Nonparametric Testing of the High-Frequency Efficiency of the 1997 Asian Foreign Exchange Markets

For the first time, non-parametric statistical tests, originally developed by Sherry (1992) to test the efficiency of information processing in nervous systems, are used to ascertain if the Asian FX rates followed random walks. The stationarity and serial independence of the price changes are tested on minute-by-minute data for nine currencies for the period from January 1, 1997 to December 30, 1997. Tested were the Thai baht, Indonesian rupiah, Malaysian ringgit, Philippines' peso, Singapore dollar, Taiwan dollar and the Hong Kong dollar, with the Japanese Yen and German Deutschmark as benchmarks (The U.S. Dollar is the base currency). The efficiency of these FX markets before and after the onset of the Asian currency turmoil (i.e., January 1 - June 30, 1997 and July 1 - December 30, 1997) are compared. The Thai baht, Malaysian ringgit, Indonesian rupiah and Singapore dollar exhibited non-stationary behavior during the entire year, and gave evidence of a trading regime break, while the Phillipines' peso, Taiwan dollar, Yen and Deutschmark remained stationary (The Hong Kong dollar was pegged). However, each half-year regime showed stationarity by itself, indicating stable and nonchaotic trading regimes for all currencies, despite the high volatilities, except the Malaysian ringgit, which exhibited non-stationarity in the second half of 1997. The Thai baht traded nonstationarily in the first half of 1997, but stationarily in the second half, while the Taiwan dollar reversed that trading pattern. Regarding Sherry's four serial independence tests of differential spectrum, relative price changes, temporal trading windows of at least 20 minutes long and price change category transitions: none of the currencies exhibited complete independence. Thus no Asian currency market - including the Yen - exhibited complete efficiency in 1997 regarding both stationarity and independence, in particular when compared with the highly efficient Deutschmark. But, remarkably, the Phillippines' peso remained as efficient as the Japanese Yen throughout 1997.

Valuation of Six Asian Stock Markets: Financial System Identification in Noisy Environments

The open financial economic systems of six Asian countries Taiwan, Malaysia, Singapore, Philippines, Indonesia and Japan - over the period 1986 through 1995 are identified from empirical data to determine how their stock markets, economies and financial markets are interrelated. The objective is to find rational stock market valuations using a country's nominal GDP and a short term interest rate, based on a modified version of the Dividend Discount Model. But our empirical results contradict such conventional financial economic theory. Various methods are used to analyze the 3D data covariance ellipsoids: spectral analysis, analysis of information matrices, 2D and 3D noise/signal determination and ''super-filter'' system identification based on 3D projections. The new ''super-filter'' method provides the sharpest identification of the Grassmanian invariant q of the empirical systems and the best computation of the finite boundaries of the empirical parameter ranges. All six Asian systems are high noise environments, in which it is very difficult to separate systematic signals from noise. Because of these high noise levels, spectral analysis is not reliable. By plotting all 3D q = 2 {Complete} Least Squares projections we find that only Taiwan has a clear q = 2 system, i.e., Taiwan's stock market, economy and financial market are rationally coherent. In contrast, Malaysia, Singapore, Philippines and Indonesia have q = 1 systems, in which stock markets and economies are closely related, but unrelated to the respective domestic financial markets. Several possible economic explanations are provided. We also quantitatively establish the incoherence of Japan's financial economic system. Japan's stock market operates independently from its economy and from its financial market, which are mutually unrelated.

When to Put All Your Eggs in One Basket.....When Diversification Increases Portfolio Risk!

Portfolio diversification may not always lower the portfolio risk, but may actually increase it. It depends on the long memory and distributional stability characteristics of the underlying rates of return. This disturbing result is based on the theoretical Fama- Samuelson proposition of 1965-67. However, there exists now ample empirical evidence for such peculiar results, since most financial return series show long memory, e.g., the S&P500 Index return series. Illiquid real estate and bank loan values are sometimes subject to catastrophic discontinuities. Adding these assets to the portfolio may increase its risk drastically.portfolio management, distibutional stability, long memory, financial risk,

Optimal Multi-Currency Investment Strategies with Exact Attribution in Three Asian Countries

Singer and Karnosky's (1995) exact and complete return attribution framework does not account for risk, since it ignores accumulated historical information. Its implied investment strategy selection is based on simple return maximization and ignores that investment strategies are correlated via intra-and inter-market risks. Using simple tensor algebra we extend their exact accounting framework to include market risk measurements for n countries. The resulting n^2 x n^2 strategy risk matrix exactly decomposes into a tensor sum of the n x n fundamental market risk matrices. Since the strategy risk matrix is singular with rank = 2n-1

Visualization of Chaos for Finance Majors

Efforts to simulate turbulence in the financial markets include experiments with the logistic equation: x(t)=kappa x(t-1)[1-x(t-1)], with 0Logistic Equation, Visualization, Strange Attractor, Chaos, Hurst Exponent

