3 Indicators Confirm A Shifting Tide In Equities

 |  Includes: SPY
by: Tiger Technologies


A dismal performance by the S&P 500 over the first quarter followed by an increase in volatility in April has many worried that the rally is over.

Comparisons are being drawn to 1987, 1929 and other past periods of market corrections.

We look at 3 key indicators: autocorrelation, distribution and volatility to confirm that the tide is indeed shifting.

Since March 2009, and especially over the last 2 years we have seen a sense of complacency in the markets. But as of the first week of April, the market is flat for 2014, which has investors worrying if the rally of the past 5 years is over and a large correction is due. The global macro-economic reasons for the rally to end are aplenty, ranging from the end of quantitative easing, the specter of rising inflation to the possibility of a debt crisis in China.

Technicians have pulled charts from 1929 to 1987 pointing to similar price patterns, looking for large corrections. We do not see the price patterns in these historical comparisons, as they are mostly overlaid charts on different scales that trick the brain in finding patterns that may or may not exist.

Our analysis instead focuses on 3 statistical indicators, which empirically show that even though the market is flat for 2014, this flatness hides some disturbing truths that are not easily seen by the naked eye.


Autocorrelation is basically a measure of certain price or trend patterns in the market. In a recent paper, we have shown that autocorrelation exists in the stock market. For the purpose of this analysis, we have simply looked at the daily S&P 500 direction pattern.

As an example, if a positive day was followed by another positive day or a negative day was followed by another negative day, the autocorrelation for that period would be a positive number. The magnitude of this positive number would be a function of how many days in a row the market went in the same direction. Conversely, if a positive day was followed by a negative day, you would see an autocorrelation number less than 0.

Looking at the data from 1952 to 2014, we see a marked change in the daily direction autocorrelation in the S&P 500. After a long period of positive years, over the last 14 years the number has been mostly negative.

Over more recent history, in 2011, 2012 S&P 500 daily returns had a positive autocorrelation, but so far 2014 is registering the largest negative number yet, at 0.18.

Daily Market Direction Autocorrelation and Annual Returns of the S&P 500 (1952-2014)

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Source: Yahoo Finance, MA Capital Management

The other interesting thing to note is the positive relationship between autocorrelation and S&P 500 returns. A positive autocorrelation has led to positive returns, while a negative one has led to negative returns, and this relationship has been true for 60% of the years.

Several factors can be attributed to why we have seen this marked change in the autocorrelation pattern since 1981. Increased market participation, efficiency of information dissemination, and computer based algorithmic trading have all contributed to this changing pattern. From an individual trader's perspective, a positive autocorrelation is easier to trade, as less choppiness can lead to fewer stop losses and profitable trades as has been the case for the last few years. But an increased negative autocorrelation becomes much harder for the same reasons.

Return Distribution and Volatility

The next thing we looked at was the distribution of the daily returns of 2014 as compared to previous years. Modern finance defines stock price movement as a stochastic process, which means that the change in stock returns over time is uncertain. The simplified process of stock market returns over a time period of 1 day is defined as:

Return(t) = Mu(t) + Sigma(t) * Epsilon


Return(t) is the expected return over 1 day

Mu(t) is the median daily return

Sigma(t) is the daily volatility

Epsilon is a random number drawn from a standard normal distribution.

Based on this model of stock market returns, the 3 most important factors that go into defining the expected S&P 500 returns will be Mu, Sigma and the nature of the distribution curve of the daily returns. The above model assumes a standard normal distribution, but in reality the stock market returns are rarely normally distributed (Eugene F. Fama's 1964 PhD thesis).

Here is a series of 4 charts, showing Mu or median daily returns since 1952, Sigma or daily volatility, skewness of the distribution and a 3 factor regression of Mu, Sigma and Skew against expected returns.

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The last 5 years have significantly high median daily returns (MU). 2014 median daily returns so far are 0.

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2014 volatility (sigma) is high on an absolute as well as on a relative basis when compared to the last 2 years as well as since 1952.

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A negative skew shows larger than expected negative daily returns and a positive skew shows larger than expected positive daily returns relative to a normal distribution. 2014 negative skew is quite high.

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The 3 factor regression of Mu, Sigma and Skew against expected returns is producing 2014 returns of +1% thus far. This regression has a 0.83 correlation between expected returns and the actual delivered returns over the past 63 years.

What has changed for 2014?

1. 2009-2013 produced years with positive Mu; 2014 thus far has a median daily return of 0 and relatively high volatility and a high negative skew. This means that the market is going nowhere and also showing big swings with a propensity of larger negative surprises!

2. After a period of positive or mildly negative autocorrelation, 2014 so far is registering the largest negative autocorrelation since 1952, at 0.18.

3. If this pattern continues, we can expect flat to mildly negative returns for 2014 with a lot of ugly choppiness.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.