Graph Trouble

Maybe my readers can help me out here. I’m researching the link between gender diversity and company performance, and having read about 20 academic papers on the subject I’m now looking at studies various companies have done. Currently I’m on this one (.pdf) from Credit Suisse, in which they evaluate 3,400 companies across 10 sectors in 40 countries including 27,000 CEOs and senior executives. This graph on page 25 is confusing me:

If you were to plot the share prices of two random companies, you’d not expect them to follow the same path. If you were to plot the share prices of two companies in the same industrial sector exposed to much the same market forces, you’d perhaps expect to see them follow similar paths. But how likely is it that you take 3,400 companies across 10 sectors and 40 countries, divide them into baskets depending on the number of women in senior management, plot the share prices and they all have roughly the same shape?

Given the only differentiation between the baskets is the number of women in senior management, I’d have expected each line to be of a different shape, reflecting the combined fortunes of each individual company in each sector in each country. Is this a complete fudge, or am I missing something here?

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44 thoughts on “Graph Trouble

  1. All equity indices have been much more volatile than that over that period, so there is a lot of smoothing going on (eyeballing, looks 12m rolling average). With a smoothing formula you can prove lots of things. Also why 2013 start date, did they have that mix then (also, by eye if you start at May 2014 it’s the opposite conclusion) What was the average mix over the period? What is “senior” does it include NEDs?

  2. Also why 2013 start date, did they have that mix then (also, by eye if you start at May 2014 it’s the opposite conclusion)

    Ah no, to be fair they are updating their 2013 study. The full graph since 2009 is here.

  3. I don’t know the answer to your question, but you might want to check if this graph has been normed for company size. Bigger businesses, which might be more profitable, might also face increased requirements or pressure to hire more female managers. And I suspect newer, less established companies are more likely to be all blokes.

  4. Bigger businesses, which might be more profitable, might also face increased requirements or pressure to hire more female managers. And I suspect newer, less established companies are more likely to be all blokes.

    That is most probably going to be the subject of my own research. But I still don’t know how that would have their share prices following the same path, unless – as Food Fighter says – some smoothing formula has been used.

  5. ” But how likely is it that you take 3,400 companies across 10 sectors and 40 countries, divide them into baskets depending on the number of women in senior management, plot the share prices and they all have roughly the same shape?”

    Not at all likely. Not only do they have the same shape, they show progressively better performance with more women in a very ‘progressive’ way.

    The data will have been normalised in some way to hide the actual performance differences.

  6. The graph certainly appears to very precisely prove that which needed to be proven. Could they have borrowed the data tweaking algorithms from the Warble Gloaming or health fascists?

  7. I’d say that the lines simply follow the market approximately. 3400 companies is a large sample, and even divided into several baskets, averaging and then plotting the performance against time will almost inevitably be similar to how the market as a whole behaved.

    What puzzles me about the graph is how come that every individual basket had better performance than the “All companies” line? The only way I can see *that* happening would be if there are baskets missing from the graph (with >50% women participation, maybe?), with their average performance being waaaaaay below average, thus pulling the global average down. But that is also unlikely because >50% senior management participation among women is probably exceedingly rare, if it exists at all.

  8. I’d say that the lines simply follow the market approximately. 3400 companies is a large sample, and even divided into several baskets, averaging and then plotting the performance against time will almost inevitably be similar to how the market as a whole behaved.

    I thought that, but surely not all sectors follow the same trends? Oil and energy don’t generally follow the same market trends, for instance.

    What puzzles me about the graph is how come that every individual basket had better performance than the “All companies” line?

    Yeah, I couldn’t work that out either. There’s no description of the baskets, either their content or method of selection, in the report. An academic paper would have given full details of this.

  9. “I thought that, but surely not all sectors follow the same trends? Oil and energy don’t generally follow the same market trends, for instance.”

    Should not matter one bit when averaging across sectors, unless some sector is over-represented in the sample.

  10. Some of the conclusions they come to are not only sexist, they are also naive beyond belief.

    “Consistent with our 2014 research, we find that
    companies with higher female top managers show a
    higher dividend payout. Here we see a consistently
    higher payout with the greater number of women in
    management. The interpretation in our previous
    report was that women seek to run a tighter balance
    sheet with less of a cash war chest to fund potential M&A and to avoid empire building practices of past
    cycles”

    For a start, drawing a conclusion that ‘women’ are a hive mind must be an insult to women

    The second being the most obvious reason is that women prefer employment at mature companies that pay bigger dividends, rather than growth companies that do not. Or, mature companies that pay high dividends, have the time to worry how many women are in senior management.

