Thursday, January 6, 2022

Monday, December 27, 2021

Celsius Network Flow of Funds

Previously we have discussed collateralized crypto lending and potential implications for prices.  It is difficult to get collateral quantity or haircut data for private lenders to help estimate parameters for models.  Fortunately Celsius publishes some flow-of-funds data that can help.

Celsius' Own Data

Celsius provides weekly updates, via Twitter at least, going back about 1 quarter*.  Here's one example. There is some daily data prior to that.  For now let's just focus on the weekly numbers for Sep through Dec 2021.  Here they are:

Taking prices from Yahoo Finance we get approximate USD amounts as:

Here we can see gross inflows of 947mm and net of 467mm.  That tells us there is an outflow of ~500mm somewhere.  If we assume this is stablecoins flowing out as loan proceeds we get an approximate average LTV of 50%.  

That tells us a lot! First we know that Celsius consumed approximately 500mm in funding during the quarter.  This is simply applying arithmetic to their own numbers.

Second,  we can make a simple model of the business.    Let's simplify for the rest of this discussion and pretend all the collateral is BTC.  They pay ~3pct on BTC deposits and earn ~8pct on stablecoin loans for half the amount.

If this entire activity is funded by equity this is a simple, positive carry business with a large need for short term funding. Whether that equity has much value is unclear...but that is a separate question.  Recent equity raises are for these kind of amounts suggesting this is precisely what is happening.

Celsius's equity investors are basically financing their loan book.  That is not a ponzi scheme!  Obviously it's not possible to confirm this without seeing the whole balance sheet.  But there is no public evidence they are raising copious amounts of debt financing.  The UK corporate filings do not suggest a tremendous amount of debt.

To the extent these loans are non-recourse the risk is a collapse in the collateral value.  They have something like a stop-loss for 40k BTC at a price of 25k from this quarter's lending.

If their total assets are 20b - as suggested elsewhere and vaguely consistent with 1b quarterly increments - and prior quarters look like this one the total is 800k coins.  Whether you think that is a reasonable stop-loss order is outside the scope of this discussion. 

This is a simplified analysis of course. But it illustrates how the word "Ponzi" is misused all over the place.  Celsius is a positive carry financing business, with a huge need for short term funding and a balance sheet running a large asset-liability mismatch.  But that is hardly a new thing in finance.

Celsius' Business Model

What we have here is a pretty standard financing business.  They are buying stablecoin denominated consumer debt with a high yield.  They are issuing crypto-denominated lower yielding debt.  And they are financing any cashflow needs by selling equity.

If a significant portion of financing is driven by CEL sales and there is questionable behaviour in the CEL market -- issues that have been raised before -- this may be more complex.  But on the available information this looks like a bog-standard carry trade.

To some extent this kind of high-yield consumer lending is new in that the backing is crypto collateral.  Rather than doing any credit analysis Celsius instead relies on liquidity in the underlying to provide a guarantee of repayment.  This is startlingly similar to housing-backed lending pre-2008.

Is This Ok?

Yes this might be a problem. Yes it might look a bit like a SIV.  Yes it would be a problem if assets were lost to hacks or mismarked.  Yes the equity might be worthless (it's equity!).  But, absent more information, its not a Ponzi.  It is quite literally a shadow bank funded almost entirely by equity.

In some ways this is more honest than TradFi: here the equity holders get hit and then the depositors.  The taxpayer is nowhere to be found.  And nobody is holding implicitly-guaranteed debt.  You can say many things about Celsius' management - but they have always been clear these are risky lending activities.

* Yes this isn't precisely Q4 but it's close enough.

Sunday, November 21, 2021

Circular Lending: Ouroboros Schemes

In a financial system without supervision leverage can grow dramatically.  Let's explore the impact of rehypothecation and lending haircuts on real balance sheets.  In this example we refer to USD as the currency.  That can be any stablecoin (or actual USD) it doesn't matter here.

Start with a BTC spot of 60k and an overcollateralization haircut of 25%.

