lambda representing the risk aversion coefficient, MINV() a matrix inversion operator, V the covariance matrix and mu a vector...

Dear forum,Where in the literature do I find good discussions of the Central Limit Theorem in the context of "long-term investing"?Thank you for your pointers in advance,Andi

<t>I wonder what the typical costs of a so-called "sophisticated" UCITS fund for risk management are(sophisticated funds are required to performance VaR calculations, backtests and stresstests, plus deliver all sorts of reportings and documentations).Has anybody seen some figures or studies/surveys ...

<t>QuoteOriginally posted by: McWulfYour market is the return of your universe so I would expect it to be the largest "factor". But first you have to convince yourself that factor analysis is meaningful. And as you say, it's the specific risk that really dominates and that by definition is not model...

<t>QuoteDid you use daily data or higher frequency?DailyQuoteAlso, do you have another chart showing how the major factor contributions have changed through time (something like one year rolling?). I would hazard a guess that factor weights become even more concentrated during periods of financial s...

QuotePS: btw, you do know what a "trend" is right?...how do you define "trend", especially in a "highly nonlinear, synthetic" context?Best,Andi

<t>QuoteOriginally posted by: SierpinskyJanitoryou mean this?The author conducts a PCA analysis of the correlation matrix betweeen six European equity indices based on weekly data.The result is that the first factor explains about 89%. I can confirm this result from my own experiments, but working w...

Thank Google Image Search, I found a very similar result calculated by somebody else independently.

<t>Hi forum,I calculated the contribution of statistical factors to explaining the covariance structure between 448 S&P 500 stocks and got the result that the top 10 factors explain about 53%, the first factor being by far the most important with a contribution of around 35%. See this chart here...

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> Mutual information...If I understand this measure correctly, then it requires the joint as well as marginal distributions as inputs. I prefer non-parametric measures of dependence. Thank you anyway for the pointers.

<t>I agree with your overfitting comment. I think in the end, manual inspection of a scatter chart cannot really be replaced by a single dependence measure. Exceedance correlations à la Longin/Solnik(2001) are quite useful and embed other interesting information. Anyway, non-monotonic functions are ...