I have since studied the effect of these factors on SP600 small cap stocks since 2004, using a survivorship-bias-free database combining information from both Compustat and CRSP. This time, the factors do produce an annualized average return of 4.7% and a Sharpe ratio of 0.8. Though these numbers are nowhere near the 26% return that Lyle and Wang found, they are still statistically significant. I have plotted the equity curve below.

Equity curve of long-short small-cap portfolio based on regression on ROE and BM factors (2004-2013) |

Equity curve of long-short small-cap portfolio based on top and bottom deciles of ROE (2004-2013) |

Notice the sharp drawdown from 2008-05-30 to 2008-11-04, and the almost perfect recovery since then. This mirrors the behavior of the equity market itself, which raises the question of why we bother to construct a long-short portfolio at all as it provides no hedge against the downturn. It is also interesting to note that this factor does not exhibit "momentum crash" as explained in a previous article: it does not suffer at all during the market recovery. This means we should not automatically think of a fundamental growth factor as similar to price momentum.

My conclusion was partly corroborated by I. Kaplan who has written a preprint on a similar topic. He found that a long-short portfolio created using the ratio EBITA/Enterprise Value on large caps generates a Sharpe ratio of about 0.6 but with very little drawdown unlike the ROE factor that I studied above as applied to small caps.

As Mr. Kaplan noted, these results are in some contradiction not only with Lyle and Wang's paper, but also with the widely circulated paper by Cliff Asness

*et al*. These authors found the the BM factor works in practically every asset class. Of course, the timeframe of their research is much longer than my focus above. Furthermore, they have excluded financial and penny stocks, though I did not find such restrictions to have great impact in my study of large cap portfolios. In place of a fundamental growth factor, these authors simply used price momentum over an 11-month period (skipping the most recent month), and found that this is also predictive of future quarterly returns.

Finally, we should note that the ROE and BM factors here are quite similar to the Return-on-Capital and Earnings Yield factors used by Joel Greenblatt in his famous "Little Book That Still Beats The Market". One wonders if those factors suffer a similar drawdown during the financial crisis.

===

My online Momentum Workshop will be offered on May 5-7. Please visit epchan.com/my-workshops for registration details. Furthermore, I will be teaching my Mean Reversion, Momentum, and Millisecond Frequency Trading workshops in Hong Kong on June 17-20.

## 67 comments:

Hi Erine

Do you have plan to conduct the Millisecond Frequency Trading workshops in singapore this year

Thanks

Hi Anon,

Please email me ... if enough people express interest, I can ask NTU to organize a course.

Ernie

Hi Ernie,

I wonder why someone like you would spend one minute on investigating results with a built-in trend bias. The Stock market has a built-in bias so any backtest of momentum based strategies just confirms the bias.

Hi anon,

By "trend bias" of the market I presume you mean the positive long term return of the market index? Please note that all my back tests, as well as that of the quoted papers, use long-short dollar-neutral portfolios. Any market trends are neutralized in such backtests, and only stock-specific effects will remain.

Ernie

Hi Ernie,

Interesting topic as usual. I am just wondering why do you think that the BM Factor doesn't add any value to the ROE Factor? I can see from your plots that combining the two factors allow to avoid the financial crisis Drawdown. The overall return is not impressive but I believe that this strategy could easily be incorporated in a bigger strategy...

Hi Anon,

If the two factors are really orthogonal to each other, such as ROE and BM, a multiple linear regression can yield better results than regressing or sorting on each individual factor alone. So yes, they can be useful as part of a larger strategy.

Ernie

Hi Ernie,

Are you working on a new book? If not any new book that you have been reading that is a good read for mean reversion strategies?

Thanks,

Hi Cristian,

I am not working on a new book at the moment.

For the fundamentals of mean reversion strategies, you can read Carol Alexander's Market Models: tinyurl.com/nh593x3

Ernie

Hi Ernie,

Do you have any good advice on working with large data sets in Matlab?

I work with one-minute bar data for US stocks going back to 1999 and each file is on average 50GB.

Looping over each file every day takes forever. I am trying to find a solution by memory mapping etc.

Do you have any good advice/tip?

Thanks

Hi Anon,

You can run the program on parallel processors (GPU or use multiple instances of EC2)

Ernie

Hi Ernie,

In your book, for futures calendar spread trading, why do we need to pick a pair of contracts based on the following criteria?

3. The expiration dates of the near and far contracts are 1 year apart.

Many Thanks.

Hi Anon,

That's the only calendar spread that gives good returns!

Ernie

Hi Ernie,

However, don't you think, for 12-month calendar spread, there is no good liquidity for far contracts?

Many thanks.

Hi Anon,

You can trade the 1 year calendar spread as a single unit on CME/Globex. Unless you have AUM>$10M, I don't think you need to worry about liquidity.

