# Using the Price of Magic to Estimate the Cost of Capital

There is math here, but also a picture of a dog looking at a piggy bank, so it gets pretty weird.

On Friday, I wrote about the delightful capital arbitrage of DTA-linked notes, in which banks are looking to "get 'capital' by securitizing tax deductions from past losses." 1 As I put it then, one way to get capital is to sell stock, which is expensive, so the banks are looking to rely on magic instead, because magic tends to be cheaper.

That was a glib but controversial statement. Broadly speaking banks can raise debt cheaply, and bankers believe that their equity is expensive. There is a notion that banks have a cost of equity of 10 percent, though that is a pretty vague notion; in any case, belief that equity capital is more expensive than debt is widespread. Some people disagree, though; Anat Admati is particularly adamant that bank capital is cheaper than the bankers let on. 2

But one nice thing about financial markets is that they occasionally let you put a price on magic, and once you've done that, you can use the price of magic to rough out a cost of capital. DTA-linked notes might be useful for doing that, but they don't yet exist. But other kinds of magic do! Or did, anyway.

After writing that post on Friday, I heard from Asaf Manela, a finance professor at Washington University in St. Louis, who recently co-wrote a paper about a different capital arbitrage. Here is that paper. It is called "The Shadow Cost of Bank Capital Requirements," and it is about asset-backed commercial paper conduits with liquidity guarantees.

The magic in ABCP conduits worked as follows:

• If you are a bank, you have assets on your balance sheet, and you need to have a certain amount of equity to support those assets. Let's say you need 10 percent equity -- \$10 of equity for every \$100 of assets -- which is sort of kind of close to true.

• But you can move some of those assets right off your balance sheet by selling them to a thing called an ABCP conduit, which issues commercial paper to the market to fund its purchase of the assets.

• Many ABCP conduits set up by banks come with "liquidity guarantees," which means that, if things go wrong with the assets, the bank will buy them back at par, so the investors lose nothing.

• So for all practical purposes (but not accounting or capital purposes!), issuing an ABCP with liquidity guarantee is the same as keeping the assets on your balance sheet: The risks and economic results are the same.

• Except for two things!

• First, you can have less capital: Until 2004, you could have zero capital against an ABCP conduit with liquidity guarantee; after 2004 (until 2010, when this went away), these conduits had a 10 percent risk-weight.

• Second, you pay a bit more for the ABCP funding than you do for on-balance-sheet funding: On average during their sample, ABCP conduits cost about four basis points more than short-term on-balance sheet debt funding.

If you more or less set those last two things equal to each other, you get the "shadow cost" of bank capital: Since lots of banks did conduits, and since no bank put all of its assets into conduits, that suggests that the marginal price of using ABCP conduits equaled the marginal price of raising more capital. 3

They do the math and calculate that the cost of bank capital is about 0.30 percent (or perhaps more accurately, 0.30 percent above the cost of debt). 4 Which ... seems low? Like, really really really really low? Much, much lower than the mythical 10 percent cost of bank capital? So low that:

We estimate that a ten percentage point increase in capital requirements would cost \$2.2 billion a year for all banks that exploited the loophole combined, and no more than \$3.7 billion for all US banks. The average cost per bank is \$143 million, or 4 percent of annual profits. Lending interest rates would increase by 3 basis points and quantities would decrease by 1.5 percent.

Whoops! Those are very, very small numbers! I mean, big numbers compared with some numbers, but very, very small compared with some other numbers. For instance, not to get all Bloomberg View on you, but some people around here estimate that banks get a "too-big-to-fail subsidy" at \$83 billion a year. You could raise bank capital requirements by 10 percentage points -- roughly doubling them, from 8.5 percent or whatever to 18.5 percent or whatever -- and cost banks less than one-twentieth of that subsidy. Let's do it!

Or not, I mean, this is one data point from an odd corner of the markets, and there are things you can quibble with. One quibble relates to non-linearity; a few extra basis points of capital might be cheaper (or more expensive! 5 ) than 10 extra percentage points. Another would be that the four basis points of incremental interest cost over short-term funding don't entirely exhaust the added costs of ABCP versus on-balance sheet financing. More broadly, banks do not simply optimize profits over an unconstrained choice of financial instruments; ABCP issuance was limited by custom and investor-base size and the need for longer-term financing and the desire to avoid too much regulatory awkardness and generally a host of things unrelated to the pure cost issues described in this paper. It's entirely plausible that issuing more ABCP would have saved banks more money, but that constraints other than costs prevented them from doing that. And if you believe that, then this paper understates the cost of bank capital -- perhaps by a lot.

Still, it's pretty neat! And it points the way to other fun research: Look at other capital arbitrages -- other transactions that allow banks to get similar economic results with different capital treatments -- and see how widely they're used and how much they cost. And then use that to triangulate around how much increasing capital requirements will actually cost banks. All you need is to have a few more capital arbitrages to study. DTA-linked notes would be perfect. That alone is a good reason for regulators to allow them.

This column does not necessarily reflect the opinion of Bloomberg View's editorial board or Bloomberg LP, its owners and investors.

1. That quoted language is I think an entirely accurate description of the situation from an Occupy group on Twitter. They call it a "new bank fraud," which is a subjective term, but they're right that it's basically securitizing tax deductions from past losses.

2. Since equity doesn't have to be repaid, or pay interest (other than optional dividends), you might naively think its cost is zero. It's not, but this debate is so complicated precisely because you go around being naive like that, cut it out.

3. As the paper puts it, "Large constrained banks exploit but do not exhaust the ABCP loophole, which facilitates estimation of the shadow cost."

4. They don't put it that way. They say, "The average shadow costs per dollar assets across all banks and over time are precisely estimated at" 0.003, 0.0022, and 0.0025, depending on whether you're using the tier 1 capital ratio, the total capital ratio, or the leverage ratio. This cost is not the "cost of capital"; it's the "shadow cost" of an incremental dollar of capital, so you can crudely think of it as the incremental cost of getting funding from capital rather than debt.

Read the paper for the math; here's my brutally simplistic intuitive way of roughing it out that gets the right order of magnitude, though it overstates the cost a bit:

[imgviz image_id:irLqgHaZ1fZQ type:image]

5. Anat Admati rests some of her argument on the Modigliani-Miller notion that better capitalized banks will be less risky to shareholders, so shareholders should charge less of a risk premium. More than doubling capital should have that effect, sure.

(Matt Levine writes about Wall Street and the financial world for Bloomberg View.)

To contact the author on this story:
Matthew S Levine at mlevine51@bloomberg.net

To contact the editor on this story:
Zara Kessler at zkessler@bloomberg.net

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