That thing about Stable Coins

16 min readJan 26, 2018

Stable coins are all the rage right now — and for good reason, because if you want an asset that you can use as a means of payment then you want this asset stable, and if there is one thing that crypto assets are not currently it is that. Of course keeping an asset stable — ie pegged to another one — is not a new problem in the world of finance. For example this issue arises in currency boards, more generally in currency pegs, and also in financial products like ETFs. Moreover, a strict peg is in fact a (very simple) financial derivative, so derivatives pricing and hedging techniques apply.

But let’s not get ahead of ourselves, and let’s define some terms. Firstly we want to consider a strict peg versus a loose peg aka a trading band:

a strict peg is a peg where the pegged asset is supposed to trade exactly at the same price as the base asset
a loose peg or trading band is a peg where the pegged asset is supposed to be trading in a reasonably sized band (say plus/minus 5–15%) around the based asset
a sliding peg is either a strict peg or a loose peg where the price or band at which the peg is set is changing over time
a risky peg is one of of the four pegs described above (strict/loose, sliding/not) that is not risk free, ie it might break at one point

Also, it is worth defining the terms introduced above for those who are not too familiar with them

a currency board is an arrangement for a national currency where the central bank holds 1:1 reserves of base currency against the pegged currency and stands ready to trade both ways at the nominal rate at any given point in time
a currency peg is an arrangement for a national currency where the central bank announces support for a given bank, meaning buys the national currency whenever it goes towards the lower end, and sells it whenever it goes towards the upper end
an ETF (short for Exchange Traded Fund) is an investment product whose price is kept constant against a basket of investible assets — eg the shares of the S&P 500 in the appropriate proportions — by a market maker / sponsor who offers to issue and redeem ETF shares against an appropriate bundle of the underlying securities

Also I want to introduce the following very important distinction

the price of an asset is the price at which you can buy or sell it in the market; typically there will be a different selling price and purchase price, and both will depend on the trading volume to be executed at that price
the value of an asset is the theoretical price at which you think you should be able to trade an asset in a perfect market, typically relying on some kind of valuation model with a number of observable and non-observable assumptions

All that we are concerned with here are prices — it does not matter that you can use a model argue that the value of two assets is the same if there is no guarantee that you can execute a trade at that value.

Strict Pegs

Having go those definitions out of the way, let’s first talk about strict pegs, ie pegs where the pegged asset is meant to trade at a precisely fixed exchange rate against the base asset. The fundamental proposition here is the following

Strict Peg Proposition: In order for a strict peg to hold with certainty in an efficient market, there must be market participants willing to buy or sell the pegged asset against the base asset at the nominal rate for an unlimited notional amount.

The presence of said market participant(s) is clearly a sufficient condition: if someone is willing to buy and sell in unlimited amounts at 1.0, and someone else would be willing to say buy at 1.1 then the infamous arbitrageurs would sweep in to buy at 1.0 and sell at 1.1 and make a risk free profit. Or, to put it slightly differently: why would you every buy at 1.1 if you can buy at 1.0 in unlimited size? Now let’s look at why it is also a necessary condition. This pretty much follow directly from the definition of price we have made above: by definition the price of the pegged asset (expressed in terms of the base asset) is only ever fixed to a certain notional value if you can both buy and sell unlimited quantities at this notional value.

As an aside: using derivatives pricing theory, the pegged asset is a “Delta One” derivative, meaning that that hedge ratio is constant regardless of the price of the base asset. This in turn means that the delta hedge of the pegged assets is to buy and hold the base asset in the appropriate proportions. I note en passant that derivative pricing theory also allows to easily deal with dividends / interest payments / storage costs etc, but this is out of scope here.

We have already introduced ETFs and currency boards above and it is easy to see that they pretty much satisfy the conditions of the Strict Peg Proposition: in case of an ETF, the sponsor is accepting packages of shares in exchange for the ETF security. They then simply hodl on to the shares, and return them whenever someone demands them back in exchange for an exchange certificate (for the time being let’s ignore transaction costs and management fees as this will lead us into Loose Peg territory, so we will discuss it there). Note that this only covers the ability of an ETF provider to provide unlimited two-way markets, but not their willingness to do so. The latter is generally ensured via contract law: if a sponsor does not honour a valid redemption request they can be sued for damages.

