A theorem fit to terrify bankers

Looking down the list of winners of the Nobel memorial prize in economics, two names are causing bankers across the world to break into a cold sweat. They are Franco Modigliani (laureate in 1985) and Merton H. Miller (laureate in 1990). Both men have been dead for years but their most important idea lives on with the undignified name of M&M.

M&M refers to an important-seeming decision for any company: how much should it be funded by borrowing, and how much through raising money by issuing shares or retaining profits? Some companies, famously Apple, have no debt to speak of. Others, including any bank you can name, raise most of their resources by borrowing rather than issuing shares.

I say “important-seeming”, because M&M, the Modigliani-Miller theorem, is an elegant proof that under certain circumstances the debt/equity mix of a company’s funding doesn’t actually affect its value at all.

Imagine a company called Papple. It has issued 100 shares, each a claim on 1 per cent of Papple’s future profits. Papple has big plans, which it could fund by issuing 100 new shares, making each old share worth only 0.5 per cent of Papple’s profits. Alternatively, Papple could borrow money, leaving each shareholder with the right to 1 per cent of Papple’s profits, but pushing shareholders to the back of a queue behind the company’s creditors. That second option is riskier, but more profitable for shareholders if the expansion plan works. If the plan fails and the debt can’t be serviced, Papple will be bankrupt.

It seems a fraught decision, but M&M says that it doesn’t matter what Papple does, because investors in the company can always hedge their bets if Papple seems too risky, or borrow money to buy extra Papple shares if they feel that Papple is too boring an investment without such leverage.

M&M requires assumptions that never hold, of course. But the core of the argument is rock solid: companies which take on debt expose their shareholders to higher rewards and higher risks; the shareholders can take steps to offset these risks at the cost of giving up some rewards; the whole decision is less important for the company’s value than you might think.

But this neat little textbook theorem turns out to be very weighty indeed for the question of bank regulation, a cause championed in a new book by Anat Admati and Martin Hellwig, The Bankers’ New Clothes. Regulators want banks to fund themselves more through equity and less through debt. Bankers are reluctant.

M&M applies to banks, too, but with a twist. Banks that get into financial trouble cause systemic damage, so even if M&M applies from the point of view of investors, society would prefer less debt and more equity. But bank investors want the opposite, because the “too big to fail” subsidy means that shareholders enjoy successful gambles while creditors are bailed out if things go wrong. This subsidy means that debt-laden banks are more valuable to investors. If M&M holds, the taxpayers’ loss is the bankers’ gain.

Bankers have tended to argue that equity is scarce and expensive and too much equity means that banks will make fewer loans at higher rates. M&M shows us that this argument is wrong in theory.

In practice, M&M roughly holds: as leverage falls, equity becomes substantially cheaper. Banks are tempted to take on more leverage not because debt is efficient but because debt is the route to an implicit government subsidy.

Banks should be obliged to use more equity funding – or in the misleading jargon of the industry, to “hold more capital”. But equity is not “held”. It’s perfectly good money, provided on flexible terms. It can be lent to businesses and homebuyers just like debt – and with far more resilient results.

Tim Harford is the presenter of Radio 4’s ‘More or Less’

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