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Managing mathematical mishaps

On 10 August 1628, crowds lined Stockholm harbour to see Vasa, Sweden’s spectacular new warship, set sail on her maiden voyage. The vessel had been constructed in the city’s naval yard and was armed with sixty four bronze cannons, also cast in Stockholm, specifically for the ship. Richly decorated as a symbol of then King Gustavus Adolphus’ ambitions for Sweden and himself, upon completion it was one of the most powerfully armed vessels in the world. Tragically, after sailing just 1,300m and in full view of thousands of now horrified onlookers, the ship promptly sank when it encountered a second gust of wind, later described as ‘nothing stronger than a breeze’.   Not long after her sinking and the subsequent salvaging of most of the valuable cannons, the story of the Vasa fell into obscurity. It was rekindled in the late 1950s after being located again, in a busy shipping lane just outside Stockholm harbour. The ship was salvaged, preserved and eventually relocated to the Vasa Museum in the Royal National City Park of Stockholm. It has proved one of Sweden's most popular tourist attractions, estimated to have been seen by over 35 million visitors. 

The ship’s remarkable state of preservation has proved a boon for archaeologists; never before had a four-story structure, with most of its original contents largely undisturbed, been available for excavation. Aside from the valuable insights it has provided to life and technologies onboard a 17th century warship, an obvious question needed answering – namely, what caused the ship to sink? A variety of reasons have emerged demonstrating its unseaworthiness, one of which is particularly noteworthy in the context of this blog. Experts discovered the hull of Vasa was asymmetric, being thicker on the port side than the starboard side. It is believed workmen on the vessel were using different systems of measurement. Archaeologists have found four rulers used by the shipbuilders; two were calibrated in Swedish feet, which has 12 inches, while the other two measured Amsterdam feet, which had 11 inches. A small difference in the scheme of things, but a mismeasurement that had disastrous consequences.

Fast forward to 1999 and NASA’s very public loss of the Mars Climate Orbiter, the first interplanetary weather satellite. Designed, built and launched at a cost of US$125m, the probe came too close to Mars as it tried to manoeuvre into orbit and is thought to have been destroyed in the planet’s atmosphere. The subsequent NASA investigation into this failure identified another example of using different systems of measurement. During construction and assembly of the satellite, the NASA team used metric units, while a software contractor worked to imperial units. The fact the latter were still being used is surprising enough, let alone the simple mathematical error which accounted for the loss of this satellite, at a significant cost to US taxpayers.

A comedy of maths errors

Thankfully, not all maths mistakes have the alarming impact created by the shipbuilders of the Vasa or the engineers at NASA. They are, however, surprisingly common. In April this year, an article entitled “a comedy of maths errors” written by Matt Parker – the author of Humble Pi – appeared in The Sunday Times. It referenced a number of similar arithmetic, statistical or trigonometry-based mistakes which continue to take place, even in this tech-assisted era, with consequential far-reaching effects. These include a miscalculation by surveyors for an oil drilling company in the US, which resulted in a salt mine flooding, a freshwater lake filling with saltwater and the ecology and local geography of the area being dramatically changed. All this caused by a 14 inch drill hole (or should this be in cm?!) appearing in the wrong place, due to a miscalculated triangulation point.

Whilst the stories told were all very interesting, a key takeaway from the article was the existence of the European Spreadsheet Risks Interest Group – yes, such a body exists. As we all know from experience, mathematical mishaps are far from uncommon and, despite the obvious benefits the beloved spreadsheet has brought to our professional and personal lives, the frequency of errors appearing in spreadsheets is a concern. This Group estimates that, across all spreadsheets containing formulas, 24% of them have a mathematical error. Given the pivotal role spreadsheets play in the workings of businesses throughout the world, it is sobering to think one in four has a maths mistake.

Spreadsheets and finance

When JP Morgan Chase announced it had lost more than US$2bn on hedging activities back in May 2012, many pointed to the actions of rogue trader Bruno Iksil as the cause. But was the "London Whale" — the nickname he was given for his outsized positions — the victim not of hubris, but a simple spreadsheet error? To manage its risk, the bank was using – indeed, it had originally invented in the 1980s – a Value at Risk (VaR) model. This statistical-based approach measures the amount of money the bank could expect to lose on its portfolio of tradable assets in different market conditions. In JP Morgan Chase’s post-mortem investigation of the losses, it revealed the VaR model that underpinned the hedging strategy “operated through a series of Excel spreadsheets, which had to be completed manually, by a process of copying and pasting data from one spreadsheet to another", and "that it should be automated" but never was.

The finance industry, including the investment management community, relies on the computational power spreadsheets provide. Statistical regressions, long term extrapolations, bell-curve distributions and standard deviation calculations are all made easier through their use.

Spreadsheets, maths and Affinity

As an investment team, we undertake the very same calculations. Furthermore, we have been developing analytical tools to enhance our understanding of factor exposures and market beta sensitivities across our discretionary strategies – all of which make use of the utility spreadsheets provide us. We are aware of the risks referred to earlier and continually think about how these can be managed. At the heart of this risk management framework has to be our people and we are delighted to employ two former Maths degree students, as well as a Materials Science graduate, in the team. Their collective mathematical skillset, creativity and simple logic have enhanced our investment process and, despite the geeky-nature of this topic – they are a fun bunch to work with too.

We should add, the Affinity investment process is a long way removed from being purely numbers driven – good old qualitative analysis is at the core of what we do too. When selecting funds for our discretionary portfolios questions such as do we respect the management team? Are their communications clear and simple? What’s our gut feel? all play an equally important role, alongside any metrics we have from spreadsheets.

As many will know, successful long term investing is built on the foundations of art, as much as science. Too much reliance on the ‘science’ is dangerous and mathematical mishaps are an ever present risk. ‘Stormy’ is a metaphor often used to describe volatile markets and we work hard to avoid being blown off course – let alone being sunk like the Vasa by anything stronger than a breeze. 

Julia Warrander and Russell Waite

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