jean-philippe bouchaud

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Capital Fund Management | Chairman and Head of research
Managing the risk of large portfolios requires the knowledge of equally large covariance matrices, describing the whole array of pairwise cross-correlation between the assets included in the portfolio. The empirical determination of such covariance matrices is however difficult. Even in a stationary world, empirical covariance matrices are soiled by a large amount of measurement noise, that only slowly goes to zero as the amount of data points increases. But the assumption of a stationary world is certainly too naive to describe financial markets. For one thing, volatility can strongly fluctuate from one period to the next, so ``out-of-sample'' risk may be larger or smaller than ``in-sample'' risk simply due to realized volatility. Another issue is correlation risk. As a striking example, think of the correlation between the daily price changes of the S\&P500 index and the US T-Bond. For many years before 1997, it hovered around +0.5, before suddenly switching sign around the so-called Asian crisis. It then remained in negative for more than 20 years before possibly switching again in 2021/2022, time will say. More generally, one can expect that as macroeconomic conditions evolve, the whole correlation structure of financial assets also evolves. The difficulty is to disentangle measurement noise, which leads to an apparent evolution of large empirical covariance matrices from any real evolution of the covariance structure.  Using Random Matrix Theory, I. Mastromatteo, M. Potters & K. Tikhonov recently proposed in https://lnkd.in/evarbs2f  a universal and versatile tool to reveal the existence of ``fleeting modes'', i.e. portfolios that carry statistically significant excess risk, signaling ex-post a change in the correlation structure in the underlying asset space. Our proposed test is independent of the ``true'' (but unknown!) underlying correlation structure. We sho