Abstract
This paper calculates the per quarter pairwise correlation coefficients (Rho) of the daily returns from December 5, 2005 to December 8, 2014 of 30 stocks randomly selected from the Russell 3000 index. For the time series correlation coefficients of 435 pairs of assets, we employ the Elliot-Rothenberg-Stock Point Optimal procedure to examine the stability of correlation coefficients. Our results indicate the inappropriateness of using correlation coefficients in portfolio management and Monte Carlo simulation. More than one-third of the correlation coefficient series generate non-asymptotic simulation volatility and using ex post correlation coefficients in Cholesky decomposition performance forecast can lead to severe deviation from the investment policy mandate.
Highlights
This paper examines the volatility of correlation and the implication of the non-constant correlation coefficients
The market capitalization of the 30 selected assets is from U.S $268.74 million to U.S $799.72 billion; the forward P/E is from 7.09 to 62; and the enterprise value (EV)/EBITDA is from -21.13 to 43.88
As of December 9, 2014, the market capitalization of the 30 selected assets is from U.S $268.74 million to U.S $799.72 billion; the enterprise value (EV) is from U.S $223.35 million to U.S $46.27 billion; the trailing twelve month P/E is from 8.72 to 222; the forward P/E is from 7.09 to 62; the PEG is from -2.26 to 23.66; the P/S is from 0.1 to 20.89; the P/B is from 0.65 to 5.7; the EV/Revenue is from 0.11 to 16.59; and the EV/EBITDA is from -21.13 to 43.88
Summary
This paper examines the volatility of correlation and the implication of the non-constant correlation coefficients. One of the most famous uses of Pearson correlation coefficient is in portfolio management, in which the variance of the portfolio is computed as: σσp2p = ∑ii ωωi2i σσii2 + ∑ii ∑jj wwii wwjjσσiiσσjjρρiiii (1) To use this variance of portfolio with historical data to simulate future performance of assets in the Monte Carlo procedure, which is the common practice in academia and industry, the implicit assumption is the stability of the correlation coefficient. This assumption has not been thoroughly discussed, and the broader issue is what the impact of instable correlation coefficient is The meanings of such question is not limited to portfolio management but to all the fields in finance theory that use previous correlation coefficients as measure the correlation nature of assets. The implication is important in terms of Cholesky decomposition, which is the standardized modeling procedure in Monte Carlo simulation
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