Leverage Effect

Description

The leverage effects refer to the tendency that past price return has the negative correlation with future volatility [Bouchaud_2001]. According to [Bouchaud_2001][Qiu_2006], this statistical property is quantified by the following lead-lag correlation function

\begin{equation} L(k)=\frac{E[r(t){|r(t+k)|}^{2}-r(t){|r(t)|}^{2}]}{E[|r(t)|^{2}]^{2}}. \end{equation}

In contrast to other statistical properties, this property is market dependent [Qiu_2006] The paper reported that the negative correlation (leverage effect) is observed in German DAX, while the positive correlation (so-called anti-leverage effect) is detected in Chinese markets.

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Fig. Averaged result for S&P500 firms daily price return

Code Example

import datetime as dt
import pandas_datareader.data as web
import numpy as np
import stylefact.finance as sff
import stylefact.visualize as sfv
st = dt.datetime(1990,1,1)
en = dt.datetime(2020,1,1)
data = web.get_data_yahoo('GM', start=st, end=en)
prices = data['Adj Close'].to_numpy()
log_prices = np.log(prices)
returns = np.diff(log_prices)
x,y = sff.leverage_effect(returns)
sfv.leverage_effect(x,y,'leverage_effect')

References

[BMP01]

(1, 2) Jean-Philippe Bouchaud, Andrew Matacz, and Marc Potters. Leverage effect in financial markets: the retarded volatility model. Physical Review Letters, 87:228701, 2001.

[QZRT06]

(1, 2) T. Qiu, B. Zheng, F. Ren, and S. Trimper. Return-volatility correlation in financial dynamics. Physical Review E, 73(6):065103, 2006.