Thread by @tarunchitra

👋🏾 A little tweetstorm to dive into this!

First off, thanks to @hosseeb for figuring out how to make my erudite writing make sense to a large audience!

Why does this behavior happen in a system of rational participants! First... let's unpack what rationality means! 👇🏾

1/21

https://twitter.com/hosseeb/status/1201532521604730880

Rational agents in PoS should *always* view their token holdings as a portfolio to be allocated. Portfolios needs to be rebalanced based on market prices and yields that an agent in a PoS network can receive.

In PoW, the asset is somewhat disconnected from the means...

2/21

... of security, as the lack of liquid hash power derivatives (@JeremyRubin, @tzhen) adds in a Coase-like transaction cost to *immediately* converting hash power to a liquid asset.

On the other hand, PoS derives security from a hidden 'cost of capital' assumption, which..

3/21

.. is implicit in papers with formal proofs such as Snow White or @Algorand. This assumes that staking and trading are the only ways to earn yield, allowing for predictable money supply control.

However, the introduction of money market protocols like @compoundfinance..

4/21

.. introduces a way for rational agents to have a larger set of alphas. @rleshner and @cjliu49 been super forward looking about this and has been analyzing the effect of lending on the *existing* @ethereum ecosystem.

The yield from these contracts, which let's on-chain...

5/21

.. traders implicitly go short on exchanges (such as @UniswapExchange) or margin trading (@dydxprotocol, @synthetix_io)
can affect security, as validators will consider yield earned from lending to shorts (security: 📉) in addn. to staking rewards, tx fees, and trading.

6/21

How do we model these portfolios? Let's look to normal finance!

Equity market portfolios of this kind are often maintained by ETFs. Arbitrageurs are incentivized to perform 'creation-redemption' arb where you can trade portfolios of stocks/assets for shares of the ETF.

7/21

For regulatory reasons, if ETFs have their net asset value (NAV) deviate from the portfolio price by too much they have to rebalance their portfolio. How do they do this? They either provide incentives to arbitrageurs (most prominent: @janestreetcap) OR they automate..

8/21

.. the rebalance via a mean-variance portfolio method. These methods, which are used to manage ***trillions** of dollars of worldwide equity portfolios (especially at quant hedge funds!), are robust and well-tested.

9/21

nytimes.com/2016/02/23/bus…

In this paper, we assume that every validator (yes, including you @BisonTrails and @coinbase!) treats staked tokens as a mean-variance portfolio that rebalances based on the rates provided by staking and on-chain lending. If hedge funds such as my old employer were...

10/21

... in this space, this their view of these assets (on-chain crypto is not so quant heavy yet and validators don't know how to optimize PNL). We show that under some distribution of risk preferences — some validators immediately turn-over portfolios from staking to...

11/21

... lending whereas others more slowly rebalance their portfolios — you can cause a 'bank run' on PoS currencies. @teo_leibowitz gives an amazing summary and history of this in this article!

12/21

https://twitter.com/TheBlock__/status/1198239947578322945?s=20

As @gakonst would make me remiss to not mention, this model makes a lot of assumptions about the PoS protocol. I do this to a) prove formal mathematical results (is this the first crypto paper that uses submartingale theorems? 🙃) and b) show that..

13/21

.. even the *simplest* of PoS systems is susceptible to this and that there is a fundamental incentive incompatibility between on-chain lending and staking. We can relax a lot of these assumptions (as mentioned in the paper), but you lose the ability for formal proofs.

14/21

That being said, we spent a lot of time using @gauntletnetwork's simulation infrastructure to stress test harder PoS models (with differing borrowing demand) and as in trading, we believe the main way to correctly model your PoS protocol is via careful probabilistic sims.

15/21

So what does this mean for your PoS protocol?

1. If you're courting DeFi, you *need* to be uber careful about your staking rewards schedule. For instance, @harmonyprotocol/@stse recently published an excellent economics model which _doesn't_ account for issues like this!

16/21

2. If you have sharding (@ethereum, @NEARProtocol @polkadotnetwork), you need to figure out how to isolate shards whose applications provide returns above the validator returns to ensure that you have shared security. Shared security can be destroyed by rational agents.

17/21

3. If you incentivize agents for different parts of consensus (e.g. separation of validator & consensus nodes in @withflow/@dapper_labs, @Libra_, ... ) you need to ensure that your revenue sharing model for different participants cannot be usurped by a lending contract.

18/21

4. PoS validators and especially investors (since they often don't do validation themselves) should *demand* rigorous actuarial analysis of block rewards & fees to measure 'jump to default' risk that should be priced into any valuation model (cc @cburniske @mrjasonchoi)

19/21

Thanks: @UthsavC, @GuilleAngeris, @ChiangRei, @jmo_mx, @hosseeb, @IvanBogatyy, Tim Roughgarden, @jreem, @htkao, @josephbonneau, @nadertheory, Tony Salvatrore, Michael Jordan, @yisun88, @hasufl, @gakonst, and others for 💯 feedback!

(Hopefully I didn't forget anyone...)

20/21

Also, P.S., @BisonTrails @aaronhenshaw @JoeLallouz @ViktorBunin: This is the stuff that caused the math that scared you to be on the whiteboard in the office :) The proof of the last theorem in the appendix was the source of the stochastic calculus that you saw

21/21

@withflow @dapper_labs @Libra_ oops, I mean @withflow_