  11. My first thought having read the previous comments is that they’re playing sneaky buggers. It gives the impression that the lines are “banded”, i.e. up to 15%, the next tranche up to 25% and so on. But actually the legend doesn’t say that.

    I suspect that they’re literally 15%, 25% etc. (to their level of granularity, so probably 14.5 to 15.4%, etc.). And that it just so happens that by choosing 15, 25, 33, 50% they get the result they’re looking for, with some values that don’t look arbitrary. And that the reader of average attention will presume is banded. It’s the only way “all companies” being the bottom line and not somewhere in the middle makes mathematical sense.

    I wonder what it looks like with 16%, 26%, 32% and 49%?

  12. For me the obvious question is— they have yearly gender employment information for 3400 companies going back to 2009? Or are they taking the gender employment ratio today and looking at those companies historical performance? Note that the latter tells you very little about the performance of female managers.

  13. I should probably read the report properly, but;

    I wouldn’t pay a huge amount of attention to that chart; it’s not necessarily all that informative.

    The shape : not that surprising, actually. Since the period is so short (three years?), and they have indexed performance across many companies in many sectors in many countries, the averaging/indexing process will produce the same shape as the whole market line. If you had the dataset, you could segregate by something else entirely, say Arsenal supporters on the board, and get the same shape in each basket. Basically, companies in the index are correlated with the index. Whoo-hoo!

    Slightly more interestingly (but not much), and it looks to the naked eye at least, that the apparent increase in share price performance (return) across the baskets comes at a cost; higher volatility (risk). This could just be down to the indexing, but it’s no great surprise; there’s always that risk/return trade off.

    Again, with the indexing; these sorts of charts are typically cumulative; that is once one of the baskets/groups gets a bit of a kick upwards or downwards, it tends to remain a leader or laggard, until there’s another kick. The important thing is to figure out what that kick was, not confuse cause and effect by claiming Arsenal supporters produce better returns.

    A couple of other points; share price performance has a major component; investor preference. The chart immediately prior, Figure 24, begins in 2009. Which I have a major problem with. That’s the year immediately following the GFC, when headline interest rates collapsed and basically did not move at all for the next ten years (thus far). Compare interest rate volatility with the previous ten years (1998-2008) and the ten years prior to that (1988-1998). Post-2008 is an entirely different set of market conditions. It is possible (IMHO, highly probable) that the apparent out-performance of these firms reflects a significant shift in investor preference towards more mature, larger, cash generative and lower risk firms in the aftermath of the GFC. The report does appear to point out that firms in the higher baskets have lower leverage (lower equity volatility), lower cash balances (lower cash drag on underlying business performance) and higher dividend yields.

    However, since interest rates are so low, we do have the zombie firm effect. How many firms that have failed over the last few years (I’m mainly thinking retail here as those are the ones most visible) had how many female execs?

  14. Should not matter one bit when averaging across sectors, unless some sector is over-represented in the sample.

    Which is exactly what would happen when they’re split into baskets depending on the number of female managers, no? So you’d (say) end up with most energy companies in the 15% basket and most media companies in the 50% basket. In that case, I can’t see how the trend lines would match the trend line of all of them combined.

  15. The thought occurs;
    For those firms that have lower leverage, lower cash balances and higher yields; did those firms have those attributes before women began to form a higher proportion of senior roles, or did those attributes form afterwards?
    Second, is there evidence that those firms differ significantly in vintage where they share the attribute in bintage?
    Is this purely a corporate lifecycle effect with a demographic overlay?
    Outside of the senior roles, what’s the turnover between male and female staff broken down by age / vintage (time with the firm)? I have my suspicions about this one in particular, and I don’t think it’s going to end well.

  16. Anton Berezin summed up my thoughts quite nicely.

    I should like to add that they are treating the %age of women as if it were a constant, unchanging attribute of the company, thereby suggesting that it is the cause of the performance difference (lots of women – good, few women – bad). But an elderly curmudgeon could interpret it the other way around with equal justification:

    E.G. All the companies start out in 2013 with about 30% women, all of whom are useless freeloaders whose only purpose is to virtue-signal. The companies’ performance follows a Gaussian distribution – some do well, some do poorly, precisely according to chance. Those which do well experience virtue-signalling-creep, and wind up with 50% women after 3 years. Those who do poorly, drop the freeloaders in a desperate bid to remain solvent, and wind up with 15% women. Voila’, your graph.

