RESEARCH

The Reactive Beta Model

  Sebastien Valeyre, Denis Grebenkov, Sofiane Aboura (2019)

We present a reactive beta model that accounts for the leverage effect and beta elasticity. For this purpose, we derive a correlation metric for the leverage effect to identify the relation between the market beta and volatility changes. An empirical test based on the most popular market-neutral strategies is run from 2000 to 2015 with exhaustive data sets, including 600 U.S. stocks and 600 European stocks. Our findings confirm the ability of the reactive beta model to remove an important part of the bias from the beta estimation and from most popular market-neutral strategies. To examine the robustness of the reactive beta measurement, we conduct Monte Carlo simulations over seven market scenarios against five alternative methods. The results confirm that the reactive model significantly reduces the bias overall when financial markets are stressed.

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Should employers pay their employees better?

  Sebastien Valeyre, Denis Grebenkov, Sofiane Aboura, Qian Liu - Working paper (2017)

We uncover a new anomaly in asset pricing that is linked to the remuneration: the more a company spends on salaries and benefits per employee, the better its stock performs, on average. Moreover, the companies adopting similar remuneration policies share a common risk, which is comparable to that of the value premium. For this purpose, we set up an original methodology that uses firm financial characteristics to build factors that are less correlated than in the standard asset pricing methodology. We quantify the importance of these factors from an asset pricing perspective by introducing the factor correlation level as a directly accessible proxy of eigenvalues of the correlation matrix. A rational explanation of the remuneration anomaly involves the positive correlation between pay and employee performance.

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Optimal allocation of trend following strategies

  Denis S. Grebenkov*, Jeremy Serror - Physica A (2015)

We consider a portfolio allocation problem for trend following (TF) strategies on multiple correlated assets. Under simplifying assumptions of a Gaussian market and linear TF strategies, we derive analytical formulas for the mean and variance of the portfolio return. We construct then the optimal portfolio that maximizes risk-adjusted return by accounting for inter-asset correlations. The dynamic allocation problem for n assets is shown to be equivalent to the classical static allocation problem for n² virtual assets that include leadlag corrections in positions of TF strategies. The respective roles of asset auto-correlations and inter-asset correlations are investigated in depth for the two-asset case and a sector model. In contrast to the principle of diversification suggesting to treat uncorrelated assets, we show that inter-asset correlations allow one to estimate apparent trends more reliably and to adjust the TF positions more efficiently. If properly accounted for, interasset correlations are not deteriorative but beneficial for portfolio management that can open new profit opportunities for trend followers. These concepts are illustrated using daily returns of three highly correlated futures markets: the E-mini S&P 500, Euro Stoxx 50 index, and the US 10-year T-note futures

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Following a trend with an exponential moving average:
Analytical results for a gaussian model

  Denis S. Grebenkov*, Jeremy Serror - Physica A (2014)

We investigate how price variations of a stock are transformed into profits and losses (P&Ls) of a trend following strategy. In the frame of a Gaussian model, we derive the probability distribution of P&Ls and analyze its moments (mean, variance, skewness and kurtosis) and asymptotic behavior (quantiles). We show that the asymmetry of the distribution (with often small losses and less frequent but significant profits) is reminiscent to trend following strategies and less dependent on peculiarities of price variations. At short times, trend following strategies admit larger losses than one may anticipate from standard Gaussian estimates, while smaller losses are ensured at longer times. Simple explicit formulas characterizing the distribution of P&Ls illustrate the basic mechanisms of momentum trading, while general matrix representations can be applied to arbitrary Gaussian models. We also compute explicitly annualized risk adjusted P&L and strategy turnover to account for transaction costs. We deduce the trend following optimal timescale and its dependence on both auto-correlation level and transaction costs. Theoretical results are illustrated on the Dow Jones index.

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Option pricing with a dynamic fat-tailed model

  Sofiane Aboura, Sébastien Valeyre, Niklas Wagner - Journal of Derivatives & Hedge Funds (2014)

In the aftermath of the 2008 financial crisis, the need to consider more realistic risk models for derivative products has received renewed attention. We introduce a dynamic model for the pricing of European-style options with various attractive features such as a mixture of heavy-tails and Gaussian distribution along with a leverage effect property. We test the model on FTSE 100 stock index options during the period of January 2008 to June 2009. Our empirical results show that the model adequately fits the volatility smile dynamics particularly during stress periods. Furthermore, we find that the leverage effect form is driven by the sticky-strike rule.

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The reactive volatility model

  Sebastien Valeyre, Denis Grebenkov, Sofiane Aboura, Qian Liu - Quantitative Finance (2013)

Ce travail de recherche introduit notre modèle de volatilité implémenté dans le fonds JL Equity Market Neutral. Il permet une mesure réactive de la volatilité en tenant compte de l’effet de levier.

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