Monday, April 26, 2021

Bitcoin Yields: Free Money or Credit Spread?

Bitcoin presents two seemingly inconsistent prices today. Futures prices are upward sloping, implying a negative interest rate. But DeFi deposits pay significantly positive interest rates. In a traditional currency trading arrangement this large mismatch would be arbitraged away. So what is going on?

Market Data

Bitcoin futures prices are available at CME and ICE. DeFi yields are all over the place. A random selection of sources has BlockFi and Other Stuff.


There are surely others.

Setting Up The Arbitrage

Futures prices are much higher than spot prices so the obvious trade to do is:
  1. Borrow USD

  2. Buy BTC

  3. Deposit the BTC at a high rate

  4. Sell futures

  5. Wait for contract expiry

Let’s look at the pricing. The futures are something like 5%-15% annualised above the spot price. To keep this simple let’s say we are doing a 1 year trade and the futures price is 8% above spot. As long as our USD loan costs less than 8% this is free money.  Interactive Brokers is a well respected trading platform and their margin rates are visible here. Nothing on there, for USD, is anywhere near 8%. Wholesale funding costs are low (ref: the entire financial press for years).

Futures Settlement

The CME contract settlement process is clearly described at here and here.  For ICE futures it’s here and here.  One is cash settled while the other is physically settled.  And they rely on well-tested approaches that have worked for decades.

In both cases the process is well documented, sensible, and low cost. Volumes are non-trivial. Of course one can always conclude the answer is “the futures are mispriced.” Here we are examining an alternative approach. What are the logical consequences of taking the futures seriously?

Free Money? What Could Go Wrong?

Is this free money? Maybe. If everything goes according to plan we get to keep the difference between the spot and futures prices, plus the DeFi yield, less our fiat loan. There are quite a few legs to this trade. Let’s take each in turn.

The USD borrowing is solid – it’s not going away. The BTC spot trade is also clear and it’s over as soon as it settles.

The CME/ICE futures are not going to disappear. There are states of the world where the exchange goes bankrupt (I guess) but a) it’s exceptionally unlikely b) there is a market price which is super low and c) if you believe that there are better trades to do.

The two unknowns are the DeFi deposit and final spot trade. The deposit can vanish for myriad reasons. Let’s put that to the side now and keep our coins offline in a cold wallet earning 0. This gives the following cash flows:

spot

50000




futures

54000

8.00%



years

1




btc yield

0.00%




usd rate

1.00%




futures end

54000










spot


fwd


flows

usd

btc

usd

btc

spot

-50000

1



loan

50000


-50500


btc interest




1

fwd



54000

-1

total

0

1

3500

0

pv

3465




def prob

6.48%





Here we borrow 50k at 1%, buy 1 coin, sell futures at 54k and run it to the end. This scenario has the final fixing at 54k (we will come back to this). Either there is $3,465 in free money or the market is saying there is a 6.5% chance our bitcoin are useless at the end.

This is the simplest version of the calculation: Prob(Survival)*PV(FwdLeg) + PV(SpotLeg) = 0.  If you know what hazard rate/default intensity is obviously this is too simple.  This is a toy model, everything is linear, and time horizon is short.

And this is before we get our DeFi yield.  The 0-yielding BTC deposit only has "thumb drive risk."

DeFi Yields



What about those DeFi yields? If we consider these to be just normal old credit risky bonds then TradFi tells us how to compute survival probability. Approximately, for low yields and short tenors, the default probability equals the credit spread:

PV = Prob(Survive)*Df*(1+Rf + Spread) – 1
Rf = 0 as a cold wallet is the risk-free thing here
At-market means PV=0
1 = Prob(Survive) * (1 + Spread)
1 / (1+ Spread) = Prob(Survive)
Prob(Vanish) = 1 – 1/(1+Spread)

So our yields of 5%-10% give us vanish probabilities of ~5% - ~10%. There is no point trying to be more careful as we are looking at broad ranges. And a default probability of 5%-10% in the 1 year is technically known as “very risky.”  These kind of default rates, for corporate bonds, correspond to quite low ratings per S&P.

Same Rate - Coincidence?



We get approximately the same survival probability from our futures arb trade and a DeFi deposit into a “more reputable” institution. The bitcoin yield that gives us a 100% survival probability is -7% – just like standard interest rate parity.

So far we have not found any DeFi product promising a negative yield.  And given the price of thumb drives that's fair enough.

But these are two entirely independent ways of deriving a survival probability involving completely separate institutions. And they give, roughly, the same answer.  That's a solid mark in favor of the estimate.

This is not an argument that 5% is too high or two low. Or that the right answer is 7.34%. It’s an argument that “the market” is currently pricing the probability the coins/network vanish as well above 0 and somewhere in the 5%-10% range.

Vanish?



What do we mean by vanish here? If for whatever reason we cannot convert those coins back to USD on the required date they are gone. It doesn’t really matter if this is a hack, a 51% attack, an empty block attack or anything else. If we cannot convert the coins back then the USD loan – which isn’t going anywhere – is going to be a problem.

