Get the measure of management

Yet it's easy to speculate that Mr Bolland has jumped before he was pushed. Marks's performance during his tenure hasn't exactly been glittering. True, no boss of what was once Britain's most successful big company has been labelled a success since Derek Rayner left the post in 1988. But, as Mr Bolland leaves, he does so having performed worse than all but eight of the 69 FTSE 100 bosses who have run their company for at least two-and-a-half years. And lest he should blame the UK's economic background, the weather, Marks's suppliers or anything else, it may be telling that the only other boss of a general retailer among the list of these 69 long servers – Simon Wolfson of Next (NXT) – sits in 10th place compared with Mr Bolland's 61st.

How do we reach this critical conclusion? By reference to our annual assessment of the FTSE 100 index's bosses. This delves into the background of the guys and just a few girls – all five of them – who run Britain's biggest listed companies. It collates the data to form an identikit picture. But most of all it attempts to assess their performance.

On that subject, we can say that Geoff Drabble, the chief of equipment-hire group Ashtead (AHT) is Britain's most successful boss – and by quite a margin. He is followed by Said Darwazah of Hikma Pharmaceuticals (HIK) and David Hathorn of Mondi (MNDI); although special praise – because of the longevity of their performance – should go to Next's Lord Wolfson and Peter Rogers of Babcock International (BAB). Those who might be fearing the wrath of their shareholders are John Fallon of Pearson (PSON) – until recently the owner of Investors Chronicle – and Mark Cutifani of Anglo American (AAL). Even Pete Redfern of Taylor Wimpey (TW.) and Paul Polman of Unilever (ULVR) might be a bit nervous (see the table, Best & Worst of FTSE 100 bosses).

Before we focus on performance – and how, hopefully, we have improved the method behind it – let's run through the changing faces in the chief executive's suite and what it means for the profile of the average FTSE 100 boss.

Given that the average tenure of a boss is five-and-a-half years – that's up by four months on last year – we would expect there to have been 18 newcomers during 2015. In fact, we only reach that figure by including the six who have arrived via companies promoted into the FTSE 100 index (see the table, The new kids on the block).

Among last year's departees, some went with honour – Wolfart Hauser at Intertek (ITRK) and Philip Bowman at Smiths Group (SMIN). Others went pretty unceremoniously – Dalton Philips at Wm Morrison (MRW), Anthony Jenkins at Barclays (BARC), who lasted barely three years, and Peter Sands at Standard Chartered (STAN).

The incoming chiefs have, as we said, made the bosses a bit older and slightly less male orientated. Veronique Laury, the new chief of Kingfisher (KGF), took the number of women bosses to five and Alison Brittain made that six when she took over from Andy Harrison at Whitbread (WTB) in December.

They have a slightly less international background – 59 of the 100 are UK nationals, compared with 57 a year ago. In large part that's because 2015 was a good year for housebuilders' shares, which meant that three of them – Barratt Developments (BDEV), Berkeley Group (BKG) and Taylor Wimpey – joined the 100 index. For companies whose activities are almost wholly UK-orientated, it seems more likely that they will have UK-born bosses, as they all do; and, incidentally, one of them – Tony Pidgley at Berkeley – single-handedly raised the average age by about eight months because he is clear of 68, the second eldest Footsie boss behind Sir Martin Sorrell of WPP (WPP), the only septuagenarian in the mix.

It was a good year for the French. Although they lost Guy Berruyer of Sage Group (SGE), they gained Ms Laury at Kingfisher and Andre Lacroix at Intertek. It was an even better year for the Americans, whose numbers rose from four to seven as James Staley at Barclays, Mike Wells at Prudential (PRU) and Bill Winters at Standard Chartered took charge. Those who suffered were the Irish and the Australians, whose number, in both cases, fell from five to three.

Overall, the 100 are now a better qualified lot, or, at least, qualified for financial engineering (a UK speciality). The numbers with accountancy qualifications rose from 15 to 17 and MBAs from 20 to 22.

On your Marks: Marc Bolland finally decided to call it a day as boss of M&S

Not that we seriously imagine there is a causal relationship between, say, the boss having an MBA and producing extra 'value added'. Still, we have isolated the relevant data and checked out the possibility, just in case. In fact, the 22 MBAs are slightly ahead of the game. Between them, they have been in harness for five-and-a-half years, which is virtually in line with the average of the 100 (although it would be more like four-and-a-half years if we excluded WPP's Sir Martin Sorrell, the doyen of Footsie bosses, who has been in his role since 1986, and is a Harvard MBA). Yet their 'value score' is 7.2 per cent against the average for the 100 of 5.3 per cent. To spell that out, it means the share-price return that we could attribute neither to the whole stock market nor to each company's specific sector and that, for good or ill, we attributed to the boss, works out at a simple annual interest of 7.2 per cent over five-and-a-half years for the MBAs, whereas all 100 averaged 5.3 per cent over almost the same period.