Our "lender" begins with the following balance sheet:

The lender borrows 1M USD, in cash, and starts there.  After making a single collateralized loan for 1 BTC they have:

The borrower has 48k in their bank account.  As long as BTC stays above 48k -- where the liquidation occurs -- this transaction is on snooze mode.  Let's say the borrower goes and buys 48k worth of BTC.  That is buying pressure of 0.8 coins.  Now pledge those coins to another lender.  The two lender balance sheets are:

Of course the next step is to buy 0.64 coins and pledge them to someone else:

The aggregate system now has:

That is not crazy.  If we allow the buy-pledge loop to run forever through these 3 banks we can generate more loans.  And that generates an aggregate balance sheet of:

The total buying here is 4 coins.  And we have 240k of loans outstanding against an initial collateral value of 60k.  This is unsurprising as max leverage is just 1/haircut.

Over time, until there is a crisis, we know lending standards get looser.  Let's say that is reflected in lower haircuts.  At 10% it is useful to compare the "3 loans" and "infinite loop" aggregate balance sheets.  Here we are still running the loans through a total of 3 banks -- total funding is still 3M:

The situation with 1 loan for each lender is pretty mild.  But the infinite loop aggregate system is far more levered!  This activity generated buying of 10 coins and leaves behind a liquidation order for 11.

With a haircut of 2%:

Now we are able to exhaust a system-wide total of 3M lending against a single coin.  This process generates buy orders for 50 coins.  And the aggregate liquidation order is for 51x the initial collateral.

Safety of the loans isn't even the primary concern here.  This activity facilitated buying 50 more coins.  This isn't someone trading 50x on an exchange -- each individual transaction here is just an at-market loan and a cash purchase of coin.

We don't even require the same person to keep taking out these loans.  The simplest sequence of events is likely:

  1. Borrow against BTC
  2. Buy BTC with loan proceeds
  3. Deposit BTC into a yield generating protocol
  4. Protocol lends the BTC
That is a circle of collateralized.  This is not a ponzi scheme and it's not a pyramid scheme.  It's a long loop of borrow-buy-borrow-buy until the marginal loan is too small to bother.  And it generates an awful lot of leveraged buying.

This does not happen in the regulated financial system because aggregate system balance sheet leverage is constrained.  Obviously problems can, and have, occurred with excessive leverage.  But each balance sheet is supervised by internal agents (i.e. the risk department), external agents (i.e. the bank's investors) and the regulators (i.e. banking, markets, securities, whatever).

It's a big ugly complex system.  It's not perfect.  But it is fundamentally different from a collection of  smart contracts unconsciously running through that loop.

At a high level it is an empirical question which is safer.  These systems have very different properties.  It is, however, quite clear that loose lending in DeFi can directly lead to large coin purchases and leave behind large liquidation orders.

Each player has their own defensive arrangements in place.  Without the possibility of extraordinary liquidity assistance it feels as though everyone will be forced to turn their cards over at once.

We propose the name "ouroboros scheme" for this configuration.  As long as the underlying asset retains adequate value this can continue forever.

Scheme is meant in the British sense that does not connote something negative -- not the American sense which does carry a suggestion of something sinister.  In the UK it is totally normal to have a "pension scheme."  This term would scare Americans and many other English-speaking groups.  Divided by a common language indeed.

Tuesday, November 16, 2021

How Big Can Collateralized Crypto Lending Get?

BTC is in fixed supply.  This is one of, if not the, top reasons people who love it love it.  However this fixed supply has interesting implications for the collateralized crypto lending markets.

As discussed previously on this blog if we start with 1 unit of stablecoin to lend out against BTC collateral and require an overcollateralization haircut of X% we can end up with 1/X in gross loans (longer discussion here).

We know stablecoins are printed and lent to various platforms from the public press.  Here we will discuss how the fixed supply of BTC constrains the growth of this lending.

The key observation here is: the aggregate liquidation order has to be for fewer coins than the total outstanding.  Simply put the price must be high enough that: \begin{equation} \frac{Stablecoins}{Haircut} = Supply \times Price \end{equation}

Assuming 18M BTC outstanding we get the following minimum prices to support lending at the given haircut:

At an average haircut of 10% with 50B raw stablecoin outstanding to lend the market requires a BTC price at least 27.8k.  At 4% and 75B the required floor is now over 100k.  With higher haircuts the prices are obviously lower.  This is not a difficult spreadsheet to build.

Take a look at the bottom few rows.  This is a real limit on non-fiat-backed stablecoin issuance!  In some sense a lower haircut is like a looser monetary policy -- lending is easier.  But with a fixed money supply the price must rise, possibly dramatically, to provide adequate collateral for non-fiat-backed loans.

