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By Robert Engle

Monetary markets reply to info nearly right away. every one new piece of knowledge impacts the costs of resources and their correlations with one another, and because the approach quickly adjustments, so too do correlation forecasts. This fast-evolving surroundings offers econometricians with the problem of forecasting dynamic correlations, that are crucial inputs to threat size, portfolio allocation, Read more...

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Yn ) . ,n (y1 , . . , yn ) = c(u1 , . . 8). The joint density function is simply the product of all the marginal density functions and the copula density. If these random variables were independent, the joint density would simply be the product of the marginals, so the copula would be the number 1. 10). Whenever the copula is different from 1, the random variables are no longer independent. The formula is closely related to the familiar 20 2. Correlations in Theory moment condition that the covariance between a pair of random variables is simply the product of their two standard deviations and the correlation between them.

2005) discuss methods using realized volatilities and correlations. Hafner et al. (2006) introduce a semiparametric specification. He and Terasvirta (2004) consider a class of multivariate GARCH models that generalizes the constant conditional correlation model. Audrino and Barone-Adesi (2006), Ledoit et al. (2003), Ledoit and Wolf (2003), and Dellaportas and Vrontos (2007) introduce models that combine static and dynamic models to give, essentially, a shrinkage style estimator. Bekaert and Harvey (1995) and Gallo and Otranto (2007) examine regime-switching models of correlation.

When μ0 is 0, the required return can be achieved with the risk-free rate, so all weights on the risky assets are 0. If all assets have the same expected return, then the portfolio weights will be selected to minimize variance; optimal portfolios will consist of the minimum-variance portfolio and cash. This is easily seen by substituting μ = ιμ1 , where ι is a vector of ones and μ1 is the excess return expected for all the assets. If μ0 = μ1 , then this solution will not involve any cash and will be equivalent to the problem when there is no riskless rate.

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