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Some readers have asked whether there is an Excel version of the ADF test for cointegration (mentioned in articles here or here.) You can download one such package here (Hat tip: Bruce H.).
And as always, you can download the Matlab version from spatial-econometrics.com.
Does Averaging-In Work?
Ron Schoenberg and Al Corwin recently did some interesting research on the trading technique of "averaging-in". For e.g.: Let's say you have $4 to invest. If a future's price recently drops to $2, though you expect it to eventually revert to $3. Should you
A) buy 1 contract at $2, and wait for the price to possibly drop to $1 and then buy 2 more contracts (i.e. averaging-in); or
B) buy 2 contracts at $2 each; or
C) wait to possibly buy 4 contracts at $1 each?
Let's assume that the probability of the price dropping to $1 once you have reached $2 is p. It is easy to see that the average profits of the 3 options are the following:
A) p*(1*$1+2*$2) + (1-p)*(1*$1)=1+4p;
B) 2; and
C) p4*$2=8p.
Profit A is lower than C when p > 1/4, and profit A is lower than profit C when p > 1/4. Hence, whatever p is, either option B or C is more profitable than averaging in, and thus averaging-in can never be optimal.
From a backtest point of view, the Schoenberg-Corwin argument is impeccable, since we know what p is for the historical period. You might argue, however, that financial markets is not quite stationary, and in my example, if the historical value of p was less than 1/4, it is quite possible that the future value can be more than 1/4. This is why I never make too much effort to optimize parameters in general, and I can sympathize with traders who insist on averaging-in even in the face of this solid piece of research!
A) buy 1 contract at $2, and wait for the price to possibly drop to $1 and then buy 2 more contracts (i.e. averaging-in); or
B) buy 2 contracts at $2 each; or
C) wait to possibly buy 4 contracts at $1 each?
Let's assume that the probability of the price dropping to $1 once you have reached $2 is p. It is easy to see that the average profits of the 3 options are the following:
A) p*(1*$1+2*$2) + (1-p)*(1*$1)=1+4p;
B) 2; and
C) p4*$2=8p.
Profit A is lower than C when p > 1/4, and profit A is lower than profit C when p > 1/4. Hence, whatever p is, either option B or C is more profitable than averaging in, and thus averaging-in can never be optimal.
From a backtest point of view, the Schoenberg-Corwin argument is impeccable, since we know what p is for the historical period. You might argue, however, that financial markets is not quite stationary, and in my example, if the historical value of p was less than 1/4, it is quite possible that the future value can be more than 1/4. This is why I never make too much effort to optimize parameters in general, and I can sympathize with traders who insist on averaging-in even in the face of this solid piece of research!
Selecting tradeable pairs: which measure to use?
A guest blog by Paul Farrington
One of the most important factors in statistical arbitrage pairs trading is the selection of the paired instruments. We can use basic heuristics to guide us, such as grouping stocks by industry in the anticipation that stocks with similar fundamental characteristics will share factor risk and tend to exhibit co-movement. But this still leaves us with potentially thousands of combinations. There are some statistical techniques we can use to quantify the tradeability of a pair: one approach is to calculate the correlation coefficient of each pair's return series. Another is to consider cointegration measures on the ratio of the prices, to see if it remains stationary over time.
In this article I briefly summarise the alternative approaches and apply them to a universe of stock pairs in the oil and gas industry. To measure how effective each measure is in real world trading, I back test the pairs using a simple means reversion system, then regress the generated win rate against the statistical results. Some basic insights emerge as to the effectiveness of correlation and cointegration as tools for selecting candidate pairs.
Please visit http://www.paulfarrington.com/research/Selecting%20tradeable%20pairs.htm for details of my methodology and results.
One of the most important factors in statistical arbitrage pairs trading is the selection of the paired instruments. We can use basic heuristics to guide us, such as grouping stocks by industry in the anticipation that stocks with similar fundamental characteristics will share factor risk and tend to exhibit co-movement. But this still leaves us with potentially thousands of combinations. There are some statistical techniques we can use to quantify the tradeability of a pair: one approach is to calculate the correlation coefficient of each pair's return series. Another is to consider cointegration measures on the ratio of the prices, to see if it remains stationary over time.
In this article I briefly summarise the alternative approaches and apply them to a universe of stock pairs in the oil and gas industry. To measure how effective each measure is in real world trading, I back test the pairs using a simple means reversion system, then regress the generated win rate against the statistical results. Some basic insights emerge as to the effectiveness of correlation and cointegration as tools for selecting candidate pairs.
Please visit http://www.paulfarrington.com/research/Selecting%20tradeable%20pairs.htm for details of my methodology and results.
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