The Reactive Volatility Model

Valeyre, Sebastien; Aboura, Sofiane; Liu, Qian

doi:10.2139/ssrn.2126483

Cited by 3 publications

(12 citation statements)

References 14 publications

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“…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 (): for instance, if the stock index loses 1%,

\frac{L true(t true)}{I true(t true)}

increases by

ℓ \times 1 % = 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} = 0.46

.…”

Section: The Reactive Beta Modelmentioning

confidence: 79%

“…The appropriate levels,

L true(t true)

and

L_{i} true(t true)

, accounting for the leverage effect on the volatility to correctly normalize the difference in price, are introduced for the stock index and individual stocks, respectively:

L true(t true) = I true(t true) true(1 + \frac{L_{s} true(t true) - I true(t true)}{I true(t true)} true) true(1 + ℓ \frac{L_{f} true(t true) - I true(t true)}{L_{f} true(t true)} true),

L_{i} true(t true) = S_{i} true(t true) \underset{specificrisk}{\underset{⏟}{(1 + \frac{L_{i s} (t) - S_{i} (t)}{S_{i} (t)})}} \underset{systematicrisk}{\underset{⏟}{(1 + {italicℓ}_{i} \frac{L_{f} (t) - I (t)}{L_{f} (t)})}},

with the parameters

ℓ

and

ℓ_{i}

quantifying the leverage. The parameter

ℓ

is introduced by Valeyre et al () to reproduce the exponential fit of the returns’ volatility correlation function

L true(τ true)

at different time scales

τ

. The initial parameters of the exponen...…”

Section: The Reactive Beta Modelmentioning

confidence: 99%

“…This section aims at capturing 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 beta by using the renormalization factor that depends on the stock's overperformance. The model describes the systematic and specific leverage effects.…”

Section: The Reactive Volatility Modelmentioning

confidence: 99%

“…This correlation induces residual correlations between the stock overperformances and beta changes. In fact, earlier studies have heavily focused on the role of the leverage effect on volatility (Black, 1976;Christie, 1982;Campbell and Hentchel, 1992;Bekaert and Wu, 2000;Bouchaud et al, 2001;Valeyre et al, 2013). Surprisingly, despite its theoretical and empirical underpinnings, the leverage effect has not been considered so far in beta modeling, while it is a measure of risk.…”

Section: Introductionmentioning

confidence: 99%

“…We aim to close this gap. Our paper starts by investigating the role of the leverage effect in the correlation measure by extending the reactive volatility model (Valeyre et al, 2013), which efficiently tracks the implied volatility by capturing both the retarded effect induced by the specific risk and the panic effect, which occurs whenever the systematic risk becomes the dominant factor. This allows us to set up a reactive beta model incorporating three independent components, all of them contributing to the reduction of the bias of the hedging.…”

Section: Introductionmentioning

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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\frac{L true(t true)}{I true(t true)}

increases by

ℓ \times 1 % = 8 %

R^{2} = 0.46

.…”

Section: The Reactive Beta Modelmentioning

confidence: 79%

“…The appropriate levels,

L true(t true)

and

L_{i} true(t true)

, accounting for the leverage effect on the volatility to correctly normalize the difference in price, are introduced for the stock index and individual stocks, respectively:

L true(t true) = I true(t true) true(1 + \frac{L_{s} true(t true) - I true(t true)}{I true(t true)} true) true(1 + ℓ \frac{L_{f} true(t true) - I true(t true)}{L_{f} true(t true)} true),

L_{i} true(t true) = S_{i} true(t true) \underset{specificrisk}{\underset{⏟}{(1 + \frac{L_{i s} (t) - S_{i} (t)}{S_{i} (t)})}} \underset{systematicrisk}{\underset{⏟}{(1 + {italicℓ}_{i} \frac{L_{f} (t) - I (t)}{L_{f} (t)})}},

with the parameters

ℓ

and

ℓ_{i}

quantifying the leverage. The parameter

ℓ

is introduced by Valeyre et al () to reproduce the exponential fit of the returns’ volatility correlation function

L true(τ true)

at different time scales

τ

. The initial parameters of the exponen...…”

Section: The Reactive Beta Modelmentioning

confidence: 99%

Section: The Reactive Volatility Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The Reactive Beta Model

Valeyre¹,

Aboura

2019

J of Financial Research

Self Cite

View full text Add to dashboard Cite

show abstract

Should Employers Pay Their Employees Better?

Valeyre¹,

Liu²,

Aboura

et al. 2016

SSRN Journal

Self Cite

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Optimal trend following portfolios

Valeyre¹

2022

Preprint

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This paper derives an optimal portfolio that is based on trend-following signal. Building on an earlier related article, it provides a unifying theoretical setting to introduce an autocorrelation model with the covariance matrix of trends and risk premia. We specify practically relevant models for the covariance matrix of trends. The optimal portfolio is decomposed into four basic components that yield four basic portfolios: Markowitz, risk parity, agnostic risk parity, and trend following on risk parity. The overperformance of the proposed optimal portfolio, applied to cross-asset trading universe, is confirmed by empirical backtests. We provide thus a unifying framework to describe and rationalize earlier developed portfolios.

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The Reactive Volatility Model

Cited by 3 publications

References 14 publications

The Reactive Beta Model

The Reactive Beta Model

Should Employers Pay Their Employees Better?

Optimal trend following portfolios

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