SPY: the trend ain't your friend any more

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Written by Forex Automaton   
Thursday, 12 February 2009 14:58

Having made so many references to bipolar disorder in the behavior of currencies, it seems appropriate, despite the forex focus of this research blog, to visit the market where the image of manic-depressive Mr Market was first conceived (by B.Graham): the stock market. I apply correlation analysis of logarithmic returns to the day data on the popular SPDR S&P 500 ETF, the SPY. This working paper on SPY autocorrelations begins a new series where currencies and other markets, such as interest rates, commodities, and stocks will be observed and studied together within a uniform framework of correlation analysis. Executive summary: 16 years of daily SPY data invalidate the behavioral pattern of waiting for and following Mr Market's "nod of approval" -- by showing the market, everything else being equal, to "self-contradict" and reward contrarians. This is particularly true in the extreme volatility environment of today.

Momentum investing, a strategy that aims to capitalize on the continuation of existing trends, requires positive autocorrelation at non-zero time lags to be justified statistically. Contrarian investing, a strategy that aims to capitalize on the trend reversals, is justifiable by negative autocorrelation at non-zero time lags. Any non-zero correlation at non-zero time lags make the market look akin to predictable correlated phenomena in our everyday experience (such as seasonal variations of temperature). Predictive correlations (those at non-zero lags) make "easy" arbitrage income possible in principle. The efficient market hypothesis (EMH) postulates that the "easy" money is perpetually "already made" -- without specifying the time scale. Therefore predictive correlations, when distinguishable from random noise, contradict the market efficiency hypothesis by quantifying both the magnitude and time scale of market inefficency. Random noise for the EMH falsification can be obtained by martingale simulations on the basis of measured (usually not so trivial) return distributions. In a nutshell for the new reader, this is the essence of the programme of market observation and analysis which complements, both intellectually and as a business project, our development of own forex forecasting engine.


Evolution of SPDR (SPY) since February 1993, day

Fig.1:Evolution of SPDR (SPY), day scale. Time axis is labeled in MM-YY format and spans the interval from February 1, 1993 to February 1, 2009.

Evolution of SPDR autocorrelation peak structure, day, 1993-2009 Evolution of SPDR autocorrelation peak structure, day, 1993-2009, zoom-in on small structure

Fig.2: Evolution of SPDR autocorrelation peak structure since 1993, day scale. Time bin is 1/4 of a year wide. The peak structure is represented by three correlation values: the one for the zero lag (essentially a volatility measure) downscaled by 10 for easier visual comparison, the one at the one day lag and the one at the two day lag. Time axis is labeled in MM-YY format and spans the interval from February 1, 1993 to February 1, 2009. The bottom panel is the same figure with the vertical zoom to enable visual inspection of the low volatility periods A and C.

Fig.2 shows the evolution of the correlation structure in the vicinity of zero time lag, representing the correlation structure as a triplet of correlation values: those at zero, one and two day lags. The increased volatility shows up as the increase in the magnitude of all these values, with variance (a measure of volatility) being fairly well represented by the magnitude of the zero time lag value.



Autocorrelation of logarithmic returns in SPDR,   day scale, from to . Autocorrelation of logarithmic returns in SPDR,  day scale, from  to . Autocorrelation of logarithmic returns in SPDR,  day scale, from  to . Autocorrelation of logarithmic returns in SPDR,  day scale, from  to .

Fig.3: Autocorrelation of logarithmic returns in SPDR shown against the backdrop of statistical noise (red). Top panel: the measurement time range is for the relatively low volatility phase of the crisis, from August 2, 2007 through August 27, 2008. Bottom panel: same for the high volatility phase, from August 28, 2008 through the end of 2008. The noise is obtained from martingale simulations based on the recorded volatilities of EUR/GBP in the trading hours under study for the period. The noise is presented as mean plus-minus 1 RMS, where RMS characterizes the distribution of the correlation value obtained for each particular bin by analyzing 20 independent simulated uncorrelated time series of the same average volatility.

In Fig.3, the correlation pattern in the vicinity of the zero time lag bin is investigated with the focus on the rest of the time lags (in addition to the three shown in Fig.2) and on the issue of statistical significance. The latter issue is addressed by Monte-Carlo simulating independent time series with the SPY volatility of the period (A,B,C, or D), from which the expectation value and the RMS of the correlation value as-if-the-market-were-efficient are inferred. Significant (several RMS) deviations of the measured values from the Monte Carlo reference form the basis for interpretation, the goal being to find the better-than-casino aspects of the markets on the time scale of observation, days in our case.

Autocorrelation of logarithmic returns in SPDR,  day scale, excluding the case D of the impact phase of the financial crisis

Fig.4: Pre-crisis autocorrelations (all the data except case D). Variations in volatility may obscure visual comparison of features common to different time periods in the same figure. For this reason, here I pre-scale all histograms (of autocorrelations) by the factor which equals inverse magnitude of the zero time-lag peak. After that, the histograms "match" each other at the peak. Large pre-scale factors correspond to low volatility and vice versa.

The top three panels in Fig.3, repeated on the same plot in Fig.4, make any kind of jumping on the bandwagon (and these studies make no difference between bullish and bearish bandwagon) hard to justify: in the range of day lags up to fifteen days, the bias towards negative correlation values is hard to deny, even though negative signals at individual bins rarely exceed 2 RMS. A negative autocorrelation value associated with a particular time lag indicates that the product of opposite-sign returns separated by this time lag outweighs that of same-sign in averaging -- either because the opposite sign returns are too large or because they are too frequent.

In the periods of high volatility, labeled B and D, next-day autocorrelation deserves a special mention as it stands out of the red noise background. The magnitude by which it does so is a lot larger in case D. Same conclusion could be reached by looking at Fig.2, top panel. It is tempting to conclude that the next-day "bipolar disorder" is the characteristic feature of high volatility periods. Being a human psychology factor, it possibly plays a considerable role in driving the dynamics of these historic periods.

The data used are from the period 1993-02-01 to 2009-02-01.

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Last Updated ( Monday, 04 January 2010 12:40 )