Chaos and Nonlinear Dynamics: Application to Financial Markets

After the stock market crash of October 19, 1987, interest in nonlinear dynamics, especially deterministic chaotic dynamics, has increased in both the financial press and the academic literature. This has come about because the frequency of large moves in stock markets is greater than would be expected under a normal distribution. There are a number of possible explanations. A popular one is that the stock market is governed by chaotic dynamics. What exactly is chaos and how is it related to nonlinear dynamics? How does one detect chaos? Is there chaos in financial markets? Are there other explanations of the movements of financial prices other than chaos? The purpose of this paper is to explore these issues.     

Nonlinearity and Low Deterministic Chaotic Behavior in Insurance Portfolio Stock Returns

This article presents new empirical evidence indicating a deterministic component in the portfolio return dynamics of life‐health and property‐liability insurance company stocks. Our research is motivated by the fact that nonlinearities are a fact of economic life for many financial applications the source of which is logically apparent, yet empirical evidence of their existence is at best weak. The primary reason attributed to the weak findings of nonlinearities reported in previous research is the use of aggregate data that can hide nonlinearities at the micro level. Insurance sector stock returns are analyzed because unique institutional characteristics indicate the possibility of identifying nonlinear dynamics. Tests based on the correlation dimension partially confirm the presence of nonlinearity. However, the more powerful Brock, Dechert, and Scheinkman (BDS) statistic strongly suggests the presence of nonlinearities in the insurance stock portfolio data. The BDS statistic applied to the standardized residuals of exponential generalized auto regressive conditional heteroskedasticity (EGARCH) models strongly rejects the null of independent and identically distributed, indicating that conditional heteroskedasticity is not responsible for the presence of the nonlinear structures in the data. In addition, tests for chaos based on locally weighted regressions indicate that insurance stock portfolio returns indicate low‐complexity chaotic behavior. This is an important result since most previous research has failed to report evidence of chaotic behavior in the time series of stock returns. Important contributions of this article are the application of tests of nonlinearities and chaos to more desegregated data sets and the findings of statistically significant evidence indicating nonlinearities and low‐deterministic chaotic behavior in insurance stock portfolio returns.     

The behaviour of some UK equity indices: An application of Hurst and BDS tests

The characterisation of equity market return series as random in nature has been questioned in recent times by the application of new statistical tools. This study uses recent advances in chaos theory to examine the behaviour of the London Financial Times Stock Exchange (FTSE) All Share, 100, 250 and 350 equity indices. The results reject the hypothesis that the index series examined in this study are random, independent and identically distributed. The results show that the FTSE stock index returns series is not truly random since some cycles or patterns show up more frequently than would be expected in a true random series. A Generalized Autoregressive Conditional Heteroskedasticity (GARCH(1,1)) process appears to explain the behaviour of the index series. The results may have implications for derivative instruments on the indices as well as for weak form market efficiency.     

Contagion effect in financial markets after the South-East Asia Tsunami

Powerful earthquakes may cause heavy damage to the financial markets of individual countries (regions), and may even spillover to other countries (regions). Using 26 international stock indexes and exchange rates, this study examines whether any contagion effect occurred across financial markets after the strong earthquake in South-East Asia on December 26, 2004. Using heteroscedasticity biases based on correlation coefficients to examine the existence of the contagion effect, this study shows that no individual country stock market suffered from the contagion effect, but that the foreign exchange markets of some countries (namely India, Philippines and Hong Kong) did suffer from the contagion effect.     

NONLINEAR DYNAMICS AND THE DISTRIBUTION OF DAILY STOCK INDEX RETURNS

Three alternative models of daily stock index returns are considered: (1) a diffusion-jump process; (2) an extended generalized autoregressive conditional heteroskedasticity (GARCH) process; and (3) a combination of the GARCH and jump processes. Non-nested tests between the diffusion-jump process and a GARCH(1.1) process with t-distributed errors reject the diffusion-jump process, but do not always reject the GARCH process. Kolmogorov-Smirnov tests of fit, however, reject the GARCH(1,1)-t process for all cases. Nonlinear dependence is not removed for the value-weighted index and the S&P 500 stock index; therefore, deterministic chaos cannot be dismissed.     