Ernie

Hi Ernie,

That sounds very interesting!

Could we buy or sell the 1 year calendar spread as a single unit on CME/Globex via IB?

Where could we find more information on this product?

Btw, for backtesting, do we need to download near and far contracts historical data one by one ourselves, and make a continuous data series?

It looks like a lot of work to deal with raw data compared with historical stocks data?

Is there better way to do it?

Many thanks.

Hi Anon,

You most certainly can trade futures calendar spreads as single units on IB. You should select CL, and choose Combinations as the instrument type at the market data line. Make sure you select the exchange as NYMEX, not Smart. For further details, please ask IB customer service.

To backtest calendar spreads, you can download the settlement (not close!) prices of each leg separately, or your data vendor may provide historical data on the spread as a unit (e.g. Nanex.net, Algoseek, and CQG all do) which is even more convenient.

You don't need to convert them to continuous data. Just treat each contract as a different "stock", but which has a begin and end date. I see no difference with backtesting stock portfolio strategies.

Ernie

Hi Ernie,

Thank you for the information.

I just think, for example, CL has 12 contracts a year, which means we need to roll over to the next contract for 12 times when we download historical one-year CL data because each CL contracts has different symbol.

For backtesting, we may need to download 4-year CL data, which means we need to do it manually 48 times for just one leg.

When we download 4-year historical stocks data, we just do it manually once to get 4-year data

It seems it is not very convenient to download historical futures data.

Many thanks.

Yes, but we have 2000 stock symbols vs 1 future symbol with maybe 100 contracts: no difference in difficulty.

Ernie

Hi Ernie,

I just check E-mini S&P 500 futures on CME website.

http://www.cmegroup.com/trading/equity-index/us-index/e-mini-sandp500.html

I take a look at chart for contracts MAR 2015 and JUN 2015.

It looks like there is almost no liquidity for these contracts.

Is that true? It is weird.

Hi Anon,

For ES, there is little reason to buy far months' futures. The situation is different for physical commodities.

Ernie

Hi Ernie,

For calendar spread trading, when we roll over front month leg, we roll over back month leg on the same rollover date too?

Moreover, it seems you recommend to use Roll Return as trading signal for calendar spread trading.

I wonder if we can still trade them as we trade stocks pairs using Price spread, Log Price Spread or even Ratio.

Thanks.

Hi Anon,

Yes, on rollover date you need to roll both front and back legs.

Sure, you can try price spread, log price spread, or ratio on calendar spreads and see if your signals work.

Ernie

hi Ernie,

Is that possible to trade currency futures and their cash spot as pairs trading, especially in IB?

Hi Anon,

I don't think so.

Ernie

Hi Ernie,

For pairs trading, it seems we can trade equal position size on both legs. However, have you tried volatility-adjusted position size for both legs?

Is it a better way?

Hi Anon,

The sizes of the two legs can be determined from a linear regression fit of their prices as discussed in Example 3.1 of my book Algorithmic Trading.

Ernie

Hi Ernie,

I am new to futures trading.

When we hold one future contract on rollover date, and move to the next front contract, will we have profit/loss impact? IB will do it automatically for us?

Shall we avoid holding futures position across rollover dates when we trade futures spread?

Rolling over futures to the next nearby contracts will not have P&L impact except for transaction costs. This is like selling one stock and buying another.

IB will not roll over futures positions automatically for you.

Rollover should not affect your calendar spread positions: you can just roll both legs forward simultaneously.

Ernie

Hi Ernie,

I mean that there is price gap between the current contract and the next contract.

Therefore, when we close the current long contract, and buy the next contract, we may make or lose money.

Thanks.

If you sell AAPL at the close, and buy GOOG at the same time, you do not incur a P&L, even though the prices of APPL and GOOG are very different (big "price gap"). Why would you incur a P&L if you sell the May contract of RB and buy the June contract at the same time?

Hi Ernie,

I see. We may just have some "price jump" on both legs, but the pairs trade has not finished yet.

Hi Ernie,

We know data vendors would create continuous contract data for near month contracts. I wonder if they create continuous contract data for other far month contracts.

Thanks.

I think csidata's software may allow you to choose how you want to create continuous contracts.

Ernie

Hi Ernie,

When we test intermarket spreads between Crude oil(CL) and heating oil (HO), we test (price*multiplier) series, such as 101.3*1000 and 2.9933*42000?

Yes, that is correct: multiplier is needed for intermarket spreads.

Ernie

Hi Ernie,

Have you ever traded Eurodollar futures? It seems they are very liquid.

Yes, it is very liquid, but I haven't traded it before.

Ernie

Hi Ernie,

Do you think in general it's more money to be made trading ETFs vs component stocks or simple ETF pairs trading?

