Arbitrage and Non-Arbitrage

There is  a lively discussion over at Warren Mosler’s modestly named blog  Center Of the Universe, revolving around Mosler’s plan for Greece. We’ve heard this story before, but this particular plan is a bit more tricky to dissect, so let’s get some background information on arbitrage first.

There is always a paradigm tension between arguing that asset prices are set by supply and demand versus arbitrage. Of course in actual markets, prices are set by auction — so supply and demand seems to win. However in certain circumstances you can argue that there will always be a demand if the price is below a certain threshold, and there will always be supply if the price is above a certain threshold, so even though actual prices will be set by supply and demand, these will arrange themselves so that the equilibrium price can be determined by arbitrage.

For example, if the central bank allows unlimited borrowing at one rate, then we can argue, abstracting from risk, that bond yields will not rise above that rate, etc. As soon as the supply of bonds increases, the central bank ensures that the demand for bonds increases to match.  Suppose on the other hand that the central bank allowed unlimited borrowing at 4%, but each time a private sector actor bought a bond, the central bank would offer to sell another bond at auction? What can you say about the equilibrium price? Each time demand increases, supply increases by the exact same amount. Furthermore, let’s suppose that the central bank did not lend unconstrained, but only against a limited quantity of collateral and only to a small group of borrowers.

Now can you argue that bond yields would not fall below 4%? No, you cannot. The only thing you can argue is that those eligible to borrow would most likely earn an arbitrage profit up until they were no longer eligible. Rather than being fixed at 4%, the actual price would be indeterminate based on just the information provided. As we are talking about Greece, the odds that the bonds would trade at the risk-free rate are slim.

And that’s what’s going on in Mosler’s proposal. He argues that by making bonds eligible for payment of taxes, that they would become risk-free instruments. But for everyone paying taxes with a bond, the government will sell another bond. Here supply increases with demand, bond for bond, so that you cannot argue that arbitrage will set the price.

As a result, there will be a select group in the economy — primarily banks — that will earn arbitrage profits as a result of this proposal, which is why it’s a signature Mosler proposal. The guy should patent progressive sounding policies that pick the pockets of the middle class and supply banks with economic rents. Those suckers whose taxes are withheld and who do not have cheap access to credit will have to pay their taxes, whereas those who do have access to cheap credit will buy bonds from the government at a haircut, and then supply those bonds in lieu of their tax obligations, up until they are no longer eligible to borrow. Effectively the government will impose radically regressive taxes on the Greek population in the event of default.

Now certainly those holding Greek debt would prefer to have this benefit than to not have it. Everyone prefers a government transfer, and no one likes to pay taxes. However, exempting bond holders from payment of Greek taxes doesn’t actually help Greece in any material sense, and it does not ensure that yields on Greek debt will be materially lower. The only thing it ensures that there will be real transfers from the non-bank population to the banks;  from those without access to cheap credit to those with this access.

The way to actually solve Greece’s problem is, of course default and exit from the Euro.  The opposite of giving bondholders an additional transfer. Greece is already transferring far too many resources to them.

UPDATE: fixed “rise below/rise above” typo pointed out by SRW.

Arbitrage and Non-Arbitrage

12 thoughts on “Arbitrage and Non-Arbitrage

  1. rsj — so i’ve been thinking about Mosler’s (with Marshall Auerback) proposal. honestly, i’m still puzzling over it, it has lots of subtle characteristics, though i’ve not come to a strong conclusion. in broad outline it is a credit enhancement, and in particular it strikes me as analogous to netting arrengements between counterparties in the derivatives market. it didn’t strike me so much as a transfer to existing bondholders, because as i understand the proposal, the redeemability against taxes would only be for newly issued and sold bonds. in theory, competitive bidders would force yields to fall sufficiently to offset the value of the transfer, abstracting away from the efficiency of the argument or limits to arbitrage by people who expect to be subject to Greek tax liability, or by banks who could transparently substitute bond redemption for customers’ tax payments. (inefficient auctions or limits to arbitrage might undo the proposal, but that’s a different discussion.)

    if redeemability were offered for the existing, outstanding stock of bonds, that would certainly be a transfer to bondholders, an ex post grant of a very valuable option for free.

