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It depends on your ETF. Some have synthetic exposure to the index sold by a sponsor (ie someone give them exactly the performance of the index) but this has a cost (a constant / deterministic drag on the NAV of your ETF which doesn't appear in your tracking error). Futures on the other hand have basis, are sensitive to changes in implied dividends and ...


2

Have you considered using 'incremental' singular value decomposition to calculate your component scores? Each future market move (or increment) forces a recalculation of component scores given the new data. This paper outlines an algorithm to do this Fast Low-Rank Modifications of the Think Singular Value Decomposition This paper develops an identity ...


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Yes. First, XLF and FAZ do not track the same underlying benchmark. -> XLF tracks the S&P Financials Select Sector Index -> FAZ tracks the Russell 1000 Financial Services Index I'll ignore that for this sake, because their baskets are likely still very similar. Pretending their benchmarks were the same, you would theoretically have a dead on (3x) ...


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Hedginge/Adjusting would be with the Beta of the inverse ETF. Usually, Long/Short strategy would involve an ETF and a stock in which you would Beta adjust the ETF position. You can use an ETF, I don't see anything wrong with this as long as their is some level of correlation between the Short and the Long. You want them to mean revert in a determined time ...


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Your approach is a good one. But before you venture too far, you should be aware of issues related to zero eigenvalues (positive semi-definiteness) of your correlation matrix $\mathbf{R}$ or covariance matrix $\mathbf{C}$. Let $p$ be the number of assets, and $t$ the number of, for example, day or bars. You probably have many more times in the time ...



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