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Maker DAO is one of the most interesting stable coin projects out there: Not because of being tried and tested and staying stable through the crypto winter, and not because of the complexity of the system, but because it’s a loan based system, that is different from conventional banking in a key respect. Let me explain.

The Maker DAO system currently has two coins: MKR and DAI. The first, MKR, is a governance token that deals with decision making in the MKR system. It has a lot of practical purposes but it’s not important for this article, so let’s ignore it for the moment, and focus on the DAI which is created through the collateralised loan mechanism.

Suppose that Alice, Bob, and Eve, are our protagonists in a nice liquid marketplace in which there are no transaction fees, and things can be done over a short, short space of time.

  • Alice wants to get USD liquidity and she knows that the DAI is kept in a stable 1:1 ratio to the USD. She also knows that the DAI is collateralised by ETH in at a 150% rate. So, for example, if she puts up 1.5ETH at a market value of 150USD as collateral, she can create a loan of 100DAI and sells this 100DAI for 100USD.
  • Bob buys Alice’s DAI for USD and holds it, knowing that if the price of ETH goes down, then he can make some gains by paying DAI for collateralised ETH. He knows that if Alice and others like her can’t pay back their DAI loan or increase their collateral, Maker will liquidate their collateral positions to reduce the supply of DAI. Bob is holding DAI as a means to go speculate on ETH: If Alice’s collateral lost 50% of it’s value and was now worth 75USD on the market, then Bob could buy 1.5ETH with 75DAI and has 25DAI to spare.
  • Eve thinks differently from Alice and Bob — she’s resourced and can pay back her loan at any time, so her game is different. She puts up 1.5ETH as collateral and then takes out 100DAI which she uses to buy 1ETH. (She sells the 100DAI for 100USD and then buys ETH.) Now, what? She takes out another collateralised position with the 1ETH and takes out 66.66DAI, sells it in the market for USD and buys 0.6666ETH. Then, she starts again and keeps going (ad infinitum). Thus, exploiting the iterative nature of the loan process.

The question is how much DAI and collateralised ETH does Eve end up with? In order to figure this out you have to sum a geometric series with ratio 2/3, since she gets 2/3 worth of her original collateral by borrowing and can re-collateralise indefinitely. It turns out to be 4.5ETH against 300 DAI created.

Now, change the story ever so slightly: Conventional banking is iterative (but most of us don’t see this since we act locally) and the financial system operates, in most parts of the world, on a system of fractional reserves. Banks can hold a fraction of their deposits as collateral, and lend out a multiple of the rest as loans and other instruments. The DAI is over-collateralised and the series converges (it’s finite!) implying that for Eve’s strategy she can’t borrow and stake collateral ETH forever. For under-collateralised systems, the series doesn’t converge, and the question is this: Are we are collectively being Eve in a non-convergent economic system where everything ends up as collateral while we borrow and inflate the money supply to keep liquid?

I don’t know. But, the promise of crypto is that the power to create arbitrary rules in crypto-token systems inspires questions like these about the ‘real-world’. And, while many crypto-token systems may not work at all, a few of them might be breakthroughs.

Viroshan's background is in pure and applied maths, economics and physics. He completed a doctoral degree in graph theory (the formal study of networks) in 2014. After working as an academic, Viroshan moved into business as a consultant, and has since disappeared down the crypto-economics rabbit hole: He wrote both the yellow papers for Project UBU - an advertising based UBI system, and has since developed the idea of a Token Exchange Game - a formal game theoretic model for a ledger. Reach out to Viroshan if you are interested in the crypto-economic space, industrial and applied mathematics, or unusual and creative business problem solving.