I have written before that my ideal trading model is one that has no parameters, and what ways there are to accomplish this. Actually, I forgot to mention that a trading strategy proposed by Dr. Andrew Lo discussed previously is in fact parameterless, and the technique is so general that it can be applied to any mean-reverting strategy.

The technique is simply this: maintain a long (or short) portfolio with capital proportional to the distance between a supposedly mean-reverting measure and its long-term mean value.

For e.g. if you are pair-trading PEP vs KO, and you believe that the spread between PEP and KO is mean-reverting, then this spread is the mean-reverting measure you should employ.

As the spread moves away from its mean, keep buying (or shorting) the spread in equal dollar amount. And as the spread reverts, keep selling (or buying) the spread in the same dollar amount. What this dollar amount should be depends on: a) the total buying power you possess, b) the expected maximum deviation of the spread from its mean, and c) how often you intend to buy/short. Note that point c is not a parameter: it is arbitrary and limited only by transaction costs, technology, and other operational issues. As for the expected maximum deviation, it can be obtained by observing the history of the spread since inception.

This scheme thus obviates the need for entry or exit thresholds, and with them, the possibility of data-snooping bias. (You may still want to impose an entry threshold based on transaction cost consideration - but that would not count as a free parameter.)

## Saturday, August 16, 2008

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## 15 comments:

That's some kind of trading auto-correlation. Unfortunately, the ask-bid and commission fee eats most almost all profit without proper parameters.

Mr. Tzang,

As I mentioned in the blog post, I agree that transaction cost consideration will necessitate entry and/or exit thresholds. However, these thresholds can be calculated based on the expected transaction costs, and thus are not free parameters to be optimized based on past model performance. In this sense, the model remains "parameterless".

Ernie

Emmm, Not that easy. Actually, it is my current project. Trans fee and AB spread are indeed the biggest problem. Maybe there is some advanced model I don't know or maybe it is just for big investors.

Thanks Ernie, I'm looking forward to your book.

Regards,

Max

This is an interesting investment idea. How do you know which pairs to choose? What are your parameters i.e. volatility, beta, volume, market cap?

I disagree with the above comment about transactions. In Canada, trades are $10 so pairing the trade won't add that much more to the cost of the transaction.

Hi Ernie,

This might be a little bit off topic for this post.

I have been following your thoughts on different strategies. Thanks for sharing.

My question is about how to get good, affordable, reliable data for retail quantitative traders.

There are many quantitative strategies I want to try on options, equities, futures etc.. But most brokers, like Interactive Brokers, etrade etc., do not provide an easy and good way for people to build and test their own quantitative strategies.

Based on your experiences, would you share some of your thoughts? Where to get the data? For example, high frequency real time data. Any good platforms retail quantitative traders should consider?

Thanks

Jing

Hi chrispycrunch,

Generally I pick pairs based on cointegration. (See my many previous blog posts on this topic, as well as my forthcoming book.) However, the whole point of parameterless trading is that we don't have arbitrary parameters except those imposed by liquidity and transaction costs!

Ernie

Hi Anonymous,

It is quite expensive to get high quality high frequency stock data. Tickdata.com is one source: it will cost several thousand dollars. For daily data, of course, it is much easier. See Hquotes.com. I use Interactive Brokers as my brokerage.

There will be a discussion of data sources in my forthcoming book as well.

Ernie

Hey there. I think I'll be digging around on your blog for some time, so I will eventually be contacting you again, for sure.

As a disclaimer, I'm only a junior college student in houston. Relating to your post; I have used a similar strategy quite nicely. I take the relative movements of the EUR/USD and GBP/USD for trades in EUR/GBP. I won't bore you with the methodology as my programming skills are crude, and access to good data are limited. Needless to say I spend time putting the old two eyes to work, which is not how I want to continue.

Thank you for the site.

Hi Orson,

Thanks for sharing your FX strategy. It sounded like you are doing something similar to triangular arbitrage, is that right?

Ernie

Steve M: it does take a lot of capital to implement this strategy, as agency bonds do not come cheap. (Alternatively, you can buy mutual funds which invest in agency bonds.)

To fund this strategy, you would have to short treasuries, which means you would have to find a broker that allows you to borrow treasuries for shorting.

Ernie

I like the idea. But isn't the long term mean also a parameter that needs to be estimated to make the strategy work? What if this mean is changing over time?

Maybe we could do some kind of Bayesian updating to keep this value in check?

Poorboy,

Long-term mean is not a free parameter, since it is determined by a moving window of historical data. Free parameters are those that you have fixed once and for all, based on optimization on a fixed training set. If you have backtested your strategy using a moving window of training set, then you don't really have a free parameter.

Ernie

OK I think I understand better now. By free parameter, you mean a parameter that affects the profitability of your trading strategy (e.g. entry/exit thresholds).

It is true that if the long-term mean is set by a moving window of data, then it is constantly adapting.

But then the question is, what size window? It seems a 30 day versus a 60 day window will yield a different long term relationship between the pair. Which one to choose? A shorter window will be more responsive to recent history, but will be more unstable. A longer window will be more stable, but less responsive to a recent deterioration of the pairs-trading relationship.

Is your experience that the choice of rolling window size isn't that important? This might be especially true if you are constantly updating the relative weighting of the strategies in your portfolio.

poorboy44:

Yes, the window size may indeed be a free parameter. However, it is less important to the strategy because profitability should not be very sensitive to the size. Even this free parameter can be "averaged out" by, say, using the average prediction of several models with different window size.

Ernie

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