Saturday, April 02, 2005

An Example of Typical Price Behavior (II)

As an example of a stock with large price swings, I select Research in Motion (RIMM), maker of the BlackBerry handheld text messaging device. Research in Motion is a large-cap company ($14 billion market capitalization) with good liquidity (average daily trading volume of 9 million shares) and a high beta (3.1).

Based on the time series of daily closing prices from the past six years (February 1999 to the present), I find the following basic statistics:

Distribution of One-Day Price Movements
Average Daily Price Movement: 0.3%
Standard Deviation: 5.8%
Skew: 0.65
Kurtosis: 8.4

Autocorrelations
3 Days Prior vs. Today: -0.01
2 Days Prior vs. Today: 0.02
1 Days Prior vs. Today: 0.01
Today vs. 1 Day Later: 0.01
Today vs. 2 Days Later: 0.02
Today vs. 3 Days Later: -0.01

This information tells us that:

1. The distribution of daily price movements has fat tails (kurtosis sigificantly greater than zero);
2. The time series as a whole does not have memory (autocorrelations all close to zero).

However, because it is still possible that predictable behavior occurs only in certain regimes (e.g., when large price movements occur), I sort the data by magnitude of the daily price movement and calculate statistics for individual deciles:

Decile: Average Daily Price Movement, Prior 20-day Historical Volatility
I: 11.6%, 6.3%
II: 5.1%, 5.7%
III: 2.9%, 5.2%
IV: 1.7%, 4.4%
V: 0.5%, 4.4%
VI: -0.5%, 4.4%
VII: -1.5%, 4.7%
VIII: -2.7%, 4.7%
IX: -4.4%, 5.7%
X: -9.1%, 6.8%

Decile: Average One-Day Price Movement 3 Days Prior, 2 Days Prior, 1 Day Prior; 1 Day Later, 2 Days Later, 3 Days Later
I: -0.3%, -0.3%, 0.4%; 0.4%, 0.0%, -0.3%
II: 0.7%, 0.6%, 0.9%; 0.9%, 0.0%, 0.6%
III: 0.8%, 0.6%, 0.2%; 1.5%, 0.1%, 0.4%
IV: 0.6%, 0.2%, 0.7%; 0.6%, 0.5%, 0.4%
V: -0.1%, 0.3%, -0.2%; -0.2%, 0.7%, 0.5%
VI: 0.5%, 0.7%, 0.5%; 0.5%, 0.3%, 0.4%
VII: 0.0%, 0.4%, -0.2%; -0.2%, 0.6%, 0.5%
VIII: 0.4%, 0.5%, 0.5%; -0.1%, 0.4%, 0.3%
IX: 0.6%, 0.5%, 0.8%; -0.2%, 0.8%, 0.9%
X: 0.2%, -0.1%, -0.3%; 0.2%, 0.1%, 0.0%

Decile: Volatility of Decile Data 3 Days Prior, 2 Days Prior, 1 Day Prior; 1 Day Later, 2 Days Later, 3 Days Later
I: 7.4%, 7.0%, 7.5%; 7.5%, 6.6%, 8.0%
II: 5.7%, 6.0%, 5.3%; 5.2%, 4.9%, 5.3%
III: 6.0%, 5.0%, 5.2%; 6.5%, 5.4%, 4.7%
IV: 4.6%, 5.1%, 4.0%; 4.9%, 4.6%, 6.2%
V: 5.9%, 5.0%, 4.6%; 4.5%, 4.4%, 4.4%
VI: 4.3%, 6.4%, 4.2%; 4.3%, 4.3%, 4.6%
VII: 6.0%, 3.8%, 4.4%; 4.7%, 6.9%, 4.7%
VIII: 4.9%, 4.9%, 6.7%; 6.5%, 5.0%, 5.8%
IX: 5.5%, 6.1%, 6.6%; 4.8%, 6.4%, 6.6%
X: 7.5%, 8.0%, 8.2%; 8.0%, 8.5%, 7.1%

I have not listed autocorrelations for the deciles above, but these are all low, indicating lack of any reliable relationship between price movement on a given day and price movements a few days earlier and later.

The conclusions I draw from the data are:

1. Large price movements tend to occur more frequently when historical volatility is high;
2. There is a lack of any clear same-directional (momentum) or opposite-directional (reversal) behavior following large price movements;
3. Volatility tends to persist, i.e., large price swings tend to be followed by larger-than-average price movements.

Unfortunately, I do not see any predictable directional price behavior anywhere in the data, even in the "fat tail" deciles comprised of the data points representing the largest price swings (deciles I and X).

Based on this very limited examination of just one stock, it is premature to draw the conclusion that the time series of price movement for stocks in general provides no information about the direction of future price movement. However, I must say that this study is yet another indication that whatever predictability exists within the time series itself is likely to be quite weak.

In short, although big price moves tend to be both preceded and followed by larger-than-average price movements (i.e., occur more frequently in volatile regimes), predictable directional behavior is absent. Without directional predictability, neither long nor short stock positions can be relied on for excess profits. Further, with volatility tending to persist rather than fade or surge, neither long nor short option trades can be expected to generate excess profits either.

2 Comments:

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11:18 PM, October 24, 2005  
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