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I think generally there are two approaches: "calendar rebalancing" (such as monthly as you mention) and "optimal corridor width". For the first option, the danger is the portfolio could stray considerably from your benchmark between rebalancing dates. For the second option, track tactical deviation on a continuous basis. When you are outside the corridor, ...

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In literature you'll find many approaches to compute the variance. As mentioned already, the standard ideas are to use MLE, Shrinkage on the Covariance Matrix (Ledoit, Wolf), Shrinkage on the inverse of the Covariance Matrix (Kourtis,Dotsis) which makes sense as in fact the inverse of the Covariance Matrix determines the shape of the efficient frontier. ...

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vega captures the two most common solutions to this problem. There are some valid criticisms of corridors as well. Because assets are correlated within a portfolio the decision to trade a particular asset should actually depend on the movements of other assets rather than having a corridor per asset. Also, finding the right corridor is often done using ...

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As you are especially interested in applications in Finance I'll recommend this book of Rachev which focus on Bayesian Methods in Finance

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It is supposed to be multiplied by 5/100 (5%). You should then be able to get $57,870.37 if you multiply it by the fund value. 1 This is because the author has assumed the approximation (6.67) $$\mathcal{S}(\alpha)\approx \tilde{\mathcal{H}} (\mathrm{E}\{\Phi_\alpha\},\mathrm{Var}\{\Phi_\alpha\})$$ That is, the index of satisfaction$\mathcal{S}(\alpha)$depends only on the first two moments of the marginals. As explained by the author in section 6.5.1, this is a good approximation ... 1 I think I figured it out. In an earlier paragraph Meucci says Suppose that we can focus on the two first moments only and neglect all the higher moments. So two random variables are equivalent if their first two moments agree. Therefore any random variable can be replaced by$\mathcal{U}(\mu - \sqrt{3}\sigma, \mu + \sqrt{3}\sigma)\$ as far as ...

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This is why Markowitz says that the diversification of the portfolio is always preferable. You have a lot of certain past data and some fallible speculations to evaluate the variance and expected return of a title. Inherently the best possible evaluation method, and there are several main ones, is not a foolproof inference. But, if you diversify your ...

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