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Flashcards in Multivariate Vol Deck (17)
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What is PCA?

A method of splitting several time series of return into orthogonal factors. Uses eigenvalues and eigenvectors. Can order factors so that R2 is decreasing from favtor to factor.


Explain Principal Component Covariance

Models Covariance matrix as driven by exposure to principal components. Multiplies factor loadings to moving average of Covariance of a set of principal components + covariance matrix of errors from regression on principal components


How does the 2006 RiskMetrics differ from the 1994 RiskMetrics?

At each time period, the 2006 RM takes a weighted average of an eponentially weighted moving average covartiance calculated at different sampling frequencies. Hence, the RM 2006 is not an EWMA. The weighting creates 'long memory', gives more weight to information far away than the 1994. The weighting is hyperbolic


What is Observable Factor Covariance?

Models Covariance matrix as driven by exposure to observable factors. Multiplies factor loadings to moving average of Covariance of factors + covariance matrix of errors from regression on factors


What is Equicorrelation?

A model assuming that all assets have the same correlation. Covariances are calculated from volatilities. Use moving average of squared errors of each asset to estimate variance (and volatilities)


How is correlation estimated for the equicorrelation model?

It inverts the equation for the variance of an equally weighted portfolio when the correlation for all assets is the same
Remember that 1/K each weight and Var(1/k * r) = k^-2 var(r)


Explain covariance targeting in scalar BEKK

Replace intercept with (1-a^2-b^2)average_sigma. Run 2 stage estimation. First estimate long-run sigma or set it as target. Estimate a and b with MLE


Explain Constant Conditional Correlation

It models correlations and variances volatilities. Uses constant correlation matrix. Correlation is correlation of devolatized residuals. Forecasts variances using individual GARCH type models. D is a diagonal matrix of univariate volatilities


Explain Dynamic Conditional Correlation

Like CCC it splits up the modelling of correlation and volatility, but uses a time-varying correlation matrix. It models it like a covariance-targetting GARCH BEKK, with a long-run variance targeting intercept, reaction to standardized residuals and persistence. Needs to normalizations terms to be correlation matrix. D is a diagonal matrix of univariate volatilities


What are some key problems with Realized Covariance?

Price humps
Noise (bid-ask bounce)
Imperfect synchronization


Explain subsampling

Can use rolling windows if higher frequency sampling is infeasible


What are some key issues to adress in multivariate ARCH?

Limiting the number of parameters when the number of assets is large
Positive-definiteness of conditional covariances


What is covariance targeting in the context of a BEKK model?

Replacing the intercept with a simple moment estimator to limit the number of parameters that must be estimated using numerical methods.


How are CCC and DCC different from the BEKK model of the conditional covariance?

They use univariate ARCH models to model volatility and then use standardized residuals to model correlation.


What feature of the cross-section of returns limits sampling when estimating Realized Covariance?

Periods where markets are closed
Public holidays
Return synchronizations

Bid-ask bounce does not appear in the cross-section


What tools are available to determine the correct sampling frequency of Realized Covariance?

R2 signature plot
Correlation signature plot
Volatility signature plot


What are some ways of measuring non-linear dependence?

1) Rank Correlation
2) Kendall's tau
3) Exceedance Correlation (correlation conditional on x and y being above a certain level)