Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLeverage Causes Fat Tails and Clustered Volatility
231
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We build a simple model of leveraged asset purchases with margin calls. Investment funds use what is perhaps the most basic financial strategy, called value investing, i.e. systematically attempting to buy underpriced assets. When funds do not borrow, the price fluctuations of the asset are normally distributed and uncorrelated across time. All this changes when the funds are allowed to leverage, i.e. borrow from a bank, to purchase more assets than their wealth would otherwise permit. During good times competition drives investors to funds that use more leverage, because they have higher profits. As leverage increases price fluctuations become heavy tailed and display clustered volatility, similar to what is observed in real markets. Previous explanations of fat tails and clustered volatility depended on irrational behavior, such as trend following. Here instead this comes from the fact that leverage limits cause funds to sell into a falling market: A prudent bank makes itself locally safer by putting a limit to leverage, so when a fund exceeds its leverage limit, it must partially repay its loan by selling the asset. Unfortunately this sometimes happens to all the funds simultaneously when the price is already falling. The resulting nonlinear feedback amplifies large downward price movements. At the extreme this causes crashes, but the effect is seen at every time scale, producing a power law of price disturbances. A standard (supposedly more sophisticated) risk control policy in which individual banks base leverage limits on volatility causes leverage to rise during periods of low volatility, and to contract more quickly when volatility gets high, making these extreme fluctuations even worse.
rate research
Read More
The leverage effect-- the correlation between an assets return and its volatility-- has played a key role in forecasting and understanding volatility and risk. While it is a long standing consensus that leverage effects exist and improve forecasts, empirical evidence paradoxically do not show that most individual stocks exhibit this phenomena, mischaracterizing risk and therefore leading to poor predictive performance. We examine this paradox, with the goal to improve density forecasts, by relaxing the assumption of linearity in the leverage effect. Nonlinear generalizations of the leverage effect are proposed within the Bayesian stochastic volatility framework in order to capture flexible leverage structures, where small fluctuations in prices have a different effect from large shocks. Efficient Bayesian sequential computation is developed and implemented to estimate this effect in a practical, on-line manner. Examining 615 stocks that comprise the S&P500 and Nikkei 225, we find that relaxing the linear assumption to our proposed nonlinear leverage effect function improves predictive performances for 89% of all stocks compared to the conventional model assumption.
Bid-ask spread is taken as an important measure of the financial market liquidity. In this article, we study the dynamics of the spread return and the spread volatility of four liquid stocks in the Chinese stock market, including the memory effect and the multifractal nature. By investigating the autocorrelation function and the Detrended Fluctuation Analysis (DFA), we find that the spread return is lack of long-range memory, while the spread volatility is long-range time correlated. Moreover, by applying the Multifractal Detrended Fluctuation Analysis (MF-DFA), the spread return is observed to possess a strong multifractality, which is similar to the dynamics of a variety of financial quantities. Differently from the spread return, the spread volatility exhibits a weak multifractal nature.
We develop a behavioral model for liquidity and volatility based on empirical regularities in trading order flow in the London Stock Exchange. This can be viewed as a very simple agent based model in which all components of the model are validated against real data. Our empirical studies of order flow uncover several interesting regularities in the way trading orders are placed and cancelled. The resulting simple model of order flow is used to simulate price formation under a continuous double auction, and the statistical properties of the resulting simulated sequence of prices are compared to those of real data. The model is constructed using one stock (AZN) and tested on 24 other stocks. For low volatility, small tick size stocks (called Group I) the predictions are very good, but for stocks outside Group I they are not good. For Group I, the model predicts the correct magnitude and functional form of the distribution of the volatility and the bid-ask spread, without adjusting any parameters based on prices. This suggests that at least for Group I stocks, the volatility and heavy tails of prices are related to market microstructure effects, and supports the hypothesis that, at least on short time scales, the large fluctuations of absolute returns are well described by a power law with an exponent that varies from stock to stock.
We investigate the large-volatility dynamics in financial markets, based on the minute-to-minute and daily data of the Chinese Indices and German DAX. The dynamic relaxation both before and after large volatilities is characterized by a power law, and the exponents $p_pm$ usually vary with the strength of the large volatilities. The large-volatility dynamics is time-reversal symmetric at the time scale in minutes, while asymmetric at the daily time scale. Careful analysis reveals that the time-reversal asymmetry is mainly induced by exogenous events. It is also the exogenous events which drive the financial dynamics to a non-stationary state. Different characteristics of the Chinese and German stock markets are uncovered.
We study the volatility time series of 1137 most traded stocks in the US stock markets for the two-year period 2001-02 and analyze their return intervals $tau$, which are time intervals between volatilities above a given threshold $q$. We explore the probability density function of $tau$, $P_q(tau)$, assuming a stretched exponential function, $P_q(tau) sim e^{-tau^gamma}$. We find that the exponent $gamma$ depends on the threshold in the range between $q=1$ and 6 standard deviations of the volatility. This finding supports the multiscaling nature of the return interval distribution. To better understand the multiscaling origin, we study how $gamma$ depends on four essential factors, capitalization, risk, number of trades and return. We show that $gamma$ depends on the capitalization, risk and return but almost does not depend on the number of trades. This suggests that $gamma$ relates to the portfolio selection but not on the market activity. To further characterize the multiscaling of individual stocks, we fit the moments of $tau$, $mu_m equiv <(tau/<tau>)^m>^{1/m}$, in the range of $10 < <tau> le 100$ by a power-law, $mu_m sim <tau>^delta$. The exponent $delta$ is found also to depend on the capitalization, risk and return but not on the number of trades, and its tendency is opposite to that of $gamma$. Moreover, we show that $delta$ decreases with $gamma$ approximately by a linear relation. The return intervals demonstrate the temporal structure of volatilities and our findings suggest that their multiscaling features may be helpful for portfolio optimization.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
