We may see more Carillion-style collapses and it’s because of this outdated financial model

Like companies the world over, Carillion used Black-Scholes to value securities – a highly risky piece of maths vulnerable to market crashes.

On Thursday, the Work and Pensions Committee and the Business, Energy and Industrial Strategy (BEIS) Committee will turn their attention to Carillion’s auditors KPMG.

The firm collected nearly £20 million in fees as auditors. It did not raise any red flags even though Carillion had low profit margins, faulty cash flow forecasts, and worthless assets in its balance sheet. It had massive debt and borrowed money to pay dividends

Anyone looking at Carillion’s audited accounts would be bamboozled by science, which only goes to confirm the poverty of the company’s audited accounts.

Carillion’s 2016 accounts had financial instruments in its balance sheet and said:

“The Group’s convertible bonds with a cash settlement option are assessed as a hybrid financial instrument, comprising an embedded derivative component (representing the option) and a debt component.

“At inception, the fair value of the embedded derivative component is determined using a Black-Scholes or a similar bespoke model.

“The fair value attributed to the debt component is the difference between the proceeds of the issue and the fair value attributed to the embedded derivative component”.

This may be gobbledegook to many people but those familiar with the options pricing theory will recognise that Black-Scholes is a mathematical model borrowed from rocket science to value securities.

The securities contain a right to buy/sell at a specified price within a specified period rather than an obligation to buy/sell. The problem is how to value those rights or options.

The value of the options depends on the underlying assets prices, instantaneous trades, time, future volatility in the market and much more.

The Black-Scholes model was developed in the 1970s by US economists Fischer Black, Myron Scholes and Robert Merton. By the 1990s, it was being used by banks, hedge funds.

The model assumed that the markets are smooth, frictionless and do not generate big swings in prices. Of course, mathematical models can’t mimic human behaviour, panics or sudden big changes in the markets whereas.

At such volatile times, some may seek refuge in the predictive power of the model to search for alternative investment strategies, but the problem is when everyone is using the same model they all get the same answer and become trapped.

Still, the Black-Scholes model was considered to be an advance in the world of finance. Fischer Black died in 1995. In 1997, Myron Scholes received the Nobel Prize in economics, which he shared with Robert Merton.

By using the Black-Scholes model and through a combination of buy/sell options, some claimed that they had found a way of eliminating, or drastically reducing financial risks.

The slavish faith in mathematical models encouraged neglect of the danger signals.

The 2007-08 banking crash soon provided a jolt. Lehman Brothers and Bear Stearns collapsed. Many other banks were bailed out. They were all using the Black-Scholes model for valuing their financial assets and managing their risks.

Whether they misunderstood or abused the mathematical equations remains an open question. Nevertheless, the crash should have encouraged reflections on the use of mathematical models and scepticism about its use in company financial reports. It did not.

It did not quite go according to plan for Myron Scholes and Robert Merton. In 1993, they set up a hedge fund called Long Term Capital Management (LTCM).

LTCM essentially placed clever bets, or arbitraged, on the price of government bonds and corporate securities. It boasted returns of 40% on its investment and always received a clean bill of health from its auditors.

In 1998, increased market turbulence due to financial crisis in East Asia and Russia made its financial position uncertain. LTCM lost about $4bn in a period of six weeks and was bailed out by a consortium organised by the US Federal Reserve.

Due to market volatility, seemingly solid valuations of financial instruments melted into thin air.

Evidently, even Nobel Prize winners in economics had difficulty in gauging market turbulence and arrive at an objective valuation of complex financial instruments.

Despite the banking crash and the LTCM debacle, the Black-Scholes model continues to be used in financial reports produced by companies. It is doubtful that company directors, accountants and auditors are more knowledgeable than Nobel Prize winners.

The model produced numbers for Carillion’s financial statements which are incapable of being independently verified. KPMG could hardly redesign the model or develop an alternative model. At best, it would have just gone along with whatever numbers came out of the model.

Carillion’s demise should encourage some reflections on how company financial statements are compiled, but it is unlikely to as there is now vast industry selling, managing mathematical models.

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