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Without the discrete constraints, the minimum tracking error/variance problem is a quadratic program. If you constrain the tracking error, you have a convex quadratically-constrained problem which is solved as an SOCP by modern commercial solvers. SOCP does not address discrete constraints like cardinality of assets or minimum investment levels. SOCP ...


3

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 ...


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This appears to be the same thing, however, in the former case, the benchmark is the FF-Model. This means you assume the model stated in their eq. 9 is correct (as per your regression), and use the vol of the residuals as TE. They go on and explain: The volatility of the residuals in equation [9] is a measure of idiosyncratic (non-systematic) risk.20 ...


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As pointed out by Hull (2012). Options, futures and other derivatives. (8th edition, p305): "A compromise that seems to work reasonably well is to use closing prices from daily data over the most recent 90 to 180 days. Alternatively, as a rule of thumb, n can be set equal to the number of days to which the volatility is to be applied."



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