    I’m not claiming that this is the case, merely pointing out that the correlation in this graph needs a lot more data to prove it is the causation it seeks to prove, even if the data has not been massaged at all.

    If I had to try to convince anyone of this, I would choose some metric which is indicative of success, but not causative – for example, generosity with dividends. I expect I would succeed in generating a very similar graph to prove my point. And if I failed, why, I would repeat the process with other categories (e.g. large land acquisitions for new offices) until I succeeded. This would be the equivalent of finding no correlation between success and hiring women, and then going on to look for correlation between success and hiring women over 45. Or 50. Or women of color. Or….

  17. Yes, you’re missing something:

    “But how likely is it that you take 3,400 companies across 10 sectors and 40 countries, divide them into baskets depending on the number of women in senior management, plot the share prices and they all have roughly the same shape?

    Given the only differentiation between the baskets is the number of women in senior management, I’d have expected each line to be of a different shape, reflecting the combined fortunes of each individual company in each sector in each country. Is this a complete fudge, or am I missing something here?”

    The biggest influence on share prices will be – say for example – the business cycle itself. Stock prices in general being leveraged to that. So, what is interesting – if anything is – is the variance between the different sub groups you’re looking at after than general movement.

    We can go further. Say, for example again, that we know there are four influences. Business cycle, then those animal spirits things, then sector, finally gender of management.

    If we look as this chart is, stock prices in general and then gender, the basic form of the chart will be dominated by our largest influence, prices in general. Y#The interesting bit, our look at gender, is the divergences from that general pattern when we look at gender.

    This will be true of any comparison between a lower importance reason for stock prices and a higher. The higher reason will always determine our general shape, our lower only the divergences from it.

  18. The second being the most obvious reason is that women prefer employment at mature companies that pay bigger dividends, rather than growth companies that do not. Or, mature companies that pay high dividends, have the time to worry how many women are in senior management.

    That’s partly what I intend to research: when do women get promoted into senior management compared with men, in terms of company size, financial performance, and public profile.

  19. If we look as this chart is, stock prices in general and then gender, the basic form of the chart will be dominated by our largest influence, prices in general. Y#The interesting bit, our look at gender, is the divergences from that general pattern when we look at gender.

    Okay, that makes sense. Thanks!

  20. I’m not claiming that this is the case, merely pointing out that the correlation in this graph needs a lot more data to prove it is the causation it seeks to prove, even if the data has not been massaged at all.

    All the studies, both academic and non-academic, state this shows correlation not causation. The latter usually follow up with a big “but”.

  21. For those firms that have lower leverage, lower cash balances and higher yields; did those firms have those attributes before women began to form a higher proportion of senior roles, or did those attributes form afterwards?

    They look at that in the paper: basically, yes. Although there is a phenomenon known as the Glass Cliff which reckons women are set up to fail by being appointed when times are hard. By refuting this, Credit Suisse inadvertently admits women are generally put into senior management in firms that are doing better than average.

  22. It gives the impression that the lines are “banded”, i.e. up to 15%, the next tranche up to 25% and so on. But actually the legend doesn’t say that.

    That’s a good spot. Again, the academic papers don’t present the data like this, they actually list the P-numbers which suggest correlation to various confidence levels.

  23. Hmm…

    “If we test the company’s actual financial perfor-
    mance rather than what the stock market is pricing,
    however, we find mixed evidence of a glass cliff. In
    Figure 39, we show the ROEs over the three years
    prior to a female or a male CEO taking over and three
    years after. As we see, there is no difference in the
    pattern of returns other than that female CEOs are
    appointed to structurally higher ROE companies –
    sectors such as consumer staples, technology, health
    care and consumer discretionary.”

  24. As we see, there is no difference in the
    pattern of returns other than that female CEOs are
    appointed to structurally higher ROE companies –
    sectors such as consumer staples, technology, health
    care and consumer discretionary

    Well indeed, and I was going to write a separate post on this. Firstly, look at Table 10. It says that firms with more female senior management enjoy increased ROE, a point rather undermined in the quote above when they confess women tend to go into higher-ROE sectors. Secondly, look at Table 10 and Consumer Staples and you see women have a negative premium of 22% on ROE.

  25. My guess is that the baskets are cumulative, so that the 50% basket contains all companies with 50%-100% female employees.

    The 33% will contain the entire 50% basket, plus the 33-49% range. I do this kind of research and overlap is pretty much the only thing that can produce that pattern.

