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Zsolt Bihary

is an associate professor of the Department of Finance at Corvinus University of Budapest (CUB). Prior to his recent position he worked as a researcher in physical chemistry, and as a financial modeler at Morgan Stanley. His research interest focuses on portfolio optimization, evolutionary finance, and financial networks.

Péter Csóka

is an Associate Professor at the Corvinus University of Budapest, Department of Finance and a senior research fellow at the game theory research group of the Hungarian Academy of Sciences. He received his Ph.D. in economics from Maastricht University in 2008. His research topics include risk measures, risk capital allocation, various aspects of liquidity, and financial networks. He has papers published in journals like Management Science, European Journal of Operational Research, Games and Economic Behaviour, and Journal of Banking and Finance.

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Zsolt Bihary, Péter Csóka, Dávid Zoltán Szabó: How Risky is it to Hold Stocks in the Long Run? Spectral Measures of Risk over Time

We investigate how the spectral risk measure associated with holding a stock rather than cash depends on the holding period. The risk can be interpreted as the amount of the necessary cash reserve. Negative risk indicates that even a leveraged stock position is acceptable. In the limit of zero holding time, the risk is zero. As we increase the holding time from zero, at first the risk grows. The question is whether risk keeps growing indefinitely, or it plunges back below zero at a certain holding time.

Previous papers have shown that within a limited class of spectral measures, and when the stock price follows a Geometric Brownian Motion, risk does become negative at long periods. In this paper, we arrive at more general results. We show that with all exponential Levy price processes that grow realistically fast, all spectral risk measures (also expected shortfall, except maximum loss), become negative at long periods.

This result would suggest that holding stocks for long periods has a vanishing risk. However, using realistic price process models, we find numerically that the risk is increasing for about 30 years and starts to decrease only after that, reaching zero at around 100 years. Therefore, our final conlusion is that holding stocks is risky for all practically relevant periods.

Last modified: 2018.11.30.