A stablecoin issuer that wants to issue more coins against collateral must make a choice: how do they balance the haircut against the number of coins they want (need) to issue?  Note that when the haircut is below 50% most of the lending is not from the original issuer -- it is instead follow-on rehypothecation loans out there in defi land.

A lender that wants to ramp up business has to monitor what fraction of the total coins they might already need to sell.  The supply of coins is currently growing slowly.  But in the short term -- in the sort of timeframe one might need to execute a liquidation order -- the supply is effectively fixed.

There Is No Free Lunch

Printing coins to push up prices, or to grease the wheels of lending platforms, or for any other purpose may at first feel like an unconstrained activity, something that can go on forever.  But this is ultimately a markets activity.  We are talking about borrowing and lending, buying and selling.

Lending against collateral is a transformation of some sort.  It is an event creating a flavor of credit.  Otherwise what purpose does it serve?  Creating credit in a system with a fixed-in-stone money supply feels like an activity that cannot continue without limit.

This is that limit: there is a price at which more than the entire monetary base needs to be liquidated to satisfy someone's liabilities.  And these liquidations may occur on platforms nobody can easily shut down.

Monday, November 15, 2021

Crypto Lending, Market Structure and Stop-Losses

Crypto lending is now a "big thing."  DeFi protocols, centralized services, stablecoin loans -- these are all very much in the news.  All of this activity is unregulated in the sense that leverage is only limited by the risks involved parties are willing to take.  Given the size and evident high risk tolerances of many participants in the space it's worth asking just how much leverage is floating around.

Market Setup

Let's start with two assumptions to simplify things:

  1. Loans are of stablecoin (STA) with crypto collateral (COL).
  2. At inception loans are X% overcollateralized with a single margin call when the value of the collateral drops to the balance of the loan.
These are broadly in line with the mid-2021 crypto markets.  The most common case looks to be USD-something lent against BTC with an X of, say, 30%.

How Much Gross Lending Is There?

Within this structure it is perfectly plausible for a borrower to use their STA loan proceeds to buy more COL and then re-pledge.  Given the lack of market-wide supervision and high risk tolerances it is reasonable to believe this kind of leveraged buying is normal.  But how much can there be?

The math is straightforward.  The first loan is for 1.  Let's assume that gets converted into COL without any fees.  The second loan is then for \begin{equation}\frac{1}{1+X}\end{equation}  And the third is for \begin{equation}\frac{1}{(1+X)^2}\end{equation}  If this process loops forever the total is \begin{equation}\sum_{i}{\frac{1}{(1+X)^i}} = \frac{1}{X}\end{equation} 

Note this takes the initial loan's proceeds as 1 rather than the initial value of the collateral. It's cleaner that way and doesn't impact the high level conclusions.  In fact it may more closely approximate the real world as discussed below.

Margin Calls and Liquidations

If all of this borrowing and lending happens at some price P (STA per COL) all the margin calls occur if P falls X%.  This is obviously simplistic but it can still be instructive.

There is an obvious relationship among the degree of overcollateralization, the liquidation level and the size of the liquidation.  Again assuming everything occurs at the same initial levels we have a liquidation at P/(1+X) for 1/X units.

Intuitively this makes sense: a lower X gives us a larger and closer stop-loss order.  Lower X = higher leverage.  This is a boring result.

Leveraged Buying

The giant stop-loss order is a sign a bunch of leveraged buying must have occured!  This is also wholly unsurprising.  Each incremental conversion of STA loan proceeds to COL is a crypto purchase.  In total we also have leveraged buying of 1/X units of COL!

Stablecoin lending of this type, even with 100% backed stablecoins, can still generate a lot of upward pressure on prices given a sufficiently-well-functioning lending ecosystem.

This is a classic feature of traditional financial markets -- and a key reason for leverage supervision.  Note that absolutely nothing dodgy is happening here.  This may or may not represent more risk than the system can bear.  But no individual actor is doing anything dishonest.

Also note there is no reason to believe sufficient backing exists for STA to liquidate COL into USD at it's price after the leveraged buying!  The quantum of leveraged buying is entirely dependent on X.  Presumably the price post-buying is therefore at least weakly dependent on X.  But this has nothing to do with the quantity of STA outstanding.  STA can be completely covered by USD reserves, and STA redemption itself be free of risk, but COL still cannot be liquidated into USD at the higher price given only STA's reserves.

