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I am not sure if I understood your question correctly but I will try to answer it anyway. If you have a standard normal random vector $z \sim N(\mathbb{0},I_n)$ (where $z,0 \in \mathbb{R}^{n\times1}$ and $I_n \in \mathbb{R}^{n\times n}$ is the identity matrix) and you want to transform it into a multivariate normal $x \sim N(\mu,\Sigma)$ you do it the ...


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The formula is $$ \mu = \lambda CX $$ in your notation. You find it in many places, e.g. here. The assumption is that you know $\lambda$ which is a strong assumption. Furthermore it only holds if investors are unconstrained (long/short not long only). It is intuitive as it says that given the weighting the return expectation increases with risk aversion ...


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The clearest and most intuitive article I have seen so far is Kritzman et al., Regime Shifts: Implications for Dynamic Strategies in FAJ (May / June 2012) It not only shows how you can use HMM for financial modelling but it also goes through the actual estimation algorithm (Baum-Welch) step-by-step and even gives full Matlab-code. From the abstract: ...


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One common "model" is to assume the correlation to be constant, such as in a CCC-MVGARCH model. If you want a review of different multivariate GARCH models, you could look at: Silvennoinen and Täräsvirta 2009, Multivariate Garch models, in Handbook of financial time series.


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Yes. Correlations max out at 1. However if the correlation is near 1 and the volatility of the spot is significantly larger than the volatility of the future the hedge ratio will be greater than 1. The intuition is if that vol of the future is much smaller than the vol of the spot you might need a lot more futures to minimize the high spot variance.



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