When doing market making or cross exchange arb in crypto we discussed some of the issues of computing fair price from multiple geo-distributed data feeds.
Your quotes will arrive asynchronously from Binance, Bybit, Coinbase and so on, and each will be an indirect measure of fair price.
For example, how do you weigh the Binance and Bybit quotes that came in 35ms and 75ms ago against that Coinbase quote that came in 15ms ago? What about when the ordering is reversed?
Each exchange has a different level of liquidity, error, and basis, so even if the quotes were all equally fresh, there'd still be some decisions to be made. But latency adds an additional layer of complexity.
One mental model for this is ruler theory. Imagine trying to combine the measurements of a bunch of different rulers, each with their own bias (μ) and error (σ), into one optimal measurement.
Bias means a particular ruler is on average off from the truth by a consistent amount. Error means there is a random fluctuation by how much it is off from this average amount, sometimes a lot, sometimes a little, but usually within one stdev around the truth.
In physics, the way to weight each measurement is via precision weighting where each ruler is weighted by its inverse variance:
~ 1/σ²
A quote from a particular exchange is like a ruler measurement of fair price in that it too has its own bias and error.
The dominant part of bias is easy to measure, it is just basis, and a good start is to compute a rolling mean.
Error is a bit more complex. It will depend on liquidity, spread, volatility ... and time elapsed.
BTC-USDT on Binance is expected to be a less errorful measurement of BTC than the same instrument on say, Kucoin. But BTC-USDT on Binance 1 second ago is expected to be more errorful than BTC-USDT on Kucoin 10ms ago.
So there is an innate component to error and a time component. Total error squared will look something like this:
error² ≈ ε²_exchange + σ_price²·τ
where τ is the amount of time that has elapsed from when the quote was emitted to when you registered it, and ε²_exchange is the error unique to that instrument on that exchange (and at that particular point in time). For the time dependence, the assumption here is Gaussian diffusion, which is a defensible first order approximation when you are not near a significant liquidity event.
So errors have a component that grows at a speed proportional to variance, creating a kind of uncertainty cone as they propagate forward in time.
This tells you roughly how to weigh different quotes from different exchanges arriving at different times.
Below are plots from two models built on this intuition. Both are measurably better than just using the Binance mid-quote, and in production, more robust against feed glitches on any single exchange.
We'll discuss in more detail some concrete models that incorporate this intuition, and some that work surprisingly well while ignoring parts of it, in a subsequent post.
@zcelestialbaby@longwashere my then ceo mentioned pltr when i was an intern in 2017. He said pltr is one of the firm’s biggest competitors. He also said that they weren’t very good so I didn’t pay much attention.
On STRC
Trying to simplify so I get the high-level idea:
1. If bond price < $100, bond coupon increases to support the price, raising the ongoing liability burden
2. If bond price > $101, sell more bonds for cash and use the proceeds to buy BTC
3. If bond-to-equity ratio rises, sell equity too to reduce "leverage and derisk" — and use that cash to buy more BTC
4. Bonds are implicitly backed because:
a. BTC goes up over time
b. They can pay coupons for the next 2–3 years without selling a single BTC
5. Basically infinite money glitch cos bond sale = stock sale = $ to buy BTC = more bond sale
Addressing some misconceptions here
1. Reflexivity works downwards as well:
If BTC drops, STRC price drops, then more coupon is needed to support the slide, which drains the reserves faster. Holding BTC is not a cash-flow accretive activity.
2. Preferred shares aren't really bonds and you cannot default:
May be true, but preferred shareholders still suffer if they don't get the dividend cash, no matter what you call it.
3. Leverage ratio is 33% which is low comparatively:
The capital base is growing, so the ratio maintains or even drops because there is a growing number of equity holders willing to purchase additional BTC collateral for the new bondholders. The bomb may not be getting hotter but it is certainly getting bigger.
4. CAGR is +ve even if coupons are 15%:
That is the long-run average. BTC has deep drawdown periods that last months.
5. Cash hoard > 2.5 years of coupon payment:
That is at current coupon rates. The larger STRC grows, the shorter the runway if negative reflexivity materialises.
🤔 The last point is perhaps the most important. The cash hoard exists because MSTR did it first. They were the first to build this financial engineering on top of BTC, and off that foundation they built the rest of the convoluted financial empire that is MSTR.
I think in many ways BTC is the largest and best cryptocurrency because Satoshi also did it first. Not just that it was one of the first cryptos to launch, but more importantly, it was the first altruistic launch. Satoshi launched it without reserving a majority of the supply for himself. If BTC was like the other shitcoins where insiders hold a majority and can dump into the market when things go bad, BTC would never have made it.
Now there are many BTC financial companies following MSTR in this financial engineering. MSTR owns about 3% of the total supply. The copycats are scooping up more.
What happens when these holders of Satoshi's coin own 8–10% or more of the total supply and negative reflexivity hits?
When that liquidation comes, it could permanently damage BTC — the one truly altruistic coin we have in this industry, the thing that makes BTC truly unique. Concentrated corporate holders being forced to dump supply is the opposite of what BTC was designed to be.
I still think the longer these convoluted innovations on BTC fester, the deadlier it will be for BTC when the reckoning comes.