Multiscale analysis of economic time series by scale-dependent Lyapunov exponent

Economic time series usually exhibit complex behavior such as nonlinearity, fractal long-memory, and non-stationarity. Recently, considerable efforts have been made to detect chaos and fractal long-memory in finance. While evidence supporting fractal scaling in finance has been accumulating, it is now generally thought that financial time series may not be modeled by chaos or noisy chaos, since the estimated Lyapunov exponent (LE) is negative. A negative LE amounts to a negative Kolmogorov entropy, and thus implies simple regular dynamics of the economy. This is at odds with the general observation that the economy is highly complicated due to nonlinear and stochastic interactions among component systems and hierarchical regulations in the world economy. To resolve this dilemma, and to provide an effective means of characterizing fractal long-memory properties in non-stationary economic time series, we employ a multiscale complexity measure, the scale-dependent Lyapunov exponent (SDLE), to characterize economic time series. SDLE cannot only unambiguously distinguish low-dimensional chaos from noise, but also detect high-dimensional and intermittent chaos, as well as effectively deal with non-stationarity. With SDLE, we are able to show that the reported negative LE may correspond to large-scale convergence, but not imply the absence of small-scale divergence or noisy chaos in the world economy. Using US foreign exchange rate data as examples, we further show how SDLE can readily characterize fractal, persistent or anti-persistent long-range correlations in economic time series.     

Stock market performance and manufacturing capability of the fifth long-cycle industries

Nearly 80 years ago Russian economist, Kondratieff, introduced the theory of economic long-cycles. Since from the start, this theory has faced controversial acceptance; for example, in the future studies researchers have used it to develop further specific applications, but in economics some leading scientists reject the entire idea still. Although, this theory is well developed, there does not exist research from the examination of relation between stock market performance, and leading innovation cycle industries manufacturing capacity addition and utilization. Based on the system dynamics model, called world dynamics, capacity addition and utilization have earlier been identified as the leading indicators of long-cycles.Our research results in this paper indicate that capacity utilization of computer manufacturing in US, and in some cases of US semiconductors, has influence on the stock market indexes of Nasdaq, S&P500 and Dow. However, it should be noted that capacity investment changes of these three examined industries (semiconductors, computers and telecommunications) are involved in the proposed regression models too. Further analysis reveals, that we are able to build regression models for all three stock indexes, containing only two variables. Notably, these two variables are capacity addition change in semiconductors and computers. This observation further increases discussion, whether we should be interested only about capacity addition changes of innovation wave industries, and possibly give secondary importance for the utilization.     

On the long-term or short-term dependence in stock prices: Evidence from international stock markets

This study examines the short- and long-term dependence in the United States and 21 international equity market indexes. Two heteroscedastic-robust testing methods, the modified rescaled range analysis and the rescaled variance ratio test, are employed to test for the existence of dependence. The evidence consistently reveals the absence of long-term dependence in these 22 stock returns indexes. The random walk hypothesis for most, but not all, stock returns indexes is not rejected. When the random walk hypothesis is rejected, the evidence supporting the rejection is weak and the stochastic dependence occurs mainly in short-horizon, rather then long-horizon holding period returns.     

The search for evidence of chaos in FTSE-100 daily returns

This study provides an elementary discussion of deterministic chaos as it applies to security returns. the study demonstrates a simple technique, well known in the physical sciences, for discriminating between random and chaotic time-series. Applying the technique to a time-series of daily returns on the FTSE-100, an index comprised of the stocks of the 100 largest British firms, results in evidence that the time-series is random, not chaotic.     

Stock market crashes,firm characteristics,and stock returns

A number of studies have investigated the causes and effects of stock market crashes. These studies mainly focus on the factors leading to a crash and on the volatility and co-movements of stock market indexes during and after the crash. However, how a stock market crash affects individual stocks and if stocks with different financial characteristics are affected differently in a stock market crash is an issue that has not received sufficient attention. In this paper, we study this issue by using data for eight major stock market crashes that have taken place during the December 31, 1962–December 31, 2007 period with a large sample of US firms. We use the event-study methodology and multivariate regression analysis to study the determinants of stock returns in stock market crashes.     