Hi Ernie,

Which asset classes do you mainly trade at the moment?

Which asset classes are performing well YTD?

It is hard to make money trading ETF vs component stocks for retail traders since latency, fees, slippage etc. are all much higher than that of institutional traders.

Pair trading ETFs is much more achievable.

Ernie

Our FX strategy has been best performing this year.

When I said ETF vs component stocks I meant an approach similar to strategy explained in your book, i.e. using a subset of component stocks. Is latency, slippage etc still a big factor in this case?

Is that momentum or mean reversion? Can you give examples of fx pairs to try mean reversion on for a beginner? Without giving away to much of your own strategies of course. Many thanks

Yes, I believe the ETF vs component stock strategy can only be profitable if you have low latency access to the markets.

However, you can perhaps find a version that doesn't.

Ernie

Our FX strategy is mean-reverting.

Ernie

Hi Ernie,

When you write "low latency", do you mean hour, minutes, seconds, or ticks in this case?

Ticks.

Hi Ernie, I found an old post of yours from 2007 regarding ETF vs components stocks:

http://epchan.blogspot.co.uk/2007/02/in-looking-for-pairs-of-financial.html

Did these strategies work in 2007 but are now not profitable due to less volatility and HFT?

Yes, ETF arbitrage is one of the favorite strategies of HFT. So I avoid trading it these days. You are also right that low volatility lower the returns of many strategies.

Ernie

Hi Ernie,

After reading your books and blog I was able to create quite a simple but profitable ETF pairs trading strategy. So many thanks for writing your books and actively answering our questions here.

However the return on the ETFs pairs are not that great and also requires quite a large capital to trade. So I like the idea of fx mean reversion. I've been looking at a few pairs, eg AUDCAD like you mention in your book. In backtests I have periods with decent performance but get killed in periods with trending markets. With ETFs I find it easier to find truly cointegrated pairs. Any help on how to deal with these scenarios would be much appreciated.

Do you also think it makes sense to limit myself to pairs that can be converted to USD as quote currency. Eg USDCAD and AUDUSD.

Yes, the trick in trading FX mean reverting pairs is to avoid periods where they are likely to trend.

E.g. after major economic announcements, rate decisions, etc. There is also significant seasonality to their trending behavior.

Ernie

Hi Ernie,

How expensive are the Compustat and CRSP databases?

thanks

I have access to CRSP and Compustat through a free academic license, so I don't know the commercial rate. But I think the CRSP database alone is going to be > $10K.

Hi Ernie,

What return and sharpe ratio is realistic for an ETF pairs trading strategy?

And do you believe that for example EWC-EWA are cointegrated at the moment? Do you have any other pair you can recommend?

In these days of low volatility, a 5% unlevered APR is considered good for a pair.

Sharpe ratio should still be over 1.

EWA-EWC may not be cointegrating in recent years. Try pair trading GLD-GDX.

Ernie

Hi Ernie,

What return and shape ratio would realistic for an fx mean reverting strategy?

Do you have a fx pair you can recommend?

For a single pair, you should expect a Sharpe of at least one.

Many related economies' pairs can be considered: e.g. AUD.CAD, but they don't necessarily mean-revert over all time periods. So finding the right condition is essential.

Ernie

Ernie,

You mention APR a couple of times. Could you clarify?

Thanks

APR=Annual Percentage Rate. I use that to express the annualized compounded return of a strategy.

Ernie

Hi Ernie,

You mention above that both fx and ETF mean reverting strategies should have sharpe ratios of around 1. You also mention you have greater return with fx. Is that just an effect of higher leverage then?

Thanks

Hi Ernie,

You mention fx pairs might not be mean reverting on all timescales. Any suggestions on how I can approach testing for mean reversion under these conditions? As I understand cointegration is a long term property so a test for that might not be useful for example for intraday mean reversion.

Many thanks

I have found returns on ETF to be decreasing in recent years due to reduced volatility, and the returns are further eaten up by bid-ask spreads.

FX has a bit higher volatility and lower bid-ask, which makes a lot of difference in the current environment.

Ernie

Correct: it is hard to find FX cointegration over long term. We have to resort to backtesting customized strategies.

Ernie

Hi Ernie,

Do you find any technical indicators useful for fx mean reversion trading? E.g. RSI

Many thanks

I find Bollinger bands to be good for mean-reversion trading for FX, or in fact any markets.

Ernie

Hi Ernie,

I have an enquiry about mean reversion strategy. I have developed a program to detect Mean Reversion. But I do not know where to start applying this strategy to HFT. thanks for your help.

Amin

Hi Ernie,

I have an enquiry about mean reversion strategy. I have developed a program to detect Mean Reversion. But I do not know where to start applying this strategy to HFT. thanks for your help.

Amin

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