Why the discrepancy?

Vitalik Buterin had a thought-provoking tweet a few days back about interest rates.

Lending DAI to Compound offers 11.5% annual interest. US 10 year treasuries offer 1.5%. Why the discrepancy?

— Vitalik Non-giver of Ether (@VitalikButerin) August 23, 2019

Today's post explores what goes into determining interest rates, not blockchain stuff. So for those who don't follow the blockchain world, let me get you up to speed by decoding some of the technical-ese in Buterin's tweet.

DAI is a version of the U.S. dollar. There are many versions of the dollar. The Fed issues both a paper and an electronic version, Wells Fargo issues its own account-based version, and PayPal does too. But whereas Wells Fargo and PayPal dollars are digital entries in company databases, and Fed paper dollars are circulating bearer notes, DAI is encoded on the Ethereum blockchain.

Buterin points out that DAI owners can lend out their U.S. dollar lookalikes on Compound, a lending protocol based on Ethereum, for 11.5%. That's a fabulous interest rate, especially when traditional dollar owner can only lend their dollars out to the government—the U.S. Treasury—at a rate of 1.5%.

Why this difference, asks Buterin?

Interest rates are a lot of fun to puzzle through. I had to think this one over for a bit—so let's slowly work through some of the factors at play.

Let's begin by flipping Buterin's question around. When the U.S. Treasury borrows from the public, the bonds it issues are promises to pay back regular dollars (i.e. Federal Reserve dollars). But what if the U.S. Treasury decided to borrow DAI by issuing bonds promising to repay in DAI? What would the interest rate on these Treasury DAI bonds be? Would it be 11.5% or 1.5%? Perhaps somewhere in between?

Credit risk

First, there's the question of credit risk. The U.S. Treasury is a very reliable debtor. It won't welch. If it issues both types of bonds, it'll be just as likely to repay its DAI bond as it will its regular dollar bond. Since the market already requires 1.5% from the Treasury to compensate it for credit risk (and a few other risks), the Treasury's DAI bonds should probably yield 1.5% too. (I'll modify this later as I add some more layers).

Now let's look at Compound. A DAI loan made on Compound (for simplicity let's just call it a Compound DAI bond) is surely much riskier than our hypothetical Treasury DAI bond. Compound is a blockchain experiment. It could malfunction due to buggy code. Maybe every single Compound borrower goes bust. To compensate for this risk, a prospective bond buyer will require a higher return from Compound DAI bonds than they will U.S. Treasury DAI bonds.

So Compound credit risk (Buterin's third option) probably explains a big chunk of the huge gap between the 11.5% interest rate on Compound DAI bonds and our hypothetical 1.5% interest rate on the U.S. Treasury's DAI bonds. But not all of it.

Collapse risk

Buterin mentions a second risk: the chance that DAI, the entity that creates blockchain dollars, collapses. Like Compound, DAI is a new monetary experiment. The code could be buggy. It might get hacked. By comparison, conventional dollar issuers—say Wells Fargo or PayPal—are far less likely to malfunction.

How does DAI collapse risk get built into the price of a hypothetical Treasury DAI bonds

The average market participant (I'm not talking about crypto fans here, but large & smart institutional actors) should be genuinely worried about purchasing a Treasury DAI bond—not so much because the Treasury is unlikely to pay it back—but because the DAI tokens that the Treasury ends up repaying could, in the even of DAI breaking, be worth 99% less than their original value. Average bond buyers will expect some compensation for bearing this risk. How much? Say 5.5% (I'm just guessing here).

Earlier I said that a Treasury DAI bond would yield 1.5%. But if we add 5.5% worth of failure risk to 1.5% in basic risk, a Treasury DAI bond should yield 7.0% before the average investor is going to hold it.

Now let's go back and look at a Compound DAI bond. As Buterin pointed out, they yield 11.5%, which is much higher than the 7.0% yield on our hypothetical Treasury DAI bond. We've already assumed that DAI collapse risk works out to 5.5%. If we subtract collapse risk from a Compound DAI bond's 11.5% yield, the remaining 6% is accounted for by risks such as Compound failing (11.5% - 5.5%). Put differently, investors in Compound DAI bonds will require 5.5% and 6.0% to compensate for collapse risk and credit risk respectively, for a total of 11.5%. Again, these are hypothetical numbers. But they help us puzzle things out.

