We may see more Carillion-style collapses and it’s because of this outdated financial model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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10 Responses to “We may see more Carillion-style collapses and it’s because of this outdated financial model”

  1. nhsgp

    Black-Scholes is a mathematical model borrowed from rocket science



    Which rockets need Black-Scholes to launch?

  2. nhsgp

    Convertible bonds are not valued with Black-Scholes.

    Because of the features you resort to finite grids.

    But as a professor of accounting, its clear you don’t know that.

    So back to financial statements

    Why does the state leave civil service pensions off the balance sheet?

    Why does the state leave state pensions off the balance sheet?

    Why does the state leave nuclear clean off the balance sheet?

    Why does the state leave PFI off the balance sheet?

    Why does the state leave unpaid wages off the balance sheet?

    Why does the state leave the EU’s debts off the balance sheet?

    Why does the state leave the black hole in BT’s pension fund off the balance sheet when its guaranteed it?

    Why does the state leave Royal Mail’s pensions off the books?

    Ah yes, its a socialist debt and because accountants like you have let them

  3. Prem Sikka

    I do not normally respond to stalkers but will make this an exception. “Rocket Science” is as per numerous interviews by the creators of the model. Mathematical concepts from Ito calculus, for calculating rocket trajectories, were introduced into the model by Merton. This even gets a mention is the this BBC story. More can be found in books/papers on the history and development of Option Pricing theory.

  4. Prem Sikka

    “Convertible bonds are not valued with Black-Scholes”
    To price the convertible bond, one of the models is the bond plus equity option method. That is, the value of convertible bonds is evaluated by finding the value of the straight bond and the value of call option on the underlying asset by option pricing model, i.e. Black-Scholes Model. There is more here

  5. patrick newman

    Good news! We do not have Labour leadership that is in naive awe of the City and financial institutions. There has to be radical reform of company and director law and if RBS has not been sold off why not make it a public sector bank run along John Lewis lines and charged with operating in the national interest.

  6. Craig Mackay

    NHSGP doesn’t seem to understand that the money that the state has to pay out for most of the items on his list are not paid for in the way you or I might pay off a mortgage but are paid for using the revenue derived from the current account (such as taxation). The difficulty that arises in so many of these estimates is trying to work out how they should be articulated. Many of the conventional accounting procedures in valuing long-term liabilities depend on a whole range of unknowns such as the rate of inflation, the return on investments and the actual magnitude of the liabilities at the time they need to be paid. This is the reason that the universities USS pension scheme half their deficit in just a few weeks because the way they were doing their accounting reflected current values of the equities and other holdings that the pension fund possessed. Nothing else in that time changed.

  7. Craig Mackay

    The piece has, what must be, a misprint. All the evidence suggests that the Black-Scholes method should actually be the Black-Holes method whereby lots of information about a company is poured into a gravitational singularity and all that comes out a little blips and burps. I think that corresponds fairly well to the model as described!

  8. Peter Crowley

    So how does an accounting prof value barrier options?

  9. A.Grant Harrison

    From where I’m sitting, someone other than Carillion is attempting to bamboozle its audience. To wit, I can spot a number of material flaws in your argument, being as follows:
    (1) the convertibles. would have been held on C’s balance sheet at the lower of historic cost or net realisable value – NOT the default Black Scholes (B-S) valuation – intrinsically capping scope for reporting abuse;
    (2) accounting conventions require securities like these converts to be reported this way, so the suggestion that Carillion was engaged in some fiendish scam on this front is fatuous;
    (3) investment decision-making by sophisticated investors place marginal reliance on historical numbers – that would be like driving using a rear-view mirror. Such investment decisions rely on prospective cashflows etc. So again, the use of the B-S model for the audited accounts is irrelevant because historic numbers don’t inform new money decisions;
    (4) your argument is of the “if God meant us to fly…”-type, meaning yes, complex financial models can get it wrong (but less and less so with algorithmic methods), but their use has allowed innovative financing practices to flourish which in part explain our standard of living today (ie: what’s your point precisely?); and
    (5) you are trying to turn a narrow (and erroneous) jibe at the B-S model into a wider anti-free market point, which strikes me as childish, given that the history of applied central planning/socialism/communism tells us that if one relies on any other agency than the market to make resource allocation decisions for you, instead of dealing the odd insolvency, you might well find yourself dealing with premeditated State-mandated famine (a la 1930s Ukraine).
    So, maybe you regularly manage to get this stuff past a non-financially literate audience, who perhaps lap up your snake oil, but I won’t.
    Best wishes, A.Grant Harrison….. @wilkesliberty45

  10. Bryn Davies

    Why does the state not have all of its assets on the balance sheet?

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