Stablecoin Issuers

What if STA is also issued in this fashion, with overcollateralized COL as backing?  Several major stablecoin issuers look to provide such loans.  This depends a bit on what you think "approved investments" and similar phrases mean precisely but we are simplifying on purpose here.

If Y% of STA that's been issued is backed by COL then we only have USD backing to liquidate (1-Y)% of STA prior to any collateral sales.  But selling COL for STA does not increase the balance of reserves!  Raising reserves would require liquidating collateral in the COL-USD market.

Plugging In Numbers

Let's continue to use 30% for X.  How much lending is there?  Well one good place to start is the balance of stablecoin issuer non-USD-equivalent holdings.  Let's take total stablecoin issuance at USD 100B and say a third is this type of lending.  And all against BTC.  This is a simplification.  It's a basic model for stylized answers.  Whatever.

This gives us total outstanding lending of USD 110B.  At a price of 65k that is a stop-loss for 110B at 50k.

Also note that this assumes cash backing of 50B.  There are not enough in the cash reserves to support this stop-loss order against USD even ignoring all other backed tokens.

The fragility of this system depends on X and Y.  A lower X raises the risk.  And a higher Y raises the risk.  If Y is 0 the system still may not be able to convert all the tokens into hard currency at the prevailing price.

Extreme Scenarios

To illustrate plausible states of the world let's look some extremes, again starting from a 65k price.

First take X as 66% and Y as 10%.  As a market-wide average this feels pretty conservative.  In this case we have:
  • 90B in USD reserves
  • 10B in initial loans, 15B in total loans
  • A stop-loss for 15B at 39k
Note that reserves are insufficient but barely.  This likely doesn't scare anyone.  Almost certainly it doesn't scare the median market participant.

At the other extreme take X as 10%, Y as 80%.  Surely some lending is occuring at these kinds of levels but this is quite aggressive for the average.  Anyway:
  • 20B in USD reserves
  • 80B in initial loans, 800B in total loans
  • A stop-loss for 800B at 59k
That stop-loss requires liquidating 13.5 million coins -- this is obviously a total train wreck.  You can find plasuible-but-too-aggressive sets of parameters where the total ecosystem market cap is insufficient to cover the stop-loss.

If X is 5% and Y is 90% then the balance of outstanding loans would be 1.8T.  A stop-loss to raise 1.8T at 61.9k is impossible -- that would require selling 29 million coins.

Perhaps the real leverage limit in this market will prove to be the capped issuance.  Any lender that sees stop-losses for 10%, or 20% or 50% of total coins outstanding knows they have a problem!

Spoiler alert: the inability to inject temporary liquidity is a known problem with fixed exchange rate regimes.

Monday, October 11, 2021

Offshore Banking: The Basics

A lot of the discussion around stablecoins, and the crypto-banking nexus in general, touches on offshore banking.  Some of this discussion is, um, confused by degrees between innocuously at fatally.  This is an attempt to sketch how the system works and highlight those components that are most relevant.


Let's start by assuming a working international banking system.  This means banks like Citibank and HSBC exist and offer accounts in both a range of countries and currencies.  Note specifically to Americans: it is common in much of the world for your bank to provide accounts denominated in several currencies both for personal and business use.  This is not a niche product -- especially where cross-border (possibly small) business is concerned.

There is also some regulatory framework for finance specifically and business in general  We can approximate that framework as: don't commit fraud, don't call yourself a bank when you aren't licensed as one and you cannot access the payment system directly without a license.  Obviously that's not exhaustive and there are 200+ banking regimes around the world so it'll have to do.

We also need to assume the existence of "offshore financial centers."  These are regimes where we can establish legal entites, enter into long term contracts under a reasonable legal system, hire corporate services firms for admin and not have to worry about taxes.  This isn't about avoiding taxes -- it's about allowing funds to flow freely through legitimate structures without always worrying about tax.

Going Offshore

Now let's say we want to set up an offshore financial institution.  We incorporate a legal entity in an offshore financial center, call it "XYZ Financial Services."  XYZ has a local company ID number and officers who can sign contracts.  It can go and get a local bank account to rent an office, pay salaries, pay legal fees etc.  This is our "operating" company: it will employ people, pay the electric bill, and generally operate as a business does.

