Estimating the Moments of Long Horizon Returns
By Anthony Neuberger
Abstract of the talk
The moments of long horizon market returns are important for asset pricing but hard to measure with any precision. In the literature, a variety of proxies have been used: option implied moments, estimates from quantiles of the historic distribution, tail statistics of the constituents of the market, and moments of high frequency returns. The moments can also be estimated by fitting parametric models to the price process. None of these methods is entirely satisfactory. The present paper shows that, under rather general conditions (the discounted price process being martingale and ergodic with finite moments), the skewness coefficient of long horizon returns comprises just two components: the skewness of short horizon returns, and a leverage effect, which is the covariance between contemporaneous variance and lagged returns. Similarly the kurtosis of long horizon returns comprises three components: the kurtosis of short horizon returns, the covariance between cubed short horizon returns and lagged returns, and the covariance between squared short horizon returns and lagged squared returns. The paper analyses the skew and kurtosis of the US market index and how they vary with horizon and over time.
About Anthony Neuberger
Anthony Neuberger read Mathematics and Philosophy at Trinity College, Cambridge where he was a Senior Scholar. He was appointed to the Central Policy Review Staff in the Cabinet Office under Lord Rothschild, and moved to a permanent position at the Department of Energy where he worked on the financial regulation of the electricity supply industry, and international trade in nuclear fuel and on a Green paper on Energy Policy. He left the Civil Service to do an MBA at London Business School. On graduating with distinction, he joined the faculty of LBS and did his PhD there. He was appointed to Associate Professor and became the first Academic Director of the full-time Masters in Finance programme. He subsequently left LBS to take up a chair at Warwick Business School where he was Director of the Financial Mathematics MSc and then became Head of the Finance Group. He joined Cass as Professor of Finance in 2013.
His research interests include option pricing and hedging, market microstructure and pensions policy, and he has published in the Journal of Finance, the Review of Financial Studies, and the Journal of Financial and Quantitative Analysis. He has consulted for Government Departments, banks, stock exchanges and other bodies.
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