The exactly same mechanism applies to a currency board: whenever someone deposits a certain amount of the base currency, they get the equivalent amount of the pegged currency, and vice versa. Like in the ETF case, in a currency board the central bank’s ability to honour the pledge is assured by holding the base currency in escrow. However, it is not easy to assure the willingness of a the central bank to honour its pledge in the future.

Taking a step back, let’s discuss what we have seen so far. Firstly, in order to have a strict peg, you need a market-maker who has both the ability and willingness to trade both ways at par in unlimited volume. It is not always obvious why a market maker would do that. In the ETF case it is to make money — but this means they will need to charge either a fee, or a trading spread, or both, and this interferes with the strict peg requirements: a bid/offer spread or transaction fee implies a loose peg, and charging a periodic management fee introduces a sliding peg, hence we will look at this again in the respective sections below.

In the currency board case the why for the central bank is typically that it is needed to support international trading: a small country’s currency can be volatile, and this volatility is hard to manage for both importers and exporters. If a country imports vital goods such as food or fuel this is particularly important. The issue with currency boards is that because there is a risk that the central bank is not willing to maintain the peg, rational investors only hold the pegged currency if it offers higher returns than the base currency, ie if it has higher interest rates.

Conclusion: a strict, risk-free peg can only work if the sponsor holds the base asset in escrow in a 1:1 ratio, and there is sufficient governance in place to ensure the sponsor’s willingness to redeem the pegged asset.

Loose Pegs

Let’s now move on to loose pegs and start with the following proposition

Loose Peg Proposition: In order for a loose peg to hold with certainty in an efficient market, there must be market participants willing to buy or sell the pegged asset against the base asset at the respective nominal rate for an unlimited notional amount.

The only difference in this proposition compared to the strict peg one is that loose replaces strict, and the insertion of respective: to say peg an asset between 0.99 and 1.01 someone must be willing to buy unlimited quantities at 0.99, and to sell unlimited quantities at 1.01. The proof of this proposition is the same as above and left as an exercise for the reader 😎.

The first thing to note is that now the market maker is happy: all they do is to buy the pegged asset at say 0.9 and sell it at say 1.1, and store the base asset in the meantime. This is a nice little profit for not much work, assuming that storing the base asset is not overly expensive. The question here is why would anyone ever go and buy the pegged asset at 1.01 in the first place if they know they can only sell it back at 0.99. The reason is that there must be some market inefficiency that makes it advantageous to hold the pegged asset instead of the base asset, and that the bid/offer spread (in this example, 2%) is a price worth paying. So let’s look at a number of examples

For ETFs the ETC certificate might be easier and cheaper to trade than the underlying shares (keeping in mind that the ETF certificate can trade multiple times before it is redeemed)
A similar structure to an ETF is the American Depository Receipt (ADR) which allow to create wrapper securities of non-US shares that allow them to be traded on a US exchange without being technically listed there
Gold-linked certificates that can be created and redeemed against physical gold at a warehouse also allow for significantly cheaper and easier trading, especially if they can be traded electronically on an exchange; they also allow gold investors who don’t want to or can’t deal with physical storage to participate in the market.

Conclusion: a loose peg allows the sponsor to earn some money providing the pegged asset, which the investor might be willing to pay if the pegged asset has some superior properties to the base asset, eg lower trading or storage cost.

Sliding Pegs

Sliding strict pegs

A sliding strict peg is a peg that at any given point in time is a strict peg — ie there is an unlimited-volume two-way market at a fixed exchange rate — but where the exchange rate moves over time. The sponsor of a pegged asset (ie the market maker in case of an ETF, or the central bank in case of a currency board) is short the pegged asset and long the base asset. He is also short an option, notably the option to buy or sell unlimited amounts of the pegged asset against the base asset. This puts a certain arbitrage limit around the way this price can slide over time: if the price of the pegged asset grows foreseeably faster than the financing cost of the base asset then market participants could make a risk free profit by borrowing the base asset, exchanging it into the pegged asset, later selling the pegged asset back at a higher price and repaying the base asset loan plus interest and still have some base asset left.