Yes in theory one could arrange a non-recourse loan to some SPV that’s running all these trades. All we are doing there is transferring the risk to whoever lends the funds.  There is a good discussion of this issue and how to pass convertibility risk off to unwitting buyers in this book.  Let’s keep it simple.

Model Extensions

That is a simple model.  There are quite a few additions.  It is worth spending a little time on a few of them to illustrate the framework's robustness.

More Scenarios


The cashflows above assume the final settlement price is unchanged from the initial futures trade. If we try a final settlement of 40k the probability is 8.75% and for 75k it’s 4.67%. At 10k it’s 35% and at 100k it’s 3.5%. Maybe there is some correlation between price and the coins disappearing. Who knows. We can safely ballpark the survival probability somewhere 90-95%.

Juicing The Arb


If we go back to the original futures arb and deposit the coins in DeFi what happens?


spot

50000




futures

54000

8.00%



years

1




btc yield

5.00%




usd rate

1.00%




futures end

60000










spot


fwd


flows

usd

btc

usd

btc

spot

-50000

1



loan

50000


-50500


btc interest




1.05

fwd



63000

-1.05

futures value



-6000


total

0

1

6500

0

pv

6436




def prob

10.32%





Unsurprisingly a higher yield gives us a higher probability it all ends in tears.

This is a little bit more complicated. Our arb blows up if either the coins vanish due to some broader network problem or our particular yield provider has an issue. People don’t arb foreign exchange forwards by investing in high yield bonds (or at least they shouldn’t).

Again the assumption is that market pricing is fair and there is no free money here.  Don't mix those concepts.  Keeping the coins in a cold wallet yielding 0 is surely lower risk than putting them into a yield farm.  It makes sense the probability of a blowup is higher in the higher risk configuration.

Collateral

The futures exchanges require USD daily variation margin.  If we can freely borrow and lend USD at 0% this has no value one way or another.  As long as the USD rate is "near 0" it's not a big deal unless the move is gigantic and the USD rate is hugely correlated with BTC futures.  Summary: this doesn't make a big difference.

If we need to finance a 50% position for 6 months at 1% that impacts the cost by 50k*0.5*0.5*0.01=$125.  Note that is irrelevant compared with any of the PVs above.  And it's always possible the exchange is posting collateral to us and we have (marginally) higher expected profits.

Using Stablecoins

You could instead borrow a stablecoin and set up the same trade. But stablecoin borrowing is nowhere near 0% and requires significant collateral. Even before collateral costs if you are borrowing at USDT-ish rates there is no arb anywhere.

History is riddled with schemes where someone borrowed only to lend to themselves and generate a profit. You are better off spending your money on an FT subscription, or at least following BondHack, to learn how that’s been going lately.

Vanishing Network Risk

It is surprisingly inexpensive to take over a blockchain network and maybe even make money.  Quite a few coins have experienced 51% attacks already. There is some discussion of the “empty block attack” around the community. Regulations are also evolving and it is conceivable something just gets banned. There are many plausible scenarios where the coins never come back.  Note that we don't care who or why or it it's profitable - we only care that it can happen.

Amazon could decide it wants to take all the coins and then use all its compute power for this purpose. That isn’t likely – but it isn’t impossible either. Tesla could be developing GPU powered FSD as a cover to run this attack. Who knows.

This is not a prediction any of those things will happen. It’s a statement that market pricing is predicting a non-trivial chance one of them – or some other unknown unknown with a similar impact – does.

“Arbing the contango in bitcoin futures” is in large part a bet on these transactions surviving and settling properly. Fair enough. But don’t call it an arb.

Convertibility Risk

This whole “vanishing network” thing sounds new. But it isn’t. Governments routinely suspend currency convertibility and cause exactly these kinds of problems. The network doesn’t vanish exactly – but the government blocks all outgoing transfers and you are stuck with a foreign currency loan and no way to pay it back.

Google “Argentina 2002” if this sounds new. Don’t think Argentina is a fair comparison? Try “Iceland 2008” or “Malaysia 1997.” This is hardly new. This happened dozens of times in Latin America throughout the later half of the 20th century. It’s happened repeatedly throughout Asia, Africa and Europe.  Try the standard reference textbook or wiki.

What’s New

There is an old expression in currency trading: lying like a finance minister on the eve of a devaluation.

Whatever is really going on here we have identified one essential difference between TradFi and DeFi. In TradFi the finance minister has a name and works out of a large building known as the “Finance Ministry” in the capital city. They also communicate via something approximating press conferences and interviews. The institutions around them may change but don’t completely vanish. Whatever you think of so-called “vulture funds” suing sovereigns regarding defaulted debt one thing is for sure: somebody shows up and the case is heard.

In DeFi that function is truly decentralised: the finance minister works at wallet address 0x1234567 and communicates via AMAs on reddit and a discord channel. You can find almost any financial service you want in DeFi these days. But for some reason googling “defi process server” yields 0.

Moving Blog

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