Two different blockchain dollars: USDC vs DAI

Interestingly, Compound doesn't just facilitate DAI loans. It also expedites loans in another blockchain dollar, USDC. We'll refer to these as Compound USDC bonds. As Buterin points out later on in the thread, the rate on Compound USDC bonds is 6.5%, quite a bit lower than Compound DAI bonds.

What might explain this discrepancy?

Not credit risk, since in both instances the same creditor—Compound—is responsible for creating the bonds. Which leaves varying levels of collapse risk as an explanation. USDC is a regulated stablecoin (i.e. it has the government's approval). DAI isn't. And USDC has genuine U.S. dollars backing it, whereas DAI is backed by highly volatile cryptocurrencies. So the odds of USDC collapsing are surely lower than DAI.

How much interest do USDC bond holders require to compensate them for collapse risk? Assuming that Compound's risk of failing is worth 5.5% of interest (as we already claimed), that leaves just 1% attributable to the risk of USDC failing (6.5%-5.5%). Put differently, investors in Compound USDC bonds will require 5.5% and 1.0% to compensate for credit risk and collapse risk respectively, for a total of 6.5%.

Oddly, the yield on a Compound USCD bond is less than the hypothetical yield on our safe Treasury DAI bond (6.5% vs 7.0%). Why is that? Even though Compound is riskier to lend to than the Treasury, a DAI-linked return is riskier than a USDC return. Another way to think about this is that if the Treasury were to also issue USDC bonds, those bond would only yield 2.5%. To account for credit (and other) risks investors would require a base 1.5% with an extra 1.0% on top for the risk of USDC breaking.

The convenience yield

Let's bring in one last layer. Something called the convenience yield is lurking behind this.

When you lend me some tokens, you need to be compensated for more than just credit risk i.e. the risk that I won't pay back the tokens. You are also doing without the convenience of these tokens for a period of time. The replacement, my IOU, won't be very handy. For instance, the convenience of a dollar bill can be though of as the ability to mobilize it whenever you need to meet some pressing need. But if you've lent a $100 bill to me then you've given up all that bill's usefulness. Instead, you're stuck with my awkward $100 IOU. You need some compensation for this. (Unconvinced? Head over to Steve Randy Waldman's classic ode to the convenience yield).

So when we break down the components of the interest rate on DAI bonds, there must be some compensation required for forgoing the convenience of DAI, its convenience yield. Earlier I attributed the big gap between rates on Compound DAI and USDC bonds to varying odds of each scheme failing. However, the gap could also be explained by varying convenience yields. If the convenience yield of a DAI token is higher than that of a USDC token, we'd expect an issuer of a DAI bond to pay a higher rate than on a USDC bond, in order to compensate DAI holders for giving up on those superior conveniences. 

If DAI's convenience yield is higher than USDC's, what might explain this gap? DAI is completely decentralized and can't be monitored. USDC isn't. It is less censorship-resistant than DAI. So perhaps USDC just isn't as handy to have around.

So some of the 11.5% rate on Compound DAI bonds—say 2%—may be due to the convenience yield forgone on lent DAI. If DAI had the same features as USDC, and thus had a lower convenience yield, a Compound DAI bond might only yield 9.5% (11.5% - 2.0%). If so, the discrepancy between the Compound DAI and USDC bonds—9.5% vs 6.5%—wouldn't be as extreme.

Summing up, let's revisit Buterin's tweet:

Lending DAI to Compound offers 11.5% annual interest. US 10 year treasuries offer 1.5%. Why the discrepancy?

— Vitalik Non-giver of Ether (@VitalikButerin) August 23, 2019

If my line of thinking is right, the discrepancy is accounted for a messy mix of the higher risk of lending to Compound (3), the danger of DAI cracking (2), and whatever convenience yield one forgoes when one no longer has DAI on hand (4-other). And of course, Buterin's first option is right too. I'm assuming that people are rational and can easily buy and sell various assets. But the sorts of large institutional players who set market prices may not be operating in crypto markets.