Monday, 5 October 2015

The cost of funding a bank just via equity is the same as funding it just via debt.

Banksters have made a good job of persuading politicians and regulators that bank capital is more expensive than bank debt.

The argument behind that claim is all to alluring, and it’s thus. Shareholders get haircuts before other bank creditors when a bank has problems, thus shareholders demand a higher return that other bank creditors. And that leads to the inescapable conclusion that equity or capital is an expensive way of funding a bank, doesn’t it?

The flaw.

One way of demonstrating the flaw in the latter argument is to consider two banks which are identical except that one is funded entirely or almost entirely by equity, while the other is funded entirely or almost entirely by debt (i.e. deposits and/or bonds).

Now if the “capital is inherently expensive” argument is correct, then funding the “equity only” bank should be much more expensive than funding the “debt only” bank. In fact the cost of funding the two is exactly the same, and for the following reasons.

I’ll assume initially that the government of the country where those two banks are located wants to maximise GDP, and to that end, government rules out all forms of subsidy (except where there are good social justifications for a subsidy as is doubtless the case with kid’s education). That is, government offers no subsidy of any sort for banks or depositors in the form of rescuing banks with taxpayers’ money.

Now the risks run by a bank are determined ENTIRELY by the nature of its assets - e.g. are the assets dodgy NINJA mortgages or more conservative mortgages? So let’s say the chance of the value of those banks assets declining to say 90% of book value in any one year is 1:20. (Replace 90% and 1:20 with X and Y if you like algebra).

So in the case of the bank funded just by equity, there’s a one in twenty chance of the assets and hence the value of shares declining to 90% of their book value in any one year. (Incidentally I assumed there that the value of shares is determined JUST BY the value of the bank’s assets and not to any extent by the bank’s perceived prospects, a factor which in the real world obviously also influences share prices. However, the latter “prospect” factor is as likely to boost share prices as to depress them, thus ignoring “prospects” is not wildly unrealistic.)

Funding a bank just with debt.

Now for the bank funded just by debt.

In this scenario, it’s debatable as to what happens when the assets of the bank decline to 90% of book value: the bank might be tipped into insolvency or it might not. But to keep things simple, let’s say there’s a law stating that when assets fall below 95% of book value, that the bank must be wound up, and that in the specific case of our hypothetical bank, assets actually fall to 90%, so the bank is in fact wound up.

Now what do bank creditors get by way cents in the dollar? Well obviously they get 90 cents in the dollar (ignoring the cost of insolvency proceedings).

But 90 cents in the dollar was exactly what those shareholders ended up with when assets fell to 90% of book value! So the risks run by shareholders and debt holders in the above two hypothetical banks is the same!

Ergo the return those two types of bank funder (shareholders and debt holders) will demand is also the same!

How does that come to be?

Now that’s an odd result. Part of the explanation is that as a bank’s capital ratio falls from 100% to 0%, the nature of debt changes from genuine debt into equity.

To illustrate, where a bank is funded about 90% by capital and about 10% by debt, the chances of debt holders losing out are very small. Thus their so called “debt” is genuine debt: that is, there’s a near 100% chance they’ll get $Z back for every $Z they deposit at or lend to the bank.

In contrast, where a bank is funded say 1% by capital and 99% by debt, it’s a complete delusion to think that debt holders don’t run a risk. That is, debt holders have in effect become shareholders: that’s shareholders as in “someone who stands to lose a significant portion of their stake in a corporation when the corporation has problems”.

Let’s assume deposit insurance.

It was assumed above that government offers no assistance to depositors where a bank goes under. If we make the alternative assumption, namely that government runs some sort of FDIC type deposit insurance scheme, and if we assume that the insurance premium is realistic, that makes no difference to the above conclusion.

Reason is that if depositors are aware of the risks they run, and demand the correct return in compensation for that, then that return will be equal to the premium that the FDIC deposit insurance system would charge.


  1. Ralph> The cost of funding a bank just via equity is the same as funding it just via debt.

    It's not clear what you mean, IMHO the word "cost" doesn't make sense here, and should be replaced with "expected return" i.e. the return expected by investors. Now, according to the well-known risk/return tradeoff argument (cfr e.g., equity holders of bank X normally should expect a higher return than bond holders of that same bank X. Because (even under normal circumstances, without default) bond return is fixed ("coupon") while equity return ("dividend") is not.

    1. Fair point. But “cost” and “expected return” are the same thing surely? I.e. if the return demanded or expected by all those funding a bank is Z%, then the “cost” of funding the bank is Z%.

      Perhaps I should have expanded on that point above. So I’ll expand on it now. What I’m saying is that the return demanded by those who fund a bank is made up of two elements: first the reward required for saving / abstaining from immediate consumption. Second, there’s the return demanded for accepting risk.

      I’m claiming that the latter first reason for demanding a return is the same for shareholders and debt holders. As regards risk, I’m saying that debt holders (if they’ve got their heads screwed on) will also be aware that they’re accepting risk (even though they might seem to be guaranteed their money back and guaranteed a return on that money). And that risk is the same for shareholders and debtholders.


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