Why VAR Fails: Long Memory and Extreme Events in Financial Markets

The Value-at-Risk (VAR) measure is based on only the second moment of a rates of return distribution. It is an insufficient risk performance measure, since it ignores both the higher moments of the pricing distributions, like skewness and kurtosis, and all the fractional moments resulting from the long - term dependencies (long memory) of dynamic market pricing. Not coincidentally, the VaR methodology also devotes insufficient attention to the truly extreme financial events, i.e., those events that are catastrophic and that are clustering because of this long memory. Since the usual stationarity and i.i.d. assumptions of classical asset returns theory are not satisfied in reality, more attention should be paid to the measurement of the degree of dependence to determine the true risks to which any investment portfolio is exposed: the return distributions are time-varying and skewness and kurtosis occur and change over time. Conventional mean-variance diversification does not apply when the tails of the return distributions ate too fat, i.e., when many more than normal extreme events occur. Regrettably, also, Extreme Value Theory is empirically not valid, because it is based on the uncorroborated i.i.d. assumption.Long memory, Value at Risk, Extreme Value Theory, Portfolio Management, Degrees of Persistence

The controllability function method

The paper is devoted to the control problem for the movement of an overhead crane with the use of a dynamic model in the form of "trolley - cargo" mechanical system and the driving force as a control parameter. To solve the system of differential equations, which describe the movement of the system taking into account constraints for the control, the controllability function method is applied. The algorithm for solving the problem is described, a program is developed as well as difficulties, which occur while implementing the method, and ways of its solution are marked. Results of constructing the control and system trajectories are also provided as an example of the program work

Dynamic Risk Profile of the US Term Structure by Wavelet MRA

A careful examination of interest rate time series from different U.S. Treasury maturities by Wavelet Multiresolution Analysis (MRA) suggests that the first differences of the term structure of interest rate series are periodic or, at least, cyclic, non-stationary, long-term dependent, in particular, anti-persistent. Each nodal time series from a particular maturity has its own uniqueness and accordingly supports the Market Segmentation theory. The findings also imply that affine models are insufficient to describe the dynamics of the interest rate diffusion processes and call for more intensive research that might provide better, most likely fractal or nonlinear, term structure models for each maturity. If this is correct, empirical term structure models may describe chaotic, i.e., diffusion processes with non-unique dynamic equilibria.Wavelet, Interest rates, Hurst exponent, Term structure, Yield curve

Persistence Characteristics of the Chinese Stock Markets

This paper identifies such fundamental characteristics as the lack of ergodicity, stationarity, and independence, and it identifies the degree of initial persistence of the Chinese stock markets when they were more regulated. The index series are from the Shanghai (SHI) stock market and Shenzhen A-shares (SZI) and B-shares (SZBI) stock markets, before and after the various deregulations and reregulations. Accurate and complete signal processing methods are applied to the complete series and to their sub-periods. The evidence of lack of stationarity and ergodicity can be ascribed to two causes: (1) the initial interventions in these stock markets by the Chinese government by imposing various daily price change limits, and (2) the changing trading styles in the course of the development of these emerging stock markets, after the Chinese government left these equity markets to develop by themselves. By computing the markets' monofractal Hurst exponents (and its accuracy range with a new statistic), using wavelet multiresolution analysis (MRA), we identify the markets' subsequent degrees of persistence. The empirical evidence shows that SHI, SZI, and SZBI are moderately persistent with Hurst exponents slightly greater than the Fickian 0.5 of the Geometric Brownian Motion. It also shows that these stock markets were considerably more persistent before the deregulations, but that they now move much more like geometric Brownian motions, i.e., efficiently. Our results also show that the Chinese stock markets are gradually and properly integrating into one Chinese stock market. Our results are consistent with similar empirical findings from Latin American, European, and other Asian emerging financial markets.Long-term dependence, degrees of persistence, Hurst exponent, wavelet multiresolution analysis, Chinese equity markets

Multifractal Modeling of the US Treasury Term Structure and Fed Funds Rate

This paper identifies the Multifractal Models of Asset Return (MMARs) from the eight nodal term structure series of US Treasury rates as well as the Fed Funds rate and, after proper synthesis, simulates those MMARs. We show that there is an inverse persistence term structure in the sense that the short term interest rates show the highest persistence, while the long term rates are closer to the GBM's neutral persistence. The simulations of the identified MMAR are compared with the original empirical time series, but also with the simulated results from the corresponding Brownian Motion and GARCH processes. We find that the eight different maturity US Treasury and the Fed Funds rates are multifractal processes. Moreover, using wavelet scalograms, we demonstrate that the MMAR outperforms both the GBM and GARCH(1,1) in time-frequency comparisons, in particular in terms of scaling distribution preservation. Identified distributions of all simulated processes are compared with the empirical distributions in snapshot and over time-scale (frequency) analyses. The simulated MMAR can replicate all attributes of the empirical distributions, while the simulated GBM and GARCH(1,1) processes cannot preserve the thick-tails, high peaks and proper skewness. Nevertheless, the results are somewhat inconclusive when the MMAR is applied on the Fed Funds rate, which has globally a mildly anti-persistent and possibly chaotic diffusion process completely different from the other nodal term structure rates.MMAR, multifractal spectrum, long memory, scaling, term stucture, persistence, Brownian motion, GARCH, time-frequency analysis