Thread by @tarunchitra

Big Short 2.0: PoS and DeFi are mortgage-backed securities!

@alexhevans & I tried to find grand unified theory for the financial derivatives hidden in PoS and DeFi ➡️ uncovered mathematical equiv. to MBSs.

Why? Same payoffs and income inequality!
👇🏾
medium.com/gauntlet-netwo…

tl;dr:
- Synthetic levered assets in PoS and DeFi are MBSs.
- Improvements over meatspace/2008 MBS:
- Used to reduce inequality
- Avoid lending competition in PoS
- Numerical, probabilistic methods are key to correct design of these systems

The post motivates and provides background for our paper which just hit arXiv

The following are equivalent as portfolios

❇️ PoS w/ derivatives
❇️ Leveraged DeFi
❇️ Mortgage-Backed Securities

arxiv.org/abs/2006.11156

One of the early hints of this equivalence was @delitzer's blog post that inspired the design of @compoundfinance v2 (as detailed by @rleshner)

We use probability and stochastic processes to formalize this connection

https://twitter.com/rleshner/status/1274063743178031104?s=20

How do we construct a mathematical theory that can encapsulate @CeloOrg, @terra_money, @compoundfinance, @MakerDAO, @synthetix_io, and more?

We introduce the concept of a derivative pricing function φ which prices the synth. asset (e.g. cTokens, Dai, staking derivative)

Analytic properties of φ — convexity, smoothness — control the security, fees, and income redistribution of a synthetic asset.

We illustrate how to construct φ for @compoundfinance, @synthetix_io, @terra_money, and more in the paper.

Does φ alone get you to MBSs? Not quite!

Synthetic assets have a boundary between 'safe' and 'unsafe' regimes

'Safe': φ takes an 'well-behaved' (e.g. Itô process) price process for the underlying collateral and prices the synthetic

'Unsafe': φ is singular and the synthetic price is uncoupled from collateral price

In the 'safe' regime, we show that the payoffs of a staking derivative replicate an MBS!

Moreover, we show a 'recurrence' theorem that says that if a staking derivative is in the 'safe' regime, you can have the synthetic pegged to a collateral price.

This is Dai, sUSD!

Other examples:
- Transition is the boundary of the default phase transition that was numerically analyzed in @gauntletnetwork's market risk assessment of @compoundfinance
- @CeloOrg / @terra_money usage of CFMMs to keep stable asset (algo. stablecoin) w/ bounded variance

Analyzing sUSD is particularly prescient — incentivized @CurveFinance pool effectively forces sUSD to the stable region

When combined with SIP-015 from @kaiynne, it turns out that SNX/sUSD is the purest form of a decentralized MBS as the liquidations exactly match defaults

But on the other hand, MBSs are the reason for #bitcoin
and this result effectively confirms OG Bitcoiner beliefs that PoS is more or less the same as the existing financial system (from a payoff/security perspective)

Is that the end of the story? No!

https://twitter.com/juthica/status/1274680053486555143?s=21

Common critique of PoS/DeFi staking: extreme concentration of wealth.

@giuliacfanti, et. al show that w/o monetary policy design, PoS concentrates

How? They map PoS to Pólya urns ('rich-getting-richer' processes)

But it misses one big thing for DeFi: slashing/liquidations

Our paper extends @giuliacfanti's framework to add in slashing

Slashing adds complexity: Money supply can go to zero!

Pólya urns do not do this — need to generalize to Pólya Birth-Death processes (urn can go to zero)

Studied in the 70s by Athreya/Ney springer.com/gp/book/978364…

But slashing/liquidations are probabilistic — need to use much stronger and more recent (2017) probability results

We find a surprising phase transition: At high borrowing and slashing rates, income equality 𝙙𝙚𝙘𝙧𝙚𝙖𝙨𝙚𝙨!

∴ Derivatives can reduce inequality in PoS/DeFi!

This is similar to @ole_b_peters ergodic economics observations: Safe derivatives ensure that the wealth distribution is ergodic and samples non-concentrated portions of space whereas unsafe / no derivatives lead to a high-degree of concentration.

Not all derivatives are bad!

Why? Well-tuned derivatives allow small lenders/validators equal access to opportunities that big validators have.

At the same time, many of the risks of MBSs still linger and designing these systems in DeFi / PoS can be a tightrope that is hard to parametrize perfectly

One particular usage of this (perhaps to combat @VitalikButerin's skepticism): If an on-chain derivative is the biggest market for borrowing a PoS coin, then you can avoid most of the staking and lending issues from my earlier paper!

medium.com/dragonfly-rese…

As we venture into this new era of reinventions of finance's past, we need too objectively assess the risks in the systems being built.

Frameworks like ours provide quantitative guidance on investor ROI in the 'safe' regime, default risk in the 'unsafe' regime, and inequality

Amazing to find an explicit proof of an @ole_b_peters-style ergodicity transition

BUT: clear that numerical methods and simulation are key to quantitatively identifying the boundary between 'safe' and 'unsafe' regimes

Using these tools, we can hopefully avoid 2008!

🙏🏾🙏🏾🙏🏾: @hosseeb, @hasufl, @celiawan2, @gakonst, @Leorzhang, @teo_leibowitz, @theyisun, @htkao, @GuilleAngeris, @mlphresearch, @tzhen, Fabian Trottner

P.S. @juthica MBSs and CDOs already exist in DeFi — Compound is technically a CDO and Maker is a synthetic CDO, but that's a future @alexhevans blog post

P.P.S. The usage of measure-valued Pólya processes was rigorously studied via some epic papers by Cecile Mailler and Svante Janson

I stumbled into them as the correct theory for PoS while rereading some old ML papers on hierarchical dirichlet processes by @ShamKakade6, et. al

P.P.P.S. The name of the paper, "Why Stake When You Can Borrow?" is an homage to @josephbonneau's famous paper "Why buy when you can rent?" which introduced attacks from hash power rental (e.g. @NiceHashMining)