## Friday, November 23, 2007

### Seasonal trades in stocks

Readers of this blog have seen my discussions of various seasonal trades in commodities futures (e.g. see this article). Recently, Mark Hulbert of the NYTimes drew our attention to a seasonal trade in stocks. The strategy is very simple: each month, buy a number of stocks that performed the best in the same month a year earlier, and short the same number of stocks that performed poorest in that month a year earlier. The average annual return is more than 13% before transaction costs, and since it is market neutral, this already considerable return can be leveraged to 2 or 3 times higher. Also, since it turns over the stocks only once a month, transaction costs should not be a major problem. The strategy was developed by Profs. Steven Heston and Ronnie Sadka, and details can be found online here. Besides its simplicity, the strategy is not as affected by survivorship bias in the data set as a mean-reverting strategy, since survivorship bias would tend to lower its backtest performance by excluding very poorly performing stocks that we would short. All in all, it seems to be a market neutral strategy made for retail trading!

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## 17 comments:

FYI I consider this analyst the authority in seasonal trading, at least in Canada. He combines technical, seasonal, and fundamental trading analysis. http://market-minute.dvtechtalk.com/

Dear Ernie

This is a very interesting trading idea. Thank you for posting about it on your blog.

First, I’m really not sure to what extent this would in fact be a profitable trading strategy after allowing for costs. I note that the authors themselves doubt that it would be a profitable stand-alone strategy once costs are allowed for. The monthly pre-cost profitability is little more than one percent per month. Round trip costs per trade of 50 bps – not too unreasonable an estimate allowing for commission, spread and financing costs - would account for all of the ‘profitability’ (keeping in mind that this is 50 bps per side i.e. 100 bps for the long and short-side together).

Second, I note that the study uses data up-to 2002, no later. Many strategies have been observed to exhibit declining profitability in recent years (you have noted this yourself in a number of posts and it is discussed in the Loe et al article that you have cited previously).

To see whether the seasonality phenomenon identified by Heston and Sadka might persist in more recent years, I tested the idea on data from 2002 to June 2007 (the sample included data from 2001 in order to determine which stocks to buy and sell in 2002). I looked at US large caps only (contemporaneous market cap greater than $2bn). The authors find that the seasonality effect applies throughout the size distribution (though I have not read the article closely enough to see whether it is particularly prnounced at certain points of the size distribution). I chose large caps simply because I currently happen to have reliable data for large caps in memory (including for delisted companies).

The results are consistent with the Heston and Sadka findings, though the effect is more modest. The authors rank stocks according to their performance in the same calendar month a year earlier and buy the stocks in the top performing decile and short the stocks in the worst performing decile. For 2002 onwards, the top decile out-performs the bottom decile by 35 bps per month (4.2% per year).

It would be interesting to repeat this exercise for mid and small cap stocks as well as for other, arguably less efficient markets. I have also not read the Heston and Sadka paper in great detail, so I may well have missed out an important part of the calculations (apologies in advance). However, given trading costs, I am not convinced that there is much to be gained from this particular seasonal trading strategy, at least as implemented above.

But there may be variations on this strategy that may be worth pursuing. For starters, selecting the top and bottom 5% rather than 10% of winners and loosers should in theory yield higher returns (though at the expense of greater noise). This is indeed the case, but the improvement in returns is extremely slight. The returns increase from 35 to 39 bps per month on average.

Heston and Sadka find the seasonablity effect to be particularly pronounced in the months of January, October and December. So, a possible strategy might involve restricting trading of this strategy to these months. The evidence suggests that this aproach seems far more promising. The strategy based on the decile groups produces an average monthly return of 189 bps and the strategy based on the 5% groups produces a an average monthly return of 231 bps (results apply to 2002-2006 i.e. completed years). These results are extremely impressive. However, the average monthly returns appear to decline over time and yield a negative return in 2006. It will be interesting to see the effect for the whole of 2007, though January 2007 (the only month for which I have data) produces a negative return.