    as i understand it, the motivation for the proposal is to restore “sovereignty” by permitting states to choose their budget deficit independently of solvency concerns. putting aside limits to arbitrage (by taxpayers or banks), for any given budget deficit, there is some level of tax obligation that would ensure the bonds trade at near the risk-free rate. at first this struck me as self-defeating — “austerian” or “neoclassical” — as the MMT-ers like to say, but as I’ve thought it through I’ve become more interested (but still uncertain). my initial skeptical intuition was directional: the credit enhancement is only valuable when there are lots of outstanding tax obligations relative to the float of bonds. but i think — i’m not sure, still working it through — the directional similarity might hide a range of options excluded by traditional solvency constraints for a noncurrency issuing government. again, i don’t have a strong view here, one minute i persuade myself that this proposal does effectively expand the range of financing options for a currency-pegged state, another minute i persuade myself that it really doesn’t, that the value of the option to redeem is basically contingent on traditional solvency, so bondholders are as usual made whole only by virtue of taxes actually collected in Euro. i’d like to try to more carefully model this to resolve my internal controversy, although i don’t know that i ever will.

    i don’t grok a piece of your argument, but i’m probably just being stupid:

    For example, if the central bank allows unlimited borrowing at one rate, then we can argue, abstracting from risk, that bond yields will not fall below that rate, etc.

    isn’t this the other way around? if a cb allows unlimited borrowing at 4%, bond yields cannot rise above 4%, as (eligible) borrowers would borrow at the central bank rather than issuing bonds at higher cost. but if the cb allows unlimited borrowing at 4%, why couldn’t yields fall lower? as a borrower, if someone else offers to lend at 2%, i’d take that. and the cb’s willingness to lend at 4% wouldn’t prevent another borrower for competing for the loan at 2%, if that other borrower thought it profitable. i think the CB’s lending rate — the rate at which it permits unlimited borrowing — is a ceiling on yields, and the central bank’s borrowing rate — the rate at which it is willing to accept unlimited lending — places a floor beneath rates by arbitrage. but maybe i’m getting signs confused in my head; it wouldn’t be the first time.

    1. Yeah, that was a typo — fixed now in the post, thanks.

      About the other points, if we contrast the Mosler Plan with the plan discussed on your site, the latter increases the tax burden of bondholders, effectively guaranteeing that the government has sufficient income to service the debt. The Mosler plan decreases the tax burden of bondholders in an attempt to make the bonds more valuable — to increase the demand for bonds. But that reduction in tax burden comes at the expense of increasing the quantity of bonds supplied — there is a loop.

      Imagine if a central bank functioned as a regular bank — in order to purchase bonds, it would need to sell its own bonds in open auction. Now the central bank announces that it will purchase any private sector bonds that yield more than 4%, when the current rate is 6%. Will this cause the interest rate to decline to 4%? Or will it represent a transfer, as households sell their own bonds to the Central Bank at 4% and buy Central Bank bonds at 6%? The transfer will end when, at some point, the central bank runs out of capital. Only in the case of infinite central bank capital can you argue that 4% is a stable equilibrium.

      If you agree on the above

  2. Sergei says:

    Tax liabilities are always cost making in the sense that if you do not extinguish them on time, you will incur additional costs. The Mosler plan turns costly tax liabilities into income bearing ones. Yes, this difference will split the economy into two classes of taxpayers: the one which suffers from cost effects of taxes and another which enjoys the income effects. However, given the institutional and political landscape of the EZ, it is not clear what the final outcome will be on tax payers from the inferior class. Mosler bonds are likely to lead to lower interest rates (they have an embedded option which clearly has value) which means lower budget deficit which means smaller budget cuts toward the required balanced budget. The Mosler plan is not supposed to solve the problem of Greece and more so for the whole EZ. It is rather presented as a potentially viable solution which at the very least could win more time to come up with real solution.

    Using your own terms, if you pull the arbitrage argument out of demand and supply equations then equilibrium prices might become indeterminable. Not in the sense that there is no valid price or multiple equilibria but in the sense that there is no way for the market to determine and anticipate it today. At this is where one gets bubble and anti-bubbles. Currently Greek bonds can be disconnected from any reality and suffer from an anti-bubble which will surely burst if not addressed. But it is the institutional setup of eurozone that eliminated the arbitrage argument from the market. However how there can be a market for financial instruments if there is no arbitrage? Mosler plan seems to provide the market with a risk-less (?) instrument to kick off its pricing process. This plan might not be perfect but it is light years ahead of anything that EU/ECB/IMF can offer. And obviously they do not offer Greece a hand-shake.

  3. Matt Franko says:

    Greece govt bond rates for 10-yr at 17% is better? Cant these same scum banks go to the ECB and get funded using these the way things stand today?

    C’mon… Resp,

    1. Greek bonds at 17% is better than Greek bonds at 15% + massive regressive tax hikes, or equivalently, Greek bonds remaining at 17% but with the bondholders exempt from paying taxes. Of course the best solution is default and exit from the Euro, as Greek bonds at 17% are terrible.

