tldr: there’s a financial instrument in the crypto world that is worth one price if you are fiat-denominated and another price if you are crypto-denominated, and this instrument trades at the fiat-denominated price.

The crypto world continues to redefine its value proposition, so it’s a bit hard to try to argue against a shifting goalpost, but as a crypto-skeptic it’s quite satisfying to see that despite all the rhetoric the crypto markets clearly indicate that the players are all optimizing for the fiat-denominated value of their holdings, and not the crypto-denominated value. No one cares about being a “Bitcoin hundredaire”: people want to be a “millionaire”.

## Background: Siegel’s paradox

There’s an interesting “paradox” in the financial world called Siegel’s paradox, in which two market participants with different wealth denominations will come up with different exchange rates for the same trading pair.

Personally I don’t consider this to be a paradox any more than any other case where two participants have different prices for things. When I buy an apple from the grocery store, it’s because I valued a marginal apple more than the grocery store did, so a surplus was generated by transferring the apple from them to me, with the exact transaction price depending on supply and demand. No one would call this a “paradox”, and I believe it’s the same thing with Siegel’s paradox: different participants with different situations will have different prices they are willing to transact at.

The relevant point for this blog post is not that there’s a paradox, but that different wealth denominations will lead to different prices. I stumbled upon a crypto instrument where one can compute the prices for different wealth denominations, and based on the market price determine which wealth denomination the market participants use.

## The Bitmex ETHUSD futures

The financial product that we can look at is the ETHUSD future series at Bitmex. These are a very curious thing — I believe they unintentionally are a very different product than what the designers intended.

For a bit of background, Bitmex is a crypto-native exchange, and at one point in time was the biggest exchange by volume. The important aspect for here is that they only accept crypto deposits, and at the time I used them they only accepted BTC as collateral (I am unsure if this is still the case). So this posed a very interesting challenge for designing a product that would allow BTC holders to bet on the ETH-USD exchange rate.

I’ll just quote how the ended up doing this:

ETHUSDH22 is a ETH/USD futures contract settling on the .BETH30M Index. Each contract is worth 0.001 mXBT per $1 price, currently 0.00288896 XBT.

Naively, this is a futures product that settles to an Ethereum price index, and is a bet on the future value of that index. This is how the product traded for a while.

But this is wrong, which you can see by calculating the payout of this instrument. One will receive an amount of BTC corresponding to the change in Ethereum price, so if the current BTC (ETH) price is B (E) and the change in BTC (ETH) price is b (e), then the payoff of this contract is

(B + b) * e = B * e + b * e

The first term is what the product designers wanted: it’s a constant times the change in Ethereum price. Perfect.

But the second term exists and is what makes this product interesting: the product of the changes in the BTC and ETH prices.

ie: *this is a ETH-BTC covariance product*, not an ETH product.

## The USD-denominated price for this contract

It’s not too hard to estimate what the expected covariance is:

cov[BTC, ETH] = cor[BTC, ETH] * stdev[BTC] * stdev[ETH]

We can estimate these quantities independently:

- The correlation coefficient is roughly 0.8 (the conclusions of this post are unchanged using different correlation coefficients)
- At Deribit the IV for ATM BTC options is 62%, and for ETH options it is 73%.
- At the time of writing there are 27 days until expiration of the future and options, or about 7.4% of a year.

I think most people don’t realize that “IV” numbers are the annualized volatility of the log process, so there’s a nonlinear conversion to non-log standard deviation. This is important for cyrpto options because the IVs are large enough that the correction is non-trivial, though in this case because the expiration is so short it doesn’t matter that much.

So anyway we expect a 17.0% stdev for BTC and 20.1% stdev for ETH, so:

So EV[b * e] = 0.8 * (0.17 * B) * (0.201 * E) = 0.0273 * B * E

So we would expect these futures to trade at a 2.7% premium to the “normal” futures price.

There’s also contango to consider: the OKX March ETH futures (a normal boring futures product) are trading at a 0.07% premium to the ETH spot price, and we would expect this to be stacked with the covariance premium, for a total of a 2.8% premium.

## The BTC-denominated price for this contract

Going back a bit, the payoff of this product is a number of bitcoins proportional to the ETH price change. So in dollar terms you end up with a second-order covariance term.

If you are BTC-denominated though, this product is a lot simpler: you receive money (BTC) proportional to the ETH price change, which is just a standard futures product. You don’t care that when you gain your bitcoins they will be worth less, because you are denominating your wealth in bitcoins.

So there is only contango to consider, and BTC-denominated players value this product at an 0.07% premium to the ETH spot price.

## What the market says

So again: USD-denominated players would pay a 2.8% premium for this product, and BTC-denominated players would pay a 0.07% premium.

The result: the March futures are currently trading at a 3.5% premium to the spot price.

Again, this is not “contango” in the normal sense, because this is greatly out of line with how the rest of the ETH futures markets trade.

Clearly, the market is valuing this product at a significant premium, putting a significant value on a covariance effect that only fiat-denominated players will experience. The effect is even larger than I calculated, which is why I said the conclusion is robust to small pricing choices.

## Conclusion

So there you have it: the market is sending a strong signal that there is agreement to value this product in fiat-denominated terms.

You might argue that this is a pretty lightly traded product these days so the evidence is weak, but this product used to be one of the dominant ETH products and exhibited the same behavior.

You could also argue that crypto-denominated investors exist, and they simply do not know about this opportunity, or lack the sophistication to take advantage of it. I could see this being the case, since for example to properly do this trade you would want to do a dynamic hedge in the options market. But the effect here is so large (36% a year of free money, and you can safely lever it to 2-3x) that one would expect savvy players to find or pay for the expertise to do this.

So in the end the market is clear: when money is on the line, people value their wealth in fiat, not crypto.

## 2 responses to “Strong evidence that no one cares about crypto-denominated wealth”

Kevin – Two things: an investor in the futures contract doesn’t have exposure to BTC. Try calculating the final USD payout under a scenario when BTC rises, and then again when BTC falls. The amount of BTC transferred at settlement changes, but the USD value is the same. This is the law of one price in action.

Also for implied volatility to affect pricing, you need some optionality in the contract. US Treasury Bond Futures are a great example where this optionality exists.

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True, the minute you buy the futures contract you are neutral to the direction of BTC. But if ETH rises, then you have a BTC credit and you are now exposed to BTC. You can see this in the `b * e` term of the payout. Are you thinking of a traditional (inverse) crypto future?

Your second statement is not correct — any time there is a nonlinear payout, the Taylor series expansion will generally have a non-zero second order term, which is exposure to volatility (and thus one can figure out the implied volatility). This is the same thing as Jensen’s inequality — if the payoff is convex, then there is a premium associated with there being a spread in outcome values. One way to construct a non-linear payoff is to have optionality, but that is not the only way — in this case the product explicitly has a higher-order payoff term.

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