    For what its worth, I expect the task of untangling woman and share performance to be nearly impossible given readily available data-sets. Any honest analysis will be inconclusive because of limited history and regime change.

    If you subscribe to academic notions of finance, if it becomes known that women-led companies outperform that information will no longer affect the share price. (At best you might expect a step change when women are hired, since at that point it is known that the company will be “better run”.)

  26. ‘All the studies, both academic and non-academic, state this shows correlation not causation. The latter usually follow up with a big “but”.’

    Reminds me of this, and specifically the punchline you get if you hover your mouse on the cartoon.

  27. Any honest analysis will be inconclusive because of limited history and regime change.

    When it comes to women on boards, that is exactly what the meta-analyses of the existing academic studies shows: no correlation between that and financial performance. There are no good meta-analyses for the academic studies which look at female senior management and firm financial performance, and the studies themselves are not consistent with one another.

    The only ones overtly claiming the financial benefits of gender diversity with few caveats are the studies produced by Credit Suisse, McKinsey’s, Catalyst, and other companies who are trying to sell you something.

  28. I would suggest that it would be wise to drill down to specific cases used in these statistics, and examine the actual data. How was it acquired? Who did that? Is it accurate?

    What I’ve found, every time I hear counter-intuitive statistics, is that when you dig down to examine where the numbers came from, they’re very often completely untrustworthy on multiple levels.

    Case in point–AGW. Locally, we have a weather station that’s been in service and providing data to the National Weather Service since the 1920s. Originally, it was a part of an agricultural extension station, and out in the countryside surrounded by orchards and other agricultural land use. Since its establishment, the city has grown up around it, and now surrounds it for several miles on all sides. The weather station was that was once out in the countryside is now adjacent to a major throughfare, and the urban heat island effect should be in full force. Yet, when you go and look at the data the AGW believers use, the numbers have not been “normed” downwards in the later decades to account for this fact; instead, they “normed” them upwards in the early years of the records–By a considerable margin. And, interestingly, the numbers that are in the “Official Record” do not come even close to those of a hobbyist of my acquaintance, whose grandfather, father, and himself kept parallel records in service of their orchard operations. The fact is that the various “activists” have so thoroughly polluted the data that you can’t really tell a damn thing from it, and be able to rely on it at all.

    Parallel question to ask is “where did the data come from, and who has had control of it… Can it be relied on?”.

    I’d be suspicious of anything statistical produced by anyone with an agenda. Even with the best of intent, when you set out to argue a point, you’re going to build bias into everything you do, statistically.

    I would recommend that one should start from the other end–Company success and failure–Working backwards from that, look at the composition of the managing boards, and then see if there is any correlation at all to the presence or absence of women. My guess is that there is going to be a huge correlation to a couple of things–Privately held companies are generally going to be managed without a lot of regard to the mandates of the activists, and companies that are on the public dole are going to be dancing their tune. The actual impact of “women on the board” is probably not a function of their presence or absence, but instead, an indicator as to the “grasp on reality” of the company management. Wokeness is not a leading indicator for business success, and if they’re susceptible to influence from the woke, well… Nature will take its course.

  29. Since share prices are exclusively attempts to predict the future, it’s hard to see what useful information can ever be extracted by graphing them against time. At each interval one is simply looking at what potential investors/divestors thought might happen then. You’re simply mapping changing levels of confidence. Maybe investors in 2015 are believing a high ratio of women is good compared to what they were thinking in ’13. So what? Doesn’t prove whether they are or they aren’t.
    And I’m speaking as an ex-stockbroker, used to do this shit as a living. Best place to file statistics on markets is in the bin. The future is & always will remain a foreign country. If it wasn’t I’d be a lot richer.

  30. If there is a connection between share price & female participation, the only thing it can show is the effectiveness of propaganda in favour of increased participation. The collective wisdom of the market is the best tool we have for anticipating the future. But it’s not a method of recording the past. Whether female participation has been successful is a matter for history, not markets.

  31. BTW, imagine it is true that female management makes companies operate better. Great.

    Thus we need do nothing at a societal level. The market will sort it out. Those companies which do better – because they have female management – will dominate the market, having driven the non-diverse out of it by doing better.

    What? This hasn’t already happened? Then we might want to look at our data showing female management outperformance then….

  32. Thus we need do nothing at a societal level.

    Ah, but that’s not how the campaigners see it. Even the academic papers which can’t find a correlation between increased women on boards and financial performance say diversity is good because it’s fairer. Others make the claim that women bring other, non-financial benefits to the company.