How does Monetary Policy Influence Capital Markets? Using a Threshold Regression Model

This study indicates that the effects of interest rate changes on stock prices could be twofold and that the net effect is determined by which effect is dominant. The study employs a threshold regression model to see if, before and after the central banks cut the interest rates, there is a nonlinear relation between interest rates and the stock index. Based on traditional economic theory, stock prices should be inversely related to interest rates. However, the present study finds that as interest rates start to increase or decrease, the stock index prices are significantly and positively related to the interest rates. The changes in interest rates affect stock indexes inversely only after interest rates have crossed a certain threshold. The inverse U-shaped relationship between interest rates and stock indexes differs from the traditional wisdom. It could make interest rates more valuable in forecasting stock indexes, and it holds implications for monetary policies of central banks. To avoid the spurious regression problem, this study uses a cointegration test and an error correction model to confirm the results from the threshold regression model and finds that there is a significant cointegration relationship before and after central banks cut interest rates.     

Speculative bubbles in emerging stock markets and macroeconomic factors: A new empirical evidence for Asia and Latin America

The purpose of this study is firstly to test for the existence of periodically collapsing stock price bubbles in Asian and Latin American emerging stock markets for the period 1990–2009. We use the new non-cointegration test developed by Taylor and Peel (1998) with the Residuals-Augmented Least Squares (RALS) method of Im (1996) and Im and Schmidt (2008) for monthly data of price indexes and dividends. The results show that the hypothesis of formation of bubbles cannot be rejected for all of the studied emerging stock markets. This evidence implies that the co-integration relation between the prices and the dividends is not always supported, indicating that the stock prices do not reflect their fundamental values in the emerging stock markets. We then link speculative bubbles with macroeconomic and financial factors, which is an interesting contribution of this study. The degree of equity market openness is found to be the key factor, positively related to the formation of speculative bubbles in these markets.     

Do economic statistics contain information to predict stock indexes futures prices and returns? Evidence from Asian equity futures markets

This research examines the impact of local and international market factors on the pricing of stock indexes futures in East Asian countries. The purpose of this paper is to present a study of the significant factors that determine the major stock indexes futures’ prices of Hong Kong, Malaysia, Singapore, South Korea and Taiwan. This study first investigates the relationships between Hang Seng Index Futures, KLCI Futures, SiMSCI Futures, KOSPI Futures, Taiwan Exchange Index Futures and local interest rates, dividend yields, local exchange rates, overnight S&P500 index and a newly constructed index, Asian Tigers Malaysia Index (ATMI). 11 years historical data of stock indexes futures and the economic statistics are studied; 10 years in-sample data are used for testing and developing the pricing models, and 1 year out-of-sample data is used for the purpose of verifying the predicted values of the stock indexes futures. Using simple linear regressions, local interest rates, dividend yields, exchange rates, overnight S&P500 and ATMI are found to have significant impact on these futures contracts. In this research, the next period close is predicted using simple linear regression and non-linear artificial neural network (ANN). An examination of the prediction results using nonlinear autoregressive ANN with exogenous inputs (NARX) shows significant abnormal returns above the passive threshold buy and hold market returns and also above the profits of simple linear regression (SLR). The empirical evidence of this research suggests that economic statistics contain information which can be extracted using a hybrid SLR and NARX trading model to predict futures prices with some degree of confidence for a year forward. This justifies further research and development of pricing models using fundamentally significant economic determinants to predict futures prices.

     

基于全市场视角的"权证热"隐患研究

尽管金融衍生品的出现符合金融发展规律,但子产品的推出必须服务于服从于母产品市场健康发展的需要与可能,即我国权证产品的创设和推进,既要反映股票市场的实际需要和未来趋势,更要考虑其所处阶段和现有条件的客观制约.如果"母""子"市场的发展呈不匹配状态,我国股票市场必将凸显诸如市场基础空心化、市场创新庸俗化、市场风险放大化、市场收益博弈化、市场功能紊乱化和市场监管式微化等多重隐患.     

Safe havens in Islamic financial markets: COVID-19 versus GFC

Using a bivariate dynamic conditional correlation (DCC) generalized autoregressive conditional heteroskedasticity (GARCH) model, this study compares the safe-haven properties of various assets against the major Gulf Cooperation Council (GCC) stock indexes during two periods of financial turmoil, the COVID-19 pandemic and the 2008 Global Financial Crisis (GFC). Sovereign bonds offered the highest hedging benefits under both crises. The traditional safe assets, gold and silver, which were reasonably productive under the GFC, have been less so during the pandemic. The Japanese yen emerged as a very safe choice for investors holding GCC stock indexes. Both sector indexes and stock indexes failed to safeguard investors most of the time during each crisis.     

