Magic Formula versus FTSE 100

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Two crashes and two bull markets in a day

After a day (and part of a night) exporting data from Sharelockholmes, ranking it, and creating portfolios from the top 30 companies using two variants of Joel Greenblatt's magic formula, I’d built a monster: 133 individual worksheets, 80 portfolios (40 for each variant of the magic formula), one chart, and a serious case of number blindness.

Constructing it reminded me of painting windows, a job I detest, because it takes days, it's interminably repetitive and one mistake and you're in a world of pain cleaning half-dried paint from glass. Sometimes it goes well, and sometimes it goes badly, and even in these most mundane of tasks, you feel desperation and elation. There's got to be a better method than building up a picture of the performance of the magic formula one portfolio, one quarter year, at a time.

At first I was elated, incredulous even, because I was fresh at the task and the early portfolios trounced the FTSE 100, sometimes by over 40%. Then dejection set in as portfolio returns fell below 10%. When three consecutive portfolios did significantly worse than the market during the crash of 2008 I began to feel desperate, questioning the formula, the data, my own unsteady hand, and finally I felt relief as the portfolios performed well in the subsequent recovery.

Doing quantitative analysis in my naive fashion, puts you through the wringer. I lived through a decade of investing, two crashes and two bull markets, in a day and for that reason I recommend the experience. After all, if you are to  follow a strategy like the magic formula (and I do for Money Observer magazine), and more importantly stick with the strategy, these are the emotions you must ignore.

After all that, Graeme tells me it's not enough. I need to test over multiple ten year periods.

Well he's right, but in my defence I only have ten years of data as opposed to the vast databases available to serious researchers and City folk, and I'm not an academic I'm an investor and blogger which means the opportunity costs of rigorous research may be higher because I've got to get on and write and invest. These results might be useful but they're not Gospel.

One final caveat: Not only did I sort each portfolio individually, but I had to calculate the relative performance of each company that delisted in the course of a year so the potential for human error is high, and I intend to take another look at the data when the blindness has receded.

Here's the chart:


You'll need to click on it to get a full sized version (and if anybody knows how to make fatter bars in Excel, please let me know!).

The good news is the green lines are positive far more often than they are negative and many of the positive bars are significantly longer. In other words the magic formula beat the market, as measured by the FTSE 100.

The light green lines show the performance of what I call the Alt-MF (alternative magic formula), which uses Return on Assets (described at the end of this blog) as a measure of quality. The dark green lines show the performance of the traditional magic formula, which uses Return on Capital

Joel Greenblatt, inventor of the magic formula favours ROC and I assume that he tested both and found ROC did better. I can't get hold of UK data that calculates ROC his way though, and I'm suspicious of the calculations used by UK data providers. Since Greenblatt proposes ROA as the best substitute for ROC I hoped the test would show that using ROA in the UK wouldn't disadvantage investors.

My test suggests it doesn't. The mean Alt-MF portfolio, which use ROA, beat the market by 13%, while the mean MF portfolio beat the market by 12%. I don't think the difference is significant, and broadly speaking the two portfolios prospered at the same time, and disappointed at the same time.

So I got the result I wanted!

But there are a couple of loose ends:

  1. I tested companies valued by the market over £500m, so the total pool of companies from which to pick the top 30 varied. The most was 288 in March 2007, and the least was 155 in March 2003. On average all companies worth over £500m beat the index, by about 4%. I say about, because I haven't gone back and filled in the missing returns for companies that delisted each year unless they were in the top 30. The performance of delisted companies could make a difference, although it didn't to the average return of all forty portfolios of each variant of the magic formula.
    Assuming this figure is right, the magic formula portfolios beat their peers by 8%-9%, less than the 12%-13% they beat the index by. That's probably because the index is weighted. The biggest companies of all have a bigger influence on its performance, whereas many of the companies in my samples are too small for the FTSE-100 and they're equally weighted. Using the FTSE-350 as a benchmark would help a little (although that contains even smaller companies than in my sample, and it's still weighted by market capitalisation).
    Only six of the Alt-MF portfolios did worse than the FTSE 100, and they didn't do much worse. Against the peer-group of companies valued at over £500m, the strategy underperformed on 12 occasions so its even more dependent on a few years of very strong performance. Since the peer group is probably a better benchmark, I probably ought to clean up the data and check the results.
  2. The extraordinarily good performance of the strategy during the crash between 2000 and 2003 is a mystery as Greenblatt found the magic formula beats bull markets handsomely and does marginally less well than the market during bears. 
  3. I'd like to add back the return of the FTSE 100 to get the absolute return of the portfolios (but it means calculating the FTSE’s return for most of 40 one year periods). I'd also like to calculate the performance of the lowest ranked companies but that means creating eighty more portfolios. I'm not sure I've got the energy!

Comment, or send me an email if you'd like to see the spreadsheet.

It's a big download.


What did you do about dividends received in your portfolio vs. the FTSE 100? Would the dividends make a difference?

In long term portfolios in the USA, dividends make up almost 50% of the total return.

Oops, meant to say it takes no account of dividends but neither does the index so I doubt dividends make much difference in terms of relative performance. I also haven't accounted for broker charges, stamp duty or spreads, which might knock off a per-cent or so from magic formula performance depending on how much was invested in each company. There would be a fee associated with index tracking too, of course, usually <1% for an index like the FTSE 100.