Note that this arbitrage does not work the other way as it is sponsor who’d be gaining in this case, and they’d simply find noone to trade with. The exception here is if having the pegged asset has some convenience yield for their holders, and the market participants are therefore willing to accept the profits made by the sponsor which in this case can be considered a fee:

Traders might save money by buying and selling ETF certificates instead of the underlying portfolio; if this is the case they might be willing a commensurate decrease in the exchange price over time
Investors wanting to hold gold might similarly accept some decrease in exchange price if this means they do not have to deal with storage, and they are insured against theft of the physical gold

Conclusion: a sliding peg can only work if the pegged asset does not appreciate faster than the financing cost of the base asset. In cases where the pegged asset appreciates lower than that — including the case where it remains constant — the sponsor earns seignorage profits, which can be considered a fee providing a service.

Sliding loose pegs

For completeness I should also want to mention the sliding loose peg where the band moves over time. As discussed above, technically any peg where the sponsor charges a bid/offer spread is a loose peg, so here the above discussion applied. For wider bands the application is less obvious — it is sometimes seen in currency pegs, but those tend to be not boards but of the risky kind discussed below.

Conclusion: None.

Risky Pegs

So far we have discussed non-risky pegs, ie pegs that will hold whatever that market conditions, and we have found that the only way to assure this is to hold the entire amount of the base asset received (minus an adjustment to account for a loose and/or sliding peg) in escrow to allow for ultimate redemptions. Now arguably even non-risky pegs have a residual risk, eg in case of fraud, or a natural disaster, or some other exogenous event, so we might allow for some residual risk as well if this makes things easier.

Risky pegs and banks

In case of a risky peg the sponsor must still hold assets backing the issued pegged assets, but those do no longer need to be the base assets. In fact, they can hold any asset they want, provided it is almost certain that

the value of their asset holdings exceeds the value of their liabilities, ie the value of the pegged assets they have been issued
they are either able to liquidate their asset holdings and purchase base assets whenever pegged assets are presented for redemption, or can at least borrow base assets against their asset portfolio as collateral

This of course means that the sponsor is a well known type of institution: it is a bank (or at least a depositary institution as they do not lend money), and the constraints above are the usually referred to as the solvency and liquidity constraint respectively. Those constraints imply that banks must have a certain capital buffer — ie their assets exceed their liabilities — and a certain liquidity buffer — ie they hold a certain amount of highly liquid assets that can be used in case of redemption requests.

The issue is that there is a strong conflict of interest between the owners of a bank and its depositors: the owners profit from the entire upside of the investment, but they can shift the downside risk to their depositors. This means that there is a certain incentive to gamble big — heads I win, tails you lose — which is of course not in the interest of the depositors. The only way a bank can reliably work is if

there are solvency and liquidity regulations in place that are monitored and enforced by a supervisor
there is a (central bank) liquidity line in place that allows a solvent bank to borrow liquid funds against their illiquid assets in case of unforeseen levels of redemption requests
there is a deposit protection scheme in place that indemnifies depositors in case of losses and that avoids bank runs in case the solvency of the institution is in doubt

The operative work here is reliably: of course banks can work without either of the above, but history shows that invariably this eventually leads to bank runs where banks that are in actual or assumed distress suddenly get flooded with redemption requests by all of their depositors who want to be rather safe than sorry, and even solvent banks are not able to serve those requests without liquidity support, ie someone willing to lend short term cash against their longer dated assets.

Conclusion: a scheme where the sponsor issues a pegged asset that they promise to redeem against a base asset but where they do not hold the base asset is essentially a bank, and the pegged asset is a certificate of deposit for the base asset.

Risky pegs and money market funds

I also want to briefly mention a second well known financial services model which is not quite a peg, but still very similar: that of the money market fund (“MMF”). A MMF is a fund that attempts to earn a small interest return for their investor by profiting from the fact that aggregate investor liquidity preferences are smaller than individual investor liquidity preferences. Or, to say it differently: a fund can offer every investor daily liquidity and still invest into longer maturity (and therefore higher yielding assets) on the basis that only a very small percentage of investor will actually put in redemption requests at any given day.

The idea in MMFs is that they invest only in assets that are highly unlikely to default, and notwithstanding the issues some MMF faced in the crisis, MMFs typically do not have solvency problems. They key issue for MMFs is to manage their liquidity, ie to ensure that they can meet redemption request even in stressed scenarios. Without a lender of last resort this can never be guaranteed, but in not too extreme market conditions, and provided a not too racy investment strategy, MMFs that are short cash can generally borrow against their longer dated assets if they have to meet redemptions.

