The reactive volatility model

Valeyre, Sebastien; Aboura, Sofiane; Liu, Qian

doi:10.1080/14697688.2013.797594

Cited by 5 publications

(10 citation statements)

References 38 publications

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“…This section aims to capture the dependence of betas on stock overperformance (when a stock is overperforming, its beta tends to decrease). For this purpose, we rely on the methodology of the reactive volatility model (Valeyre et al 2013) to derive a stable measure of the beta by using the renormalization factor that depends on the stock's overperformance. The model describes the systematic and specific leverage effects.…”

Section: The Leverage Effect On Betamentioning

confidence: 99%

“…with the parameters ℓ and ℓ i quantifying the leverage. The parameter ℓ is introduced by Valeyre et al (2013) to reproduce the exponential fit of the returns' volatility correlation 2 In practice, a filtering function is introduced to attenuate the contribution from eventual outliers (extreme events or wrong data). The filter is applied to z ¼ Ls t (4) and (5) and is defined as F f z ð Þ ¼ tanhðfzÞ=f with f ¼ 3:3 (in the limit f ¼ 0, there is no filter: F 0 z ð Þ ¼ z).…”

Section: The Leverage Effect On Betamentioning

confidence: 99%

“…This reactive volatility captures a large part of the heteroskedascticity; that is, a large part of the volatility variation is completely explained by the leverage effect. That is the main result of Valeyre et al (2013): for instance, if the stock index loses 1%, L t ð Þ I t ð Þ increases by ℓ Â 1% ¼ 8%, and the stock index volatility increases by 8%. This effect is enough to capture a large part of the VIX (VIX Index is a measure of the one-month implied volatility of the U.S. stock market) variation, with R 2 ¼ 0:46.…”

Section: The Leverage Effect On Betamentioning

confidence: 99%

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The Reactive Beta Model

Valeyre¹,

Aboura

2019

J of Financial Research

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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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Section: The Leverage Effect On Betamentioning

confidence: 99%

Section: The Leverage Effect On Betamentioning

confidence: 99%

Section: The Leverage Effect On Betamentioning

confidence: 99%

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The Reactive Beta Model

Valeyre¹,

Aboura

2019

J of Financial Research

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“…Rigorously speaking, we consider additive logarithmic returns resized by realized volatility which is a common practice on futures markets [6,28]. Although asset returns are known to exhibit various non-Gaussian features (so-called "stylized facts" [29,30,31,32,33,34]), resizing by realized volatility allows one to reduce, to some extent, the impact of changes in volatility and its correlations [35,36], and to get closer to the Gaussian hypothesis of returns [37]. mean zero and the following covariance structure:…”

Section: Market Modelmentioning

confidence: 99%

Optimal allocation of trend following strategies

Serror¹

2015

Physica A: Statistical Mechanics and its Applications

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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 n 2 virtual assets that include lead-lag 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, inter-asset correlations are not deteriorative but beneficial for portfolio management that can open new profit opportunities for trend followers.

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“…For these reasons, we will study a simple model in which standardized logarithmic returns are Gaussian random variables [14] whose auto-correlations reflect random trends. Even though heavy tailed asymptotic distribution of returns and some other stylized facts are ignored [15,16,17,18,19,20,21,22,23,24], the Gaussian hypothesis will allow us to derive analytical results that can be later confronted to empirical market data. We will compute the probability distribution of P&Ls of a trend following strategy in order to understand how the Gaussian distribution of price variations is transformed by systematic trading.…”

Section: Introductionmentioning

confidence: 99%

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

Grebenkov

Serror²

2014

Physica A: Statistical Mechanics and its Applications

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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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The reactive volatility model

Cited by 5 publications

References 38 publications

The Reactive Beta Model

The Reactive Beta Model

Optimal allocation of trend following strategies

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

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