    The non-academic studies are saying what all lobbyists say: we need to more, and when we’ve done that, we need to do more again. So going from 10% to 30% women isn’t enough, we want 50%. And it might surprise some people how many countries, including the UK, have imposed mandatory percentages for women on boards.

  33. Since share prices are exclusively attempts to predict the future, it’s hard to see what useful information can ever be extracted by graphing them against time.

    Most academic papers look at Return on Assets, Return on Equity, and Tobin’s Q.

  34. Tim Newman

    “Although there is a phenomenon known as the Glass Cliff which reckons women are set up to fail by being appointed when times are hard.”

    How long before we get the Glass Tower, when women get everything they want and they realise they are still no happier and it’s still all men’s fault?

  35. On p13 why have the guy and pregnant woman get their hands on the arse of the woman in the middle?

    More seriously, as others have pointed out there’s so many confounding factors this does look a bit like conclusion based evidence making.

    One factor to consider is that female talent is distributed just the same as male talent. However we know that women are more risk averse than men so we should expect the most talented women to be attracted to the larger, more successful companies. This leaves the less talented women working for the smaller less successful companies. This could explain some of the compounding effect.

    Figure 16, females as % of MBAs at leading business schools, also asks some questions.

    It looks like only about 30% of them (across all schools) so 70% of the top educated business managers are men. We aren’t told about graduating rates and scores but lets assume normal distribution of talent amongst those men and women and therefore final grades.

    If a company wants to employ the best talent to ensure it succeeds it should be looking to recruiting the best talent. That implies a 70/30 female female split. If they start employing more than 30% women then they are employing lower qualified females than males, which, all else being equal, means a reduction in overall performance – so how to explain the 50% results? Bear in mind that’s business schools now, 35 years ago when today’s senior managers were going through business school it was more likely that <20% were women.

    If women bring something more than just educated talent they need to explain what it is so that it can be measured for firms to use when recruiting women.

  36. Hi Tim

    None of this stuff passes the causation test. The problem is that we do not know if better performing firms, or firms that expect to perform better are appointing female execs, because they can afford to make the gesture. Just as is true for ESG participation. Even looking at new female execs only tells us that firms that are going to perform better may be appointing female execs. To measure something like this one needs a perfect instrument for randomly assigning female execs to new roles. This is not possible and the best papers in the field acknowledge this – and simply try to determine whether female execs have an impact on actions – as opposed to drawing conclusions about performance.

    This paper uses the gender of first children to determine whether family succession is good or bad. (this works because males are more likely to take over and the performance of the firm at succession is almost certainly not linked to gender of first born children, who would have been born decades prior to succession). This is what an instrument looks like:

    https://academic.oup.com/qje/article/122/2/647/1942108

    Given the paucity of properly qualified senior women – and the evidence that directors who are “busy” (hold multiple positions) are bad for performance, the odds are that the drive to increase the number of female directors in many countries will lead to a deterioration in performance. You might want to take a look at something like the number of “busy” female directors in recent years and the estimated effect of “busy” directors on performance and ask whether the rush is bad. (I’m agnostic on the impact of female directors on performance per se – I favour more senior women for rational discrimination reasons, but that is a different argument from saying they improve short term performance.)

    this paper claims women are a good thing but dependent on proper qualifications:

    https://www.emeraldinsight.com/doi/abs/10.1108/17410400610702160

    (And it still really doesnt resolve causation)

  37. https://www.sciencedirect.com/science/article/pii/S0304405X14001093

    A good paper showing causation on why busy directors are bad for firm performance. (natural experiment using board deaths)

    We use the deaths of directors and chief executive officers as a natural experiment to generate exogenous variation in the time and resources available to independent directors at interlocked firms. The loss of such key co-employees is an attention shock because it increases the board committee workload only for some interlocked directors—the ‘treatment group’. There is a negative stock market reaction to attention shocks only for treated director-interlocked firms. Interlocking directors׳ busyness, the importance of their board roles, and their degree of independence magnify the treatment effect. Overall, directors׳ busyness is detrimental to board monitoring quality and shareholder value.

  38. You might want to take a look at something like the number of “busy” female directors in recent years and the estimated effect of “busy” directors on performance and ask whether the rush is bad.

    Indeed, that would be an interesting line of enquiry. One paper I read mentioned that female directors tend to hold more directorships than men, presumably because there aren’t many female directors around and every company is now scrabbling around trying to appoint women.

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