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.

Were Cobb and Douglas Prejudiced? A Critical Re-analysis of their 1928 Production Model Identification

In 1928 Cobb and Douglas (C&D) presented a system analysis which established the first empirically identified production model, which forms the foundation for Solow's growth theory and research into productivity growth factors, such as 'technological progress ' and 'human capital development '. C&D claimed that their production model ('function') showed neutral economies of scale, i.e., constant returns to scale, with a labor production elasticity of 3/4 and a capital production elasticity of 1/4. A simple CLS analysis shows that C&D's data were incorrectly identified by an (n,q)=(3,1) linear model. C&Ds claim that their neutral 'constant returns of scale ' was the inevitable scientific conclusion of their analysis was also incorrect, since that conclusion is strictly determined by their subjectively chosen projection direction. In fact, the data shows that with their model and identification technology constant, increasing and diminishing returns to scale are all three compatible with the uncertain data. Their (n,q) = (3,1) model was never identified with an acceptable level of scientific accuracy, with a maximum coefficient value variation of 212%). In contrast, a simple two-equation (n,q) = (3,2) system model can be accurately identified from C&Ds data set, with an acceptable level of accuracy, with a maximum coefficient value variation of 7.4%).System identification, growth theory, production elasticities, projections, Complete Least Squares, noisy data

Optimal Asian Multi-Currency Strategy Portfolios with Exact Risk Attribution

In an earlier paper (Los, 1998a), the exact and complete return attribution framework of Singer and Karnosky (1995) was extended to include market risk measurements for n countries. Exploiting a selection matrix based on the cash accounting identities, the resulting degenerate portfolio choice problem is solved as a lower dimensional, non- degenerate problem of fundamental investment choices between stock market premiums and currency swap returns. The original n2 multi- currency strategic investment allocations are uniquely retrieved from the resulting 2n optimal fundamental choice allocations. This new optimal return-risk attribution accounting framework is applied to monthly return data of Hong Kong, Indonesia, Japan, Malaysia, the Philippines, Singapore, Thailand, the USA and Germany from June 1992 through December 1997. This includes the illustrative period of the Asian currency crisis of July - December 1997. The USA and Germany are included as alternative low risk strategic investment allocations in the Asian portfolio for further diversification. Throughout this five and a half year period, Asian risk levels, as measured by the GMV standard deviations of return, were about five times the corresponding average returns. The evidence shows that most of the strategic investment risk in Asian countries is attributable to the risk amplitudes of the stock markets, followed by those of the currency markets and, least, the cash markets. The Thai stock market was the most volatile market to invest in throughout the period. The currency swaps caused the spreading contagion. For a U.S. dollar based Asian investor, GMV portfolio risk could have been reduced by half and his return could have been doubled, when the USA would have been included in his portfolio. In contrast, diversification to Germany (Europe) would only marginally have contributed to portfolio risk reduction. Risk management in Asia was hazardous. Spectral analysis of the covariance risks shows that during the investigated period the Asian portfolio efficiency frontier was non- stationary and that the Asian diversification risk and systematic risk changed over time in a few specific countries.

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

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

Visualization of Chaos for Finance Majors

E¤orts to simulate turbulence in the financial markets include experiments with the dynamic logistic parabola. Visual investigation of the logistic process show the various stability regimes for a range of the real growth parameter. Visualizations for the initial 20 observations provide clear demonstrations of rapid stabilization of the process regimes.chaos, intermittency, nonlinear dynamics

The Unscientific Incompleteness and Bias of Unidirectional Projections (= Regressions): A Questionnaire

Why do statisticians (econometricians, economists, financial analysts, etc.) continue to incompletely identify the algebraic/geometric structure of the multi-variate data series they profess to analyze, and instead continue to publish the results of incomplete, prejudiced and biased unidirectional projections (= 'regressions') of such covariance structures? Such incomplete, prejudiced and biased representations cannot lead to scientific knowledge, as has been demonstrated already more than twenty years ago.system identification, noisy data, regression analysis, projection, incompleteness, prejudice, bias

The Degree of Stability of Price Diffusion

The distributional form of financial asset returns has important implications for the theoretical and empirical analyses in economics and finance. It is now a well-established fact that financial return distributions are empirically nonstationary, both in the weak and the strong sense. One first step to model such nonstationarity is to assume that these return distributions retain their shape, but not their localization (mean ) or size (volatility ) as the classical Gaussian distributions do. In that case, one needs also to pay attention to skewedness and kurtosis, in addition to localization and size. This modeling requires special Zolotarev parametrizations of financial distributions, with a four parameters, one for each relevant distributional moment. Recently popular stable financial distributions are the Paretian scaling distributions, which scale both in time T and frequency . For example, the volatility of the lognormal financial price distribution, derived from the geometric Brownian asset return motion and used to model Black-Scholes (1973) option pricing, scales according to T^{0.5}. More generally, the volatility of the price return distributions of Calvet and Fisher's (2002) Multifractal Model for Asset Returns (MMAR) scales according to T^{(1/(_{Z}))}, where the Zolotarev stability exponent _{Z} measures the degree of the scaling, and thus of the nonstationarity of the financial returns. Keywords: Stable distributions, price diffusion, stability exponent, Zolotarev parametrization, fractional Brownian motion, financial markets.Stable distributions, price diffusion, stability exponent, Zolotarev parametrization, fractional Brownian motion, financial markets