Thus, I believe there may be a trading strategy in this but I am not yet convinced. If the results for January, October and December 2007 together generate decent returns, then this trading idea might merit some consideration for January, October and December 2008.

Many strategies building on market inefficiencies have been found to persist longer in mid cap compared to large cap stocks (see, for example, the article by Loe et al, 2007). I intend to repeat the above exercise on mid cap stocks. It will be especially interesting to observe the results for 2006 (and 2007 when available).

JR

Dear JR,

Thank you for publishing your detailed analysis here! Actually, I just did a backtest myself using SP500 stocks (this data has survivorship bias as I use the current constituents of SPX). I found that the returns were negative even without transaction costs from 20050102 - present. In the earlier years, where my data is less reliable because of survivorship bias, a small positive return can be found, but with high volatility, such that the Sharpe ratio was never greater than 1.

I agree with your conclusion: it is not a strategy I would personally engage in, whether in conjunction with other strategies or not.

Ernie

Thank you for your backtest. A possible explanation for bad results in the last years is the very low volatility. Low volatility is the worst enemy of every algorithmic strategy.

In my opinion if a strategy has proven robustness in many many years (and isn't overfitted) one/two years of bad results wouldn't change our opinion about its 'goodness'.

Otherwise, do you know strategy that works every single years for many many years?

I think it's impossible.

Bye

Dear statarb,

I agree that it is not easy to find strategies that keep working year after year

going forward. However, there are many strategies that I know of which have worked every year inbacktest. If a strategy hasn't worked for a year or two in the recent past, I would not trade it. As a stat arb trader, the goal is to achieve a maximum drawdown duration that is shorter than 1 month.Ernie

a) strategies which have worked every year in backtest. The question is: how many years? Five, six? Is it enough? In accademic literature (scientific method) i haven't read nothing which use less then five economic cycle of data (5 years).

b) can you tell approximately which strategies are you talking about? So we can do our backtest on more history/market.

c) Drawdown shorter then 1 month. My problem is: how you can know first the length of your future Drawdown? It's impossible to know ex-ante. So the best thing that statistic can do for us is to give a positive mathematical expectancy, not for the next month, but for the next years. Do you agree with this?

1) Yes, I believe 5 years is a good number. Financial market is not stationary, so longer history is not necessarily better.

2) I am referring to high frequency mean-reverting strategies.

3) It is true that one won't know what one's drawdown is in the future, but it is safe to say that the future drawdown is going to be longer than the drawdown in backtest. Thus if the dd is already longer than 1 year in backtest, there is no hope for a desirable future dd.

Ernie

Ok, however there is a difference beetwin high frequency trading and almost position strategies. In this seasonal strategies you are always IN the market.

The high frequency trading strategies you are talking about is what you give in premium section of your blog? Is it a long/short strategy on single stocks?

Dear statarb,

The high frequencies strategies include those that have been disclosed to me in confidence, as well as those that I am currently actively pursuing. As a result, I have not publicized them in any form.

Ernie

What could one imagine under these secret high-frequency strategies. Is it cointegration /pairs trading in a much smaller time frame? Momentum strategies? Maybe you can gibe a hint ;-) or a link to some ressources?

I am reading your book, and i can see that your seasonal pattern on natural gas has disappeared in the last few years. Isn t it difficult to establish a seasonal rules or make statistically significant when test sample is only 20 years for instance

nikkus,

Actually, what you said applies to any trading strategy: practically no trading strategy works for ever!

Ernie

Ernie, the link to the seminar that you provided no longer seems to work. Is there another source for that file?

Gili,

A google search of the authors turned up this link:

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=687022

Ernie

Thanks, yes I had found that paper, but I was looking for the seminar which you linked to, which I assumed was something different. Never mind...

This is a great strategy AND there is a great Seasonal Stock Trading Service at http://www.blashing.com that provides Stock Seasonality information for every stock, ETF, and mutual fund. It also provides a Seasonal Stock Scanner that gives you the best equities going Up and Down for every Month and every Week of the year!

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