Have a guess what the above formula is telling us. No? Well, it is an integral part of the job description of Euro 2016 stars Gareth Bale, Dmitri Payet and Cristiano Ronaldo while David Beckham used to have it down pat. Published by Leicester University physics students in a paper in 2012 – and for whatever reason picked up by certain UK tabloids only this March – it is the secret of the curved free kick.
For what it may or may not be worth, the four masters students calculated that the distance a ball bends (D) as a result of something called ‘Magnus force’ is related to the ball’s radius (R), the density of air (ρ), the ball’s angular velocity (ω), its velocity through the air (v), its mass (m) and the distance travelled by the ball in the direction it was kicked (x).
Astonishing really that Bale and the others can work all that out in their heads – you would think they would at the very least have to drag a whiteboard onto the pitch every time they line up a free kick. But we are being ridiculous, you say? Footballers do not work out ‘D’ – it is all down to skill, experience, instinct and practice. And, actually, we agree – so what do you make of this next formula?
𝑟𝑡 – 𝑟𝑡𝑓 − 𝛽Buffett 𝑀𝐾𝑇𝑡 = 𝛼 + 𝑚𝑀𝐾𝑇𝑡 + 𝑠𝑆𝑀𝐵𝑡 + ℎ𝐻𝑀𝐿𝑡 + 𝑢𝑈𝑀𝐷𝑡 + 𝑏𝐵𝐴𝐵𝑡 + 𝑞𝑄𝑀𝐽𝑡 + 𝜀𝑡
This one relates not to the work of footballers but of a different and, at least in the eyes of The Value Perspective, far more talented superstar – Warren Buffett. It appears in a paper by Andrea Frazzini, David Kabiller and Lasse Heje Pedersen called Buffett’s Alpha, which first appeared around the time of the Leicester students’ work and sets out to square a particular circle.
Essentially, Frazzini, Kabiller and Pedersen set out to pinpoint the secret of Buffett’s success. Bearing in mind the Sage of Omaha’s investment vehicle Berkshire Hathaway has produced double the annual return of the S&P 500 index over the last 50-odd years, they are by no means the first to try this but the trio reckon they are onto something everyone else has missed.
One interesting point they make is that, if you could travel back in time to pick just one US stock in 1976, which is when their data starts, then Berkshire Hathaway would be your bet. In other words, Buffett has not only outperformed every other US investor over that period, he has also outperformed every other US equity investment. How?
Frazzini and co argue all previous academic analysis that has been done on Berkshire Hathaway is inappropriate because it ignores a number of factors. It is not just that Buffett invests in value and quality but that he “bets against beta”, he targets “quality minus junk” and – something to which we will return a bit later – he uses leverage.
So could other investors replicate Buffett’s magic touch? The paper’s authors evidently believe so – hence the above formula, whereby they “capture Buffett’s stock selection tilts by running a regression of his monthly beta-adjusted returns on the factors that help explain his performance”. Here on The Value Perspective, however, we are not so sure.
That, over the years, Buffett has done a spectacular job for his investors is beyond any doubt – but focusing on whether or not this can be explained in retrospect misses the point on a couple of levels. For one thing, Buffett came up with a way of spanking the market 50 years before huge amounts of back-testing, regression algorithms and computer power enabled this paper to be written.
Indeed, we would suggest, it all rather diminishes the skills that were needed to achieve all that Buffet has achieved – particularly as the formula makes use of knowledge that simply did not exist in 1976. Arguably more important, however, is the question of whether investors should be trying to copy what Buffett is doing in the first place – after all, the way he operates is tailored to his own unique situation.
For a start, Berkshire Hathaway is not a portfolio but an insurance company, which means it is overseen by an insurance regulator that checks every quarter whether or not it holds enough capital. That is why Buffett buys the likes of Coca Cola and Heinz – quality businesses with underlying earnings streams that (hopefully) tick up every year and that (again, hopefully) offer no nasty cyclical peaks and troughs to upset the regulator.
Furthermore, Berkshire Hathaway has in the region of $550bn (£413bn) of assets so – if they are going to have any meaningful impact on performance – the only companies Buffett can really buy are very large ones. Again, this is not something most investors are in a position or would necessarily want to do – and the same goes for his use of leverage, which we mentioned earlier.
If, since 1976, Berkshire Hathaway has outperformed every single stock on the US market and yet this is the pond in which it principally fishes, then there must be another factor at work. One possibility, if it were not anathema to Buffett’s approach, might be brilliance at timing the market but, as a little analysis of the Berkshire Hathaway balance sheet reveals, the real answer is it borrows to invest.
The company’s leverage is currently around two to one so, when it says its return on equity is around 20%, its return on assets is half of that – which is good, but not too dissimilar to a top-quartile equity fund manager. Thus, even if you did copy Buffett and buy Coca Cola and all his other quality-franchise mega-businesses, you still would not see Berkshire Hathaway’s returns because, we would presume, you are not two times levered.
It should go without saying none of this is to denigrate Warren Buffett in any way. He is truly one of the investment greats – but that does not mean his recipe for investing these days is to other people’s tastes. Indeed, rather than worrying about any sort of special formula, investors would be much better served by tracking down Buffett’s shareholder letters – particularly his older ones.
These were written when he had far fewer assets under management than he does today and thus far greater leeway to invest as he wanted. Reading these, to mangle the well-known phrase, you will teach yourself how to catch manageable fish rather than merely watching Buffett land his sea-monsters or, even less productively, setting sail to try and catch them yourself.