So what does XYZ after moving in to swanky new offices and buying computers?  It sets up "XYZ Capital" as a subsidiary, with it's own ID number.  Capital is going to hold the client assets and maintain links with the financial system.  The operating company now contacts banks around the world to set up accounts for XYZ Capital.  There is probably a contract between them laying out the terms of the relationship.

The operating company then maintains two "spreadsheets."  The first one tracks all of Capital's bank account balances.  And the second one tracks all the money owed to clients.  This second spreadsheet is what we mean by a "client account."  There are no physically segregated piles of cash and securities: an account is simply internal recordkeeping.

If a client demands real hard separation that amounts to setting up a clone of "XYZ Capital" with all it's accounts for that client alone.  The recordkeeping is then identical with perhaps a third spreadsheet tracking which clone is owned by which client(s).

Onboarding Clients

At this point we are ready to take in client money.  Clients are instructed to transfer funds into any of Capital's many bank accounts in whatever currencies are available.  The operating business then records those incoming transfers and credits on both the internal and external spreadsheets.

Note that there is 0 money or credit creation going on here.  We assumed the existence of a global financial system.  The client money now sits in our accounts within that system.  Transfers, withdrawals, investments etc all run out of our accounts.

Our first client is likely the management company itself.  The business model is to charge clients fees in exchange for services.  How do we do that?  Mechanically a fee is simply a notation in the internal books of a transfer from a client account to the management account.  Nothing moves in the outside world -- we just assign a slightly larger ownership share in the external bank accounts to the management company.

Every so often the operating business will request a withdrawal to it's own accounts -- to pay salaries or whatever -- and the external account balances will drop a little.

Commingling Funds Much?

Isn't this scheme commingling client funds?  This behaviour is not what that term means.  Note that all of the operating expenses of the business are paid out of accounts in the name of the management company and those are totally separate from the thing that holds client money.  We a commingling of corporate and client funds when the rent and salaries are paid out of the same bank account used for client transfers.

But how can this be?  All our money sits in one common set of accounts!  No.  The basement of your local bank does not contain individual piles of cash corresponding to each customer.  The bank likely has one (or a handful) of clearing accounts which hold the balances and everything else is an internal record.

Bad Practices

So now it's pretty obvious how this can go wrong.  We can only instruct transfers in the real world for amounts sitting in our external bank accounts.  But we can create any internal records we want!  We can just credit one client, internally, an arbitrary amount of money and let them pay other people.

And in fact as long as they are making payments only within XYZ Capital there are no limits.  However we have a serious problem once withdrawals begin.  If we start with 100 in real client assets and inject 50 of made-up money we can still process 100 in outbound payments.  But the 101st dollar cannot leave out little walled garden

There is nothing stopping the management company from entering into the following deal with a client: we will credit you $100 now and you promise to pay us $101 in 30 days.  And we can roll this 101/102 and 102/103 forever.  Well not forever -- only until someone tries to withdraw and we are out of money in our external accounts.

This is not, in an of itself, a problem.  If the promise for $101 is real -- if it's some kind of tradeable debt security with a market price near 101 -- we can top up our external balances by selling it in the outside world in exchange for an incoming funds transfer.  This is precisely why there is an interbank market for loans and bonds and the like.

But if it's not real, or it's worth dramatically less than $101 in the market, then we have a problem.


Our little offshore business dies the day someone asks for an outbound transfer that we cannot service.  It is perfectly reasonable that we need to sell something to service an outbound transfer.  But if we simply cannot raise the funds we are insolvent.

It is therefore in our interest, if we want to do bad things, to keep as much of the action within our little walled garden as possible and keep out prying eyes.

In practice this is how regular banks work too -- except the banking regulator is (supposed to be) constantly checking the spreadsheets for chicanery.  And the deal with a banking license is that the contracts and ownership relationship between the XYZ Capital and XYZ Financial Services get torn up when the regulator says so.

Tuesday, June 1, 2021

Tether: Bahamian 2021Q1 Data

The 2021Q1 data is out.  The overall banking system shrank.  The only significantly-changed asset is "due from financial institutions, head office or branches outside the Bahamas."  That's the inside-large-global-banks cross-border banking entry.  Everything else +/- unch.

So it's unlikely there are any crypto-related assets getting reported here at all, whether it's reserves or just exchange/fund cash balances.  Cause the crypto space wasn't exactly flat in Q1.

Report here.

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