    2. Sergei,

      See my comment JKH. The enhancement makes the bonds “default-free” only if they are priced at a level equal to the expected stream of primary surpluses, discounted by the (EU-wide) risk-free rate that Greece does not control. Any value above that is unstable, in the sense that it relies on self-fulfilling prophecies, or the option of being able to re-sell the bonds to someone else. So it is useful, in that it prevents Greece from just walking away from the debt (assuming that Greece does not walk away from the tax benefit plan), but that usefulness needs to weighed against the distributional effects.

  4. JKH says:

    I agree with the thrust of the post, and said essentially the same thing repeatedly in earlier comments at Mosler’s.

    Redemptions of bonds for taxes are non-cash transactions. Such redemptions must be matched by new debt issuance for cash, in order to fund the budget where cash taxes are no longer forthcoming.

    If the required redemption refinancing mechanism uses M bonds, that creates an M bond float that by construction cannot be redeemed in total for taxes, over ANY time period.

    That being the case, there is always residual default risk prevailing for M bonds holders – the fact that it is physically impossible for all to redeem in any given period means that the effective exercisability of the redemption option cannot be guaranteed for all bond holders over any given period – no matter how long that period. This means buyers of M bonds in such refunding operations (and all other holders) are taking on that risk of non-exercisability. That risk must be compensated with a premium interest rate.

    I referred to this in my comments at Mosler’s as Ponzi-like. It is not Ponzi in the sense that funding is required to pay interest. It is Ponzi in the sense that new buyers of M bonds must take on residual default risk in order to facilitate that some subset of M bond holders will be able to exercise their par redemption option successfully.

    This is essentially the same thing as your feedback loop idea.

    The relevant risk will increase due to an additional dimension, which is the size of the M bond float as a proportion of total debt float and as a multiple of some periodic tax revenue measure. The larger the M bond float measured in these terms, the greater the risk that bond holders will get left out in the cold and not be able to get par for their bonds.

    The ultimate, extreme case is where M bonds eventually become the entire bond float. Other things equal, the default risk that existed pre-M bond still exists. The government’s promise to pay par on M bonds is essentially a promise not to default, which in this extreme case becomes as useful as such a promise might be on a pre-M bond basis. This is a case of total risk feedback, in which there is nothing left to transfer the risk to (i.e. no non-M bond holders).

    There is a way around this problem. That is to issue M bonds whose tax redemption is only refunded with non-M debt.

    This would define an M bond portfolio that declines over time to zero.

    Only in this way can the default risk be transferred fully (or nearly fully) from the M bond portfolio component to the non M bond portfolio component.

    Note that in this latter sense, the Mosler plan could be effective as a temporary bridge financing mechanism, allowing for the possibility of other favourable developments. However, this essentially creates a two-tier senior/junior government debt structure that I question could gain approval from a constitutional perspective.

    1. JKH,

      That’s very well put. The fundamental value the proposal is a put option with strike price equal to the discounted stream of primary surpluses. Any value above that is speculative — e.g. ponzi in nature. The value is positive, but it needs to be weighed against the distributional effects.

  5. Anders says:

    There’s one point about the M bonds I haven’t seen made yet (may have missed).

    The problem with Greece’s budget deficit is that if it tries to narrow it by cutting spending, it risks both civil unrest and GDP spiralling down and exacerbating debt/GDP; but there is not the political and cultural support for increasing taxes at all, let alone in a progressive and affordable manner.

    So the real benefit of M bonds seems to me the fact that they allow the Greek govt to say to Greek domestic bondholders (institutions or individuals): OK, you are going to shoulder the burden of fiscal adjustment via higher taxes – but don’t worry – your ability to pay taxes is greater than you had thought, because all of those bonds are good against your increased tax liability.

    1. Anders says:

      In fact on reflection, this suggestion will not address jkh’s concern that what Greece needs is euros to fund its spending. Whilst the Mosler plan would facilitate tax rises, this would clearly not per se help provide cash to help narrow the budget deficit.


  6. JKH says:

    I also think that Mosler’s admonition to me, on his blog, “to be the bondholder” is, in effect, a case of the fallacy of composition.

    I’d say, “be the bondholder, but beware the company you keep”.

    This latter admonition applies to those who hold bonds, but having satisfied their own tax liability needs, are now looking for other taxpayers to buy them.

    1. “You can buy this house, because someone else will buy it from you for the same price at a later time.” It may work — it often does work, but it’s not a stable equilibrium. In the case of Greece, I don’t think the confidence fairy will make a visit.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s