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

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.

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

Measurement of Financial Risk Persistence

This paper discusses various ways of measuring the persistence or Long Memory (LM) of financial market risk in both its time and frequency domains. For the measurement of the risk, irregularity or 'randomness' of these series, we can compute a set of critical Lipschitz - Hölder exponents, in particular, the Hurst Exponent and the Lévy Stability Alpha, and relate them to the Mandelbrot-Hoskings' fractional difference operators, as occur in the Fractional Brownian Motion model (which is our benchmark). The main contribution of this paper is to provide a compaison table of the various critical exponents available in various scientific disciplines to measure the LM persistence of time seies. It also discusses why Markov- and (G)ARCH models cannot capture this LM, long term dependence or risk persistence, because these models have finite lag lengths, while the empirically observed long memory risk phenomenon is an infinite lag length phenomenon. Currently, there are three techniques of nonstationary time series analysis to measure time - varying financial risk: Range/Scale analysis, windowed Fourier analysis, and wavelet MRA. This paper relates these powerful analytic techniques to classical Box-Jenkins-type time series analysis and to Pearson's spectral frequency analysis, which both rely on the uncorroboated assumption of stationarity and ergodicity.Persistence, long memory, dependence, time series, frequency, critical exponents, fractional Brownian motion, (G)ARCH, risk measurement

Measuring Financial Cash Flow and Term Structure Dynamics

Financial turbulence is a phenomenon occurring in anti - persistent markets. In contrast, financial crises occur in persistent markets. A relationship can be established between these two extreme phenomena of long term market dependence and the older financial concept of financial (il-)liquidity. The measurement of the degree of market persistence and the measurement of the degree of market liquidity are related. To accomplish the two research objectives of measurement and simulation of different degrees of financial liquidity, I propose to boldly reformulate and reinterpret the classical laws of fluid mechanics into cash flow mechanics. At first this approach may appear contrived and artificial, but the end results of these reformulations and reinterpretations are useful quantifiable financial quantities, which will assist us with the measurement, analysis and proper characterization of modern dynamic financial markets in ways that classical comparative static financial - \ economic analyses do not allow.Financial Cash Flow, Term Structure

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

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,

Galton's Error and the Under-Representation of Systematic Risk

Our methodology of 'complete identification,' using simple algebraic geometry, throws new light on the continued commitment of Galton's Error in finance and the resulting misinformation of investors. Mutual funds conventionally advertise their relative systematic market risk, or 'betas,' to potential investors based on incomplete measurement by unidirectional bivariate projections: they commit Galton's Error by under-representing their systematic risk. Consequently, far too many mutual funds are marketed as 'defensive' and too few as 'aggressive.' Using our new methodology we found that, out of a total of 3,217 mutual funds, 2,047 funds (63.7%) claimed to be defensive based on the current industry standard methodology, but only 608 (18.9%) actually are. This under-representation of systematic risk leads to inefficiencies in the capital allocation process, since biased betas lead to mis-pricing of mutual funds. Our complete bivariate projection produces a correct representation of the epistemic uncertainty inherent in the bivariate measurement of relative market risk. Our conclusions have also serious consequences for the proper 'bench-marking' and recent regulatory proposals for the mutual funds industry.