But we would need lots of data before we seriously considered that chief executives with an MBA on their CV are likely to bring extra value any more than we imagine that those over six-feet tall or who do 100 press-ups before breakfast or write novels in their spare time are likely to produce above-average returns.

That's because – as we discovered last year – on average the FTSE 100 bosses are, well, pretty average. Back then we assessed the chief's performance simply by removing the effect of stock market movements on each company's share price. This year we have gone one better and removed the effect of the relevant industry sector, too.

This has had a noticeable effect on the rankings compared with last year. Those bosses who had benefited from a strong sector tail wind found it more difficult to do well. For example, last year, Simon Borrows, an MBA and the chief executive of private-equity house 3i (III), was top of the long-term leaders (those bosses with a tenure of at least two-and-a-half years). This year, Mr Borrows did not fare nearly so well, slipping to 25 out of 69. This was because the workings of our model calculated that 157p of the 303p gain in 3i's share price since he became the boss in 2012 was down to the rise in the financial services sector of which 3i is a component. Meanwhile, Mr Borrows was responsible for just 104p of the gain.

Means business: The number of FTSE bosses that have MBAs rose from 20 to 22 last year, and includes WPP boss Sir Martin Sorrell

On the other hand, David Hathorn, chief executive of paper and packaging group Mondi has leapt up the rankings from 21st out of 62 last year to third place this year. That was because Mondi's share price has had to fight against a weak forestry and paper sector. According to our model, since Mr Hathorn became the boss in 2007, the sector's fall has cost Mondi 176p per share. This means that all the 500p gain in the share price since then and more is attributed to Mr Hathorn's efforts.

Yet in whatever way we re-engineered the model that ranks the bosses, the chances are we would find that, in aggregate, their average was nothing to get excited about. In a way, how could it be otherwise? If we assess all the chief executives in relation to the share-price performance of their companies then ineluctably they will be anchored to the returns of the London stock market, which are dominated by the FTSE 100 index. So if the bosses in aggregate comprise all the components of the average, any sizeable sample of them will produce near-to-average performance.

That does not exclude the possibility of excellence – wherever you have an average, you also have the performance of the outliers. If the same names keep cropping up among the outperformers, something significant may be happening.

In that context, it might be useful to focus on the three among this year's top 10 long-term performers who made last year's top 10 when the selection criteria were different – Ashtead's Geoff Drabble, Babcock's Peter Rogers and Ian Gorham of financial services group Hargreaves Lansdown (HL.). Actually, all three of those are chartered accountants, though – based on what we said about MBAs – we don't think that's significant. Beyond that, the ordinariness of their backgrounds is noticeable – no glittering academic institutions attended, no flitting from one great job to another in what might seem like an inexorable drive to the top.

This may tell us to be sceptical about bosses with a super CV. Beyond that, it does not help us too much because if most chiefs have a similarly ordinary background that gives us no clue to their future success, nor – and more important – how that could affect their company's performance. The likelihood is that whatever makes the boss outstanding won't show up in a broad-based exercise such as this. The sad truth is that this exercise can judge performance after the event but can't predict it.

But if its underlying message is that bosses are actually very average, then that raises the familiar question: why are these people paid so much? One might not begrudge the £4.3m that Mr Drabble received in pay and bonuses for 2014-15 (or even the £7.3m he received the year before). Ditto the £4.2m that Mr Rogers received or the £1.9m that was Mr Gorham's 2015 package. It might even be pleasantly refreshing that the two long-term bosses who fell into the bottom 10 both this year and last – Ivan Glasenberg of Glencore (GLEN) and David Fischel of Intu Properties (INTU) – received comparatively modest amounts shorn of almost all bonuses. The figures were £0.97m for Mr Glasenburg and £1.2m for Mr Fischel.

Yet on average FTSE 100 bosses were paid £4.96m in 2015, according to the High Pay Centre, a think-tank. True, that's probably about the same as a good footballer in England's Premier League, though it's clearer that footballers compete in a well-defined talent pool. The chief talent of Footsie bosses may be less to do with running their company and more about being able to manoeuvre themselves into the position where they can extract rents and exploit the system of corporate governance to sustain that.

And this means that the next task of this exercise is to find out which FTSE 100 bosses provide the best value for money. That will be done by linking their 'idiosyncratic' performance – the bit that's unaffected by the stock market or the market sector – to their pay. But that's for next time.

Working out the score

Question: how do you compare the performance of one FTSE 100 boss against another? Tricky because you are making a comparison across industries and across time. So, how is it fair to compare the performance of, say, Dave Lewis, the boss of Tesco (TSCO), with Jean-Paul Luksic, who runs Chilean copper miner Antofagasta (ANTO)? Similarly, how can you rate Andrew Reynolds Smith, newly installed as the boss of Smiths Group, against David Fischel, who has been running shopping-centres owner Intu Properties (INTU) for almost 15 years?