One could consider an MMF an asset with a one-sided peg against the base asset, which in this case is the underlying currency: there is a promise to always redeem the units at a certain minimum rate, but there is no peg on the other side as the unit holders profit from all gains the fund made, less of management fees of course.

Conclusion: a scheme where the sponsor holds the base asset (typically a currency), but not necessarily in form of cash put possible in low-risk longer dated investments, and where the pegged asset benefits from the return of those investments, is effectively a money market fund

Risky pegs and managed exchange rates

Sometimes exchange rates are managed to diverge not too far from each other, on famous case being the ERM where the exchanges rates in the European Union were managed to trade within certain bands to each other (this was obviously before introduction of the Euro). Those bands were managed by

(a) clearly and strongly announcing where those particular bands were, and repeating this periodically in case someone forgot, and

(b) defending them vigorously, meaning that the central banks would buy and sell the respective currencies whenever they traded close to the band boundaries, and

(c) clearly and strongly announcing that the central banks were going to defend those currency bands until the better end, and repeating this periodically in case someone forgot

That’s really a bit like the bank case above, except that the central banks could create money in their own currency at will, and they controlled (short term) interest rates which gave them in principle a few weapons to fight. To cut a long story short, Soros noticed that the pound was overvalued, tried to attack it, and got defeated. Just kidding of course: the pound fell out of the ERM when Soros attacked.

Conclusion: even mighty central banks that can print money can not always defend a risky peg — it is stable until it is not.

Stable Coins

Yes, but what does this mean for
 
(•_•) ( •_•)>⌐■-■  (⌐■_■)

#StableCoins?

(ht Sean Tuffy)

Having spent longer than I expected on all the ways pegs can be and are implemented in traditional financial services we can finally discuss what this means for stable coins. As a quick reminder we discussed pegs that could be strict or loose, sliding or not, and risky or not, as well as various combinations thereof. We found that for risk-free pegs the sponsor forcibly has to hold enough base assets in escrow to redeem all outstanding pegged assets. For risky pegs however this condition could be relaxed, and we found that instead the sponsor needed to fulfil a solvency and a liquidity constraint, making the sponsor effectively a bank, or possibly a money-market-like fund. We have also seen that even central banks find it hard to maintain a risky peg.

So let’s look at what this means for stable coins. The first one is a strict and risk free peg to the base currency that we assume to be the dollar. In this case the only option is to hold all dollars received in cash accounts, ideally with the central bank to completely eradicate the default risk. Assuming the peg is non-sliding the issuer earns the interest on the dollar deposits, which in the banking world is referred to as seignorage. This of course is not a lot in the current low interest environment, but at more normal rates of 2–4% this can be substantial. However, in the current low interest rate environment the sponsor might instead opt for a loose peg with say a bid/offer spread of 4%, meaning that the stable coins would trade somewhere between 98c and 102c, and the sponsor would make some profit whenever stable coins are redeemed.

If the base currency has high interest rates, seignorage profits will be high, and there is a chance that competition amongst stable coin sponsors leads to a situation where they offer a sliding peg with an increasing redemption price, thereby sharing some of the seignorage profits with their investors. In the current environment, sponsor might on the other hand opt for a decreasing redemption price, allowing them to earn higher seignorage profits.

Moving on to stable coins with a risky peg there are two different models, notably the bank model where investment gains go to the sponsor, and the money market fund model where investment gains are shared between the sponsor (as fees) and the stable coin holder. In the bank model there is a conflict of interest between the sponsor who likes high risk / high return investments (because they keep the upside but have no downside risk) and the investor who likes safe investments (because they incur the downside risk, with commensurate upside). In order to manage this conflict, the sponsor must undertake to comply with certain solvency and liquidity requirements that ensure that the risk of the peg breaking is de minimis, and the investor must be assured that the sponsor does indeed comply. Due to asymmetric information this is a hard problem to solve. In the mainstream financial world it is addressed via a combination of regulation, supervision, deposit insurance, and central bank liquidity lines, ie a pretty heavy toolkit that is difficult to replicated in the private sector alone.

Conclusion: My personal conclusion is that eventually we might get to a bank-like solution for stable coins, but the infrastructure to manage this is not yet in place. This means that for the time being unless a stable coins is backed 100% by cash deposits — and verifiably so — I’d consider it stable only up to the point where it is not. But this is of course only my personal opinion…