Out of Sample Performance of Factor Copulas

This paper investigates the effects of several different copulas in combination with different data frequencies on risk forecasts, such as 1% 10-day Value at Risk, for a stock portfolio. The copulas enable a multivariate distribution to be defined as a function of marginals and a dependence structure, the copula. The marginals are estimated using the normal distribution and for the copulas the Normal, Student-t, Clayton and factor copula are chosen. The factor copula is a newly proposed copula by Oh and Patton (2012) based on a new estimation method and supposedly incorporates more characteristics than the other copulas such as asymmetric dependence and scalability. The 1% 10-day VaR is best modeled using the Student Copula as the thick tails capture the extremeties. The most accurate 1% VaR forecasts are obtained by using high frequency data in combination with the Student-t copula. The best 5% VaR forecasts are also obtained using high frequency data with a Student-t copula. The factor copula turns out to be a hard to estimate copula that depends on large simulations in order to maintain accuracy, which becomes a computational burden.