Robust Structure Without Predictability: The “Compass Rose” Pattern of the Stock Market

Plotting daily stock returns against themselves with one day's lag reveals a striking pattern. Evenly spaced lines radiate from the origin; the thickest lines point in the major directions of the compass. This “compass rose” pattern appears in every stock. It is caused by discreteness. However, counter-examples demonstrate that the existence of exchange-imposed tick sizes (e.g. eighths) is neither necessary nor sufficient for the compass rose. The compass rose cannot be used to make abnormal profits: it is structure without predictability. Among other consequences, the compass rose may bias estimation of ARCH models, and tests for chaos.     

Realizing stock market crashes: stochastic cusp catastrophe model of returns under time-varying volatility

This paper develops a two-step estimation methodology that allows us to apply catastrophe theory to stock market returns with time-varying volatility and to model stock market crashes. In the first step, we utilize high-frequency data to estimate daily realized volatility from returns. Then, we use stochastic cusp catastrophe theory on data normalized by the estimated volatility in the second step to study possible discontinuities in the markets. We support our methodology through simulations in which we discuss the importance of stochastic noise and volatility in a deterministic cusp catastrophe model. The methodology is empirically tested on nearly 27 years of US stock market returns covering several important recessions and crisis periods. While we find that the stock markets showed signs of bifurcation in the first half of the period, catastrophe theory was not able to confirm this behaviour in the second half. Translating the results, we find that the US stock market’s downturns were more likely to be driven by the endogenous market forces during the first half of the studied period, while during the second half of the period, exogenous forces seem to be driving the market’s instability. The results suggest that the proposed methodology provides an important shift in the application of catastrophe theory to stock markets.     

A Likelihood Ratio Test of Price Volatilities: Comparing Stock Index Spot and Futures

This paper uses three methods to estimate the price volatility of two stock market indexes and their corresponding futures contracts. The classic variance measure of volatility is supplemented with two newer measures, derived from the Garman-Klass and Ball-Torous estimators. A likelihood ratio test is used to compare the classic variance measure of price volatilities of two stock market indexes and their corresponding futures contracts during the bull market of the 1980s. The stock market volatilities of the Standard & Poor's 500 (S&P 500) and New York Stock Exchange (NYSE) indexes were found to be significantly lower than their respective futures price volatilities. Since information may flow faster in the futures markets than in the corresponding stock market, our results support Ross's information-volatility hypothesis. It was also noted that the NYSE spot volatility was lower than the S&P 500 spot volatility. If the rate of information flow and firm size are positively related, then the lower NYSE spot volatility is explained by the size effect. The futures price volatilities for the two indexes were insignificantly different from each other. With stock index spot-futures price correlations approaching unity, one implication of our results for index futures activity is that smaller positions in futures contracts may suffice to achieve hedging or arbitrage goals.     

Responsible investment in the Chinese stock market

This paper provides insights into the current development of responsible investment in the Chinese stock market. We find that responsible investment can bring portfolio benefits to investors, and institutional investors have a holding preference for stocks in responsible investment indexes. By using a national air pollution proxy, we find that investors’ pessimistic mood on days with heavy air pollution has a negative influence on the stock return of A-shares, while stocks in responsible investment indexes display improved performance over the same time period. We use aggregated trading data to study the trading preference of Chinese retail investors on days when they are influenced by air pollution, and find that their total trading ratio shows a negative influence for both A-shares and responsible investment indexes. Moreover, there is more seller-initiated trading of the whole sample but more buyer-initiated trading of stocks in responsible investment indexes on air pollution days. This finding is consistent with the different stock return performances of these two samples. Our finding extends the studies of responsible investment to emerging markets and presents new evidence about the influence of environmental factors on trading behavior and return performance.     

Public Information Arrival and the Fisher Effect in Emerging Markets: Evidence from Stock and Bond Markets in Turkey

We examine the impact of inflation on nominal stock returns and interest rates in Turkey's emerging economy, which has a moderately high, persistent, and volatile inflation rate. Empirical evidence indicates that Turkey's inflation increased more than nominal stock returns and interest rates, implying that real returns to investors declined during our sample period. Among the different sector indexes we study, the financials sector serves as the best hedge against expected inflation, and the Fisher effect appears to hold only for this sector. We also find that public information arrival plays an important role, especially in the stock market.