Equity Arbitrage

Asset Corporation is a leader in statistical arbitrage of stock prices. Here, we illustrate one of our several techniques.

We have found that in certain cases, it may be possible to systematically detect stock mispricings and trade accordingly. We look for clusters of stocks that are highly correlated in their price behavior. It is within this context that price predictions can be made. We use statistical techniques to determine the best clusters at a given time.

With very tightly knit stocks, it is possible to obtain what amounts to a "consensus of the group" as to what each individual stock's price should be, given what all the other prices are and what they have been recently. Statistical indicators have been developed to make this a rigorous process.

What stocks are clustering changes all the time, on a scale of a few months, according to what is happening in the larger economy. In recent days, stocks in the oil services area, gold mining, general metal miners, and home building groups have behaved almost as proxies for each other.

Below we have tables that form the structure for our prototype. In recent weeks, a tightly knit cluster is occurring in the oil service stocks. The stock symbols for the five stocks that are involved are shown in the screen shot. They have been moving totally in lockstep.

Historical prices of Oil Service Stocks

Stock ESV NBR WFT RIG BJS
T - 1 days $38.82 $56.70 $58.70 $48.96 $50.26
T - 2 days $40.19 $57.94 $60.18 $50.00 $51.64
T - 3 days $40.93 $58.40 $60.65 $49.75 $51.82
T - 4 days $40.87 $59.58 $61.10 $49.31 $51.80

The table above shows recent historical prices that are used to compute all statistical indicators.

Snapshot of real-time analysis

Stock ESV NBR WFT RIG BJS
Predicted Prices $38.90 $56.11 $58.85 $47.49 $48.71
Actual Prices $38.44 $55.98 $58.23 $48.08 $49.55
Difference -1.2% -0.2% -1.1% 1.2% 1.7%

And this table shows the heart of the analysis. You can see the current real market prices.You can see the corresponding predicted prices based on group behavior, and, more pertinently, you can see the difference between the two. What might be of interest here?

BJ Services (BJS) is 1.7 percent too high.

Ensco International (ESV) is 1.2 percent too low.

Perhaps one should short BJS and go long on ESV for a quick trade lasting a few days before the prices come back into their more normal relationship.

Further Analysis

Stock ESV NBR WFT RIG BJS x̄ RSQ
T - 0 days -1.2% -0.2% -1.1% 1.2% 1.7% 0.93
T - 1 days -1.8% -0.4% -1.2% 2.2% 1.8% 0.94
T - 2 days -1.5% -1.7% -0.5% 2.1% 2.0% 0.94
T - 3 days -0.3% -1.9% -0.1% 0.9% 2.2% 0.93
T - 4 days -1.0% 0.3% 0.6% -0.6% 2.6% 0.87
T - 5 days -0.2% 1.2% 0.7% -1.0% 2.0% 0.82

The columns with the stock symbols shows the same analysis (to get the difference between actual and predicted prices), as if it had been done with yesterday's closing prices, or two days ago, or three days ago, etc. Signatures develop out of the trends that can be observed.

Lastly, the last column is a composite statistic that measures how well all the stocks in the group are cohering together. It is the average squared correlation figured over every stock pair in the group. Clusters don't last forever, and when this number falls off too much, it means the market is no longer treating these stocks as almost interchangeable.

Every part of this process requires statistical calibration in order to be done effectively, and we have been developing similar and effective indicators.