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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 ...


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There are many techniques, but I would begin with Stambaugh Analyzing Investments Whose Histories Differ in Lengths. The full information maximum likelihood approach he describes basically involves regressing the short history series against the long history series to obtain the covariance with the longer history securities and adding back the covariance of ...


2

When performing a tracking error optimization, you will obtain the same result by using the tracking error squared, which is just the variance of the relative portfolio weights. This would be just finding the minimum variance portfolio, but with conditions on the weights. For instance, it would be equivalent to instead set up the variance minimization ...


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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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It is better to use a factor model, if one is available. Are you asking this question because you don't have access to one? Also, what is the nature of the asset you want to track? Is it an index or a single security? What asset class? What risk factors is it exposed to (e.g. interest rate and credit risk vs. stock market volatility and other equity ...



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