Post by Sapphire Capital on Aug 14, 2008 4:18:05 GMT 4
Modeling the Time Varying Dynamics of Correlations: Applications for Forecasting and Risk Management
Michael Jacobs Jr.
OCC/Risk Analysis Division/Credit Risk Modeling
June 21, 2008
Abstract:
In this study we compare the time series correlation modelling techniques, and document the effectiveness of various correlation forecasting models for different asset types, using a broad database from Commodity Research Bureau (CRB) and Bloomberg. First, we examine time varying correlations computed from different moving windows (rolling window moving average - RWMA) and pairs of assets. We document distinct patterns in the behavior of the RWMA estimates across window lengths for different pairs of assets. As the window length increases, average daily correlation between most stock indices and short- (long-) term bond yields increases from positive but negligible to substantially positive (is negative and flat), whereas the correlation between short and long term interest rates decreases, and the correlation amongst various equity and various commodity or precious metals indices exhibits different non-monotonic patterns. Then we build time series models to forecast correlation at different holding periods, the Engle (2002) dynamic conditional correlation (DCC) model, and compare the properties of these to the RWMA estimates. Focusing on a single pair representative of equity and bond markets, the S&P500 index and 10 Year Treasury Bills, we find that correlation estimates using DCC are significantly different from that using RWMA, and that this diverges extremely with increasing holding period: while both show moderate negative correlation between equity index returns and yield changes at a daily holding period, both the level and variability of the DCC estimates drops off sharply at longer holding periods (showing effective lack of association), whereas RWMA estimates become increasingly negative, highly volatile and bimodal. We conclude that the RWMA correlation estimates are unable to adequately model longer holding period returns, as one cannot correct for dependence in returns induced by overlapping holding period in that framework. The second exercise involves analyzing hedging portfolios formed with these instruments based upon RWMA, DCC and constant (naýve) correlation models. The DCC hedge portfolios outperform all of the RWMA estimations in terms of volatility of hedge portfolio returns, as well as other distributional characteristics, such as skewness and kurtosis. While it becomes increasingly difficult to hedge as we increase the holding period for all correlation models, DCC holds up best, and for shorter (longer) holding periods the constant correlation model performs better than RWMA and comparably to DCC (much worse than either DCC or RWMA).
papers.ssrn.com/sol3/papers.cfm?abstract_id=1149412
Michael Jacobs Jr.
OCC/Risk Analysis Division/Credit Risk Modeling
June 21, 2008
Abstract:
In this study we compare the time series correlation modelling techniques, and document the effectiveness of various correlation forecasting models for different asset types, using a broad database from Commodity Research Bureau (CRB) and Bloomberg. First, we examine time varying correlations computed from different moving windows (rolling window moving average - RWMA) and pairs of assets. We document distinct patterns in the behavior of the RWMA estimates across window lengths for different pairs of assets. As the window length increases, average daily correlation between most stock indices and short- (long-) term bond yields increases from positive but negligible to substantially positive (is negative and flat), whereas the correlation between short and long term interest rates decreases, and the correlation amongst various equity and various commodity or precious metals indices exhibits different non-monotonic patterns. Then we build time series models to forecast correlation at different holding periods, the Engle (2002) dynamic conditional correlation (DCC) model, and compare the properties of these to the RWMA estimates. Focusing on a single pair representative of equity and bond markets, the S&P500 index and 10 Year Treasury Bills, we find that correlation estimates using DCC are significantly different from that using RWMA, and that this diverges extremely with increasing holding period: while both show moderate negative correlation between equity index returns and yield changes at a daily holding period, both the level and variability of the DCC estimates drops off sharply at longer holding periods (showing effective lack of association), whereas RWMA estimates become increasingly negative, highly volatile and bimodal. We conclude that the RWMA correlation estimates are unable to adequately model longer holding period returns, as one cannot correct for dependence in returns induced by overlapping holding period in that framework. The second exercise involves analyzing hedging portfolios formed with these instruments based upon RWMA, DCC and constant (naýve) correlation models. The DCC hedge portfolios outperform all of the RWMA estimations in terms of volatility of hedge portfolio returns, as well as other distributional characteristics, such as skewness and kurtosis. While it becomes increasingly difficult to hedge as we increase the holding period for all correlation models, DCC holds up best, and for shorter (longer) holding periods the constant correlation model performs better than RWMA and comparably to DCC (much worse than either DCC or RWMA).
papers.ssrn.com/sol3/papers.cfm?abstract_id=1149412