First, you assume that the performance of a chief executive will somehow be encapsulated in the share-price performance of the company that the boss runs. Sure, there will be a lot of extraneous matter in there, too; but company performance, for which the chief is ultimately responsible, must be embedded in the share price somewhere.

Second, you attempt to eliminate the background noise and amplify the relevant signal. There are two bits of background noise that we can identify and whose effect on a company's share price we can quantify. These two extraneous sources are the stock market itself, whose performance is shaped by all sorts of big factors. Then there is the effect of each stock market sector – support services, pharmaceuticals, whatever – which is a proxy for the industry-specific forces that will help or encumber a company regardless of how well the boss does his job.

In effect. therefore, our method of scoring each boss's performance is to say that the stock market acts upon a company's share price and each relevant stock market sector affects the price, too. Eliminate the effect of these two and what remains is the share-price performance that we can lay at the door of the boss. Sure, it's super simplified, but it's a darn sight better than relying solely on share price performance in a bull market, as so many bosses and remuneration committees would have their shareholders do.

So the raw data is each company's share price, the FTSE All-Share index (the proxy for the market) and each sector index to which a company belongs. There are several ways we could use these to assess the bosses and, by way of cross-checking, we have used two distinct bits of arithmetic to ensure that the results are fairly consistent – that, by and large, the best are the best and the worst, the worst. The full data and the results for each method are in the Excel tables attached to the online version of this feature.

However, for a detailed run-through of what's happening, let's focus on the method that we prefer – the one we have labelled 'the value-added method'. We favour it because it generates a value that is intuitively easy to grasp since it estimates the pence per share that the boss has added to – or subtracted from – the share price. Then, to make one boss's performance comparable with the others, we have expressed that value added as an annual interest rate spread over the period he has been the chief.

To explain, let's use the data that took Ashtead's Geoff Drabble to the top of the list. Mr Drabble became the chief executive in January 2007 when Ashtead's share price was 160p, the FTSE All-Share index stood at 3221.4 and the index for support services, of which Ashtead is a component, was 359.4. Since then, the All-Share index has bounced around, but hasn't actually risen much. On 31 December 2015 – the date at which all performance has been assessed – it was 3444.3, or 7 per cent higher.

From that, we can say that the value added to Ashtead's share price by the stock market alone was 11p. That's derived from the 7 per cent increase in the All-Share over the relevant period applied to Ashtead's 160p share price in January 2007. Simultaneously, the support services sector has fallen almost 11 per cent. So, apply the same logic as used for the effect of the All-Share and we can say that the sector-specific factors subtracted 17p from Ashtead's share price.

Now apply both these adjustments to Ashtead's 160p share price at the date of Mr Drabble's appointment and we can say that the share price he was 'given' without any input from himself or the company was 154p (160p plus 11p minus 17p). Yet Ashtead's share price had risen to 1,119p by the end of 2015. So the value added for company-specific reasons – which, rightly or wrongly and for the purposes of this exercise we are attributing to the boss – was 1,119p minus 154p, or 965p. Next, we use an Excel formula to give us the simple interest rate that raises 154p to 1,119p over nine years and that's 69.6 per cent.

True, it's easy to quibble with the logic, most especially because factors affecting the performance of the stock market will be embedded in the sector's performance. However, the method's merits are its simplicity and clarity, which are achieved by separating the gain or loss in a company's share price into three components – the market, the sector and the boss (or – if you like – any factor other than the first two).

Eliminating market and sector effects also puts the spotlight on company-specific performance. Thus companies – and bosses – that appear to have performed well might be shown in a more critical light and some laggards can be seen actually to have done quite well.

Take David Potts at supermarkets operator Wm Morrison. In Mr Potts's spell in charge, his company's share price fell 28 per cent to the year end – pretty pathetic, you might think, given that he has been the chief for just nine months. Yet the effect of both a falling stock market in that period and a plummeting food retail sector meant that the share price should have fallen 38 per cent anyway. In effect, therefore, Morrison's shares have done better than they should have since Mr Potts has been the man. Express that as an interest rate and the shares returned an annualised 21 per cent since he took the reins, which put him in 15th place out of the 100.

The alternative method we used to confirm that our logic was running along the right lines – which we have labelled 'the price-relative method' – is based on taking a company's share price relative to both the market and the sector at the date that the boss was appointed and 2015's year end. With a bit of division and multiplication we got a 'value' for both the day of the appointment and for the 2015 year end. Then we converted the changes in those values into an annual interest rate.

The point is that the rankings were similar using both methods. Of the best 10 long-term performers using our favoured method, eight were in the alternative top 10. Among the long-term laggards, six appeared in the bottom 10 of both lists. For full details, see the Excel sheets attached to the online version.

For a special feature on six newly appointed chief executives and the challenges they face, click here.