Thanks for reminding me Carolyn.

Dividends are a significant proportion of overall stockmarket returns, but I'm trying to capture the excess return from buying shares in undervalued companies. That will come mostly from capital gains as the shares re-rate(though it is possible magic formula stocks pay a higher dividend yield - it would be interesting to check).

That is monster outperformance, and Greenblatt's formula has the further benefit of making some logical sense. (i.e. It's not "Always buy companies with an R in their name, and short the Ks" class silliness).

Presumably the edge will be arbitraged away in the shopping baskets of now, though? ;)

[...] Magic formula versus the FTSE 100 – Richard Beddard [...]

Hi Monevator, thanks for your comments. I haven't been following your blog as assiduously as perhaps I should have as I notice you've set up a passive model portfolio, which is an interesting experiment.

The difference between the performance of the FTSE 100 and an equally weighted basket of companies with market capitalisations above £500m has got me thinking about index trackers. The average 'portfolio' beat the market by an uncompounded 4% by my reckoning (that's a rough figure for the reasons mentioned in the blog). Of course the last 10 years might have been anamolous (and the really big companies that dominate the FTSE might just have had a bad time of it), but it looks to me that the cap weighting of indices is a hindrance so tracking them would be too. I'd be interested in your thoughts.

As for the monster performance, I must admit it I'm still wondering what checks I can do to add weight to the analysis as I slightly disbelieve it myself!

Greenblatt argues that the edge will never be arbitraged away because people will drop the formula in the years it does badly leaving only the disciplined few to profit. I can vouch for the fact that in my decade of investing in a day of backtesting I felt the emotions that might cause an investor to give up on the formula, which is one of the reasons I think it's a good exercise - I'm now prepared for the eventuality of bad years in the model Greenblatt portfolio I run.

Hi Richard,

Thanks for stopping by Monevator. The passive portfolio is actually being run by my co-blogger ('The Accumulator') who started on the site back in October.

I was getting concerned about all the wayward posts I was doing (I'm currently writing a series on subscription shares, for instance!) so I am very glad to have his back-to-basics (and the academic evidence!) approach to investing on the blog!

I have wondered a lot about index trackers 'breaking', especially with the rise of ETFs and the growing flows of passive-only funds. Intuitively one feels there must be more room for active outperformance. I researched this a couple of years ago, but there was a surprising lack of academic research into the idea. I'll have another look soon, perhaps.

That said I do definitely feel the last 10 years was a bad one for blue chip large caps, which de-rated compared to the FTSE 250, say. You see this in other markets too (especially the US).

If inflation starts to rise than that could be one reason for large companies with higher quality earnings to re-rate upwards again?

Anyway, I'm not convinced its an index effect as much as an economic effect, personally.


Aha! I hadn't realised you were two different people.

I see what you're saying, and it certainly wouldn't surprise me if we experienced another example of reversion to the mean and large cap shares re-rated.

[...] magic formula, discussed to death here, here, and [...]

Quick question: Why did you limit it to companies >£500m? Was it because you were using the FTSE 100 as the benchmark?

Hi Gravitas, it was partly because I was using the FTSE 100 as a benchmark (I might have used the FTSE All-Share but Sharelockholmes doesn't have that facility). However I was also interested in another aspect of the MF. Greenblatt's testing shows it works for any size of company and often we see value metrics than generally perform much better with smaller companies but less well with larger companies. So I wanted to give the MF a stern test.

Thanks for the response. Forgot to mention - GREAT WORK!

I've been getting a bit of a headache try to work out whether the ROCE supplied by sharescope would suffice for the MF. For some reason, they use pre-tax profit as the return rather than the more commonly used EBIT for this calculation. Your data has partially satisfied me that its the general principle of finding some evidence of efficient operations rather than the exact ratio used thats key.

I also see the ROCE as secondary to the low PE/high earnings yield, having been convinced by Dreman's work.

Would be great to compare your portfolios to a simple low PE benchmark portfolio to see how much the return on assets/capital adds.

So many questions, so little time!

Thanks Gravitas

Wouldn't it!

I think Greenblatt fiddled with other weightings - so 25% EY say, and 75% ROC and vice versa and found it didn't make much difference which rather implies he thinks they are of fairly equal weighting.

If you look in Montier's Behavioral Investing ( he compares EBIT/EV to P/E and finds that EBIT/EV produces higher returns with only minimal amounts of extra risk . The actual finding is between 1993-2005, average annual return for EBIT/EV, not combined with ROC, was 19.8% whilst PE returned 12.1%. More importantly, the beta for EBIT/EV was 0.3 compared to 0.8 for PE.
Another interesting finding is that whilst adding ROC to EBIT/EV doesn't make much difference to returns, adding ROA to P/E does.

Sounds interesting Calum, I'll look it up.

Thanks Calum. Will have to look that up and confuse myself further!

The decrease in volatility is highly attractive. I noted when looking at the T30 how it appeared to produced superior returns with seemingly lower volatility than the FTSE benchmark ( - don't you just love efficient markets!

T30 had quite a bit of cash in it over that period, which may explain some of the lack of volatility. However, it also makes the returns more impressive!


Just checked the data for the FTSE 350. In the book Greenblatt excludes any company with less than 25% ROA. Currently that leaves 6 companies. If you are still having problems with your Excel bar chart send it me and I should be able to fix it.


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