Endogenous Stablecoins and the Fisher Equation

Previously I wrote about different ways that stable coins can maintain stability. One of those ways is to buy and sell bonds, or futures contracts. This post is about measuring stability by targeting bond rates.

Endogenous Stable Coins

Seigniorage Shares, one of the foundational papers about stable coins, differentiated between exogenous strategies and endogenous strategies for defining stability.

An exogenous strategy measures stability based on external information, like the price of a coin relative to the dollar (i.e., using an oracle).

An endogenous strategy only relies on information internal to the network itself.

The strategy mentioned in Seigniorage Shares is to measure miner’s fees. The idea is that miner’s fees will depend on electricity and computational prices. Even if the fees aren’t perfectly stable, at least they depend on something external to the network.

Namely, the price that you have to pay miners to process transactions (denominated in coins) will go up if the coin experiences inflation. So keeping miner’s fees stable can help maintain stability in the coin price. But miner’s fees aren’t the only endogenous measure of stability.

Using Bond Prices to Measure Stability

Bond prices can also be used to measure stability, but bonds are a little different from miner’s fees. Miner’s fees provide information about the price of the coin relative to electricity and computation power.

Bonds, on the other hand, allow us to compare the present value of the coin to the future value of the same coin. Theoretically, you can achieve stability by ensuring that the present value of the coin is always equal to the future value.

Before I go into more detail, let me provide a simple model of a bond, and some examples that demonstrate how they provide information about fluctuations in value.

Imagine you have a contract that pays out 100 coins in one year. If you expect inflation, you won’t pay 100 for this contract because 100 coins today are worth more than 100 coins 1 year from now. So, for example, you might be willing to pay 95 coins today for a guaranteed payout of 100 coins one year from now. The amount of a discount required to get people to buy the bonds is the interest rate. In this case, the nominal interest rate (R) is (about) 5%.

Targeting Real Interest Rates

The Fisher equation states that the nominal interest rate (R) has two parts: a real interest rate (r) and inflation (π):

R = r + π

A stable coin can be defined as having zero (or at least predictable) inflation. So if we set π = 0, we have the simple equation:

R = r

If the value of a currency is perfectly stable (i.e., no inflation or deflation), the price of a bond would be based purely on the real interest rate (r). Thus, if you peg bond prices right at the real interest rate, you could have a perfectly stable coin.

Unfortunately, there are a few problems with this approach: first, targeting bond prices in this way only provides stable expectations, not stable prices. Second, the real interest rate itself isn’t stable.

The first problem is a pretty serious one, but it is beyond the scope of this post. But briefly, since bonds reflect the ratio of current to future coin prices, they don’t provide information about information about past changes in price. This is particularly important when there is a sudden, unanticipated, change in coin value. Bond prices will be based on the new current value, and won’t help you get back on a target. But that is all I’m going to say about that now.

The Stability of Real Interest Rates

According to this chart from https://www.longtermtrends.net/real-interest-rate/, real interest rates have fluctuated quite a bit over the last 150 years:

Note that real interest rates are pretty strongly correlated with inflation. However, the correlation is a negative one. When inflation is high, real interest rates are low, and when inflation is low, real interest rates are high.

One reason for this is that we can’t actually measure real interest rates. We can measure nominal interest rates with pretty high granularity (e.g., based on bond prices). And looking backward we can come up with various measures of inflation (although in my opinion, none of them are that great). But they key is that the numbers used for real interest rates just come from rearranging the Fisher equation:

r = R - π

So any inaccuracy in measuring inflation will show up in estimates of the real interest rate.

Monetary Policy Impact on Real Interest Rates

One of the reasons one might want to have a stable cryptocurrency is that it could, in theory, be independent of the Federal Reserve. Thus, for example, it could be insulated from political pressures that might lead to hyperinflation.

But if we target bond prices based on real interest rates, the stability of the coin will be depend on the stability of real interest rates. In the long run, real interest rates seem to depend on fundamental aspects of the economy that don’t change very fast. Here, they argue that real interest rates have been steadily declining over the last 700 years! How many economic trends do you know of that can be tracked back that long?

But in the short run, the actions of the federal reserve can have a pretty significant impact. Most people are familiar with the idea that the Fed buys and sells bonds to manipulate nominal interest rates. The usual idea is that if the economy “heats up” the Fed can cool it down by selling bonds and raising interest rates. Or, alternatively, if the economy is slow the Fed can get it moving by buying bonds and (thereby lowering rates).

Remember that for bonds, higher prices = lower interest rates. Therefore, buying bonds creates more demand for bonds, which increases bond prices and lowers interest rates. Selling bonds satisfies/reduces the demand for bonds, which lowers bond prices and increases interest rates.

Interestingly, many people think that if the Fed keeps interest rates low by continuously buying bonds, it will lead to inflation. Thus, you will sometimes hear people argue that the Fed needs to raise interest rates to prevent overheating. However, according to the Fisher equation, in the long run higher interest rates result in higher inflation.

The precise impact of Federal Reserve bond purchases is a little beyond the scope of this article. If you are confident you understand it, you should probably do more research. But I think one thing is clear: the Fed has so much economic power that it not only impacts the price of the dollar, it can temporarily change the economy in real terms. As a result, if the Fed targets a new interest rate, it will not only impact the price of dollar denominated bonds. It can also impact the price of all bonds in the whole economy, including the price of bonds denominated in stable coins.

If we could measure real interest rates with fine granularity, we could compensate for Fed interventions by targeting a new bond price in the short run. However, if you use bond prices to measure inflation (even bond prices that have nothing to do with dollars), sudden actions by the Fed can distort the picture by causing changes to real interest rates.

Tradeoffs between Long Term and Short Term Stability

Any coin pegged to the dollar will experience whatever inflation the dollar experiences. Thus, one of the reasons to consider an endogenous stable coin is to achieve long term stability even if the dollar is subject to inflation.

However, because the Fed has such a big impact on the economy, it’s influence is really hard to avoid. Even endogenous stablecoins can be tossed about by the Fed’s open market operations. For example, if the Fed targets a higher nominal interest rates, it will lead to higher real interest rates in the short term. This can eventually cause inflation of the dollar. But in the short term, it might cause stable coins that measure inflation using bond prices to think there is inflation in coin value and to overcompensate reducing supply.

In other words, actions of the Fed that are inflationary to the dollar in the long run can be deflationary to bond-based endogenous stable coins in the short run. This makes it more difficult to escape the influence of the Fed.