Why is bitcoin inherently volatile?

inherent_volatility.pdf

So the argument is that if Bitcoin is expected to constantly and predictably grow in value year over year, that this same growth will be arbitraged away and the price of Bitcoin will be today what it was supposed to be in 100 years?

How does volatility spring from that?

Maybe the argument is that traders would realize their arbitration was not very smart and then reverse the process in between?

Or is the argument one of necessity instead of a cause-and-effect description? Are you saying it has to be this way because otherwise the world would be broken but not attempting to explain the process by which things would be this way?

Please consider this argument:

Bitcoin's fixed supply makes it so it is expected to grow in value in relation to all the other goods in the economy, right? But that is only true if we assume the economy will grow, i.e. there will be more goods or better goods produced in total as the time passes. If the quantity of goods stayed the same each bitcoin would still buy the same amount of goods, and if the quantity of goods diminished each bitcoin would then buy less goods.

If the above is true, then holding Bitcoin wouldn't be a risk free activity, it would be a bet on the overall increase in productivity. A bet that cannot be arbitraged away.

Once we discount marginal holding costs, nothing can "predictably grow in value", otherwise it would be stupid not to hoard more or it (intertemporal arbitrage). At the margin, returns equate holding costs.

Volatility is a holding cost, derived from the uncertainty/risk about the future value of an asset. The riskier an investment, the less people will be willing to hold it, and the greater the expected return they will require. Similarly, most people is willing to pay significant insurance premiums to reduce risks. I.e. you wouldn't play lottery with the money you need to pay rent, even if it had a positive expected return.

Bitcoin's deterministic supply implies that any changes in its utility expectations imply price fluctuations. Not only if demand grows, which I used in the article to illustrate the impossibility of having positive returns with certainty. The price of bitcoin can only stabilize if the expectations about its future utility remained stationary. But the future is always uncertain.

I believe bitcoin is a bet on r being depressed below g by government intervention and other risks derived from trust requirements. This is a utility with a fluctuating and uncertain magnitude. Increases in output are uncertain themselves, as you can observe in the volatility of broad stock indexes.

Once we discount marginal holding costs, nothing can "predictably grow in value", otherwise it would be stupid not to hoard more or it (intertemporal arbitrage).

This isn't true. Things can grow in value predictably because of the discount rate. If people are indifferent between 1 util in 1 year and 0.99 utils now, then the predictable return you can get is 1/0.99 per year.

To be precise, nothing can grow in value with certainty beyond productivity growth expectations.

Wait, wait, but Bitcoin is only expected to grow in value exactly as much as productivity growth, no more than that, no? Why would Bitcoin grow more than productivity?

A drastic increase in wealth taxation could easily cause bitcoin to multiply its value. Like an environment of global deregulation and lowering taxes could lead bitcoin price to collapse. I think that is a bold assumption you made.

To be precise, nothing can grow in value with certainty beyond productivity growth expectations.

Then I have a hard time understanding your counterpoint to @fiatjaf's point of view that Bitcoin can predictably get the risk-free rate of return.

It seems to me that your conclusion "no asset can grow in value without the corresponding volatility" should be modified to "no asset can grow in value at a rate higher than the risk-free rate without the corresponding volatility". That is a well-accepted conclusion in finance.

A drastic increase in wealth taxation could easily cause bitcoin to multiply its value. Like an environment of global deregulation and lowering taxes could lead bitcoin price to collapse.

I always assumed your theory about Bitcoin's inherent volatility assumed an economy in which the only money was Bitcoin. And in that economy Bitcoin would be growing constantly because of increased productivity, but that brought inherent volatility.

So now what do you say about the situation of a Bitcoin-only economy, assuming no change in taxation or anything else, just normal productivity gains, as surreal as all that could be, would Bitcoin be volatile there?

Bitcoin can predictably get the risk-free rate of return

For this to happen, the real demand for bitcoin would need to decrease without uncertainty when the economy grows for causes other than productivity growth (e.g. an increase of labour input). If M is fixed and Y increases, either P decreases to offset it (i.e. the price of bitcoin rises with volatility) or V increases (real demand for bitcoin decreases). I don't think this is realistic.

assumed an economy in which the only money was Bitcoin

That is only an illustration of the impossibility of bitcoin stability. But, even if we could be certain of the absence of economic growth, the demand for bitcoin would be uncertain, and its price volatile.

what do you say about the situation of a Bitcoin-only economy, ..., would Bitcoin be volatile there?

Yes, the volatility of bitcoin wouldn't disappear even if was the only money available.

Couple things.

1. An increase of labor input increases productivity, so I'm not sure what you're stipulating in your response to me.

2. Reading your essay, you seem to imply that there's no such thing as a risk-free return. Do you intend to imply this?

3. On your conclusion, you say that Bitcoin's volatility will be similar to the volatility of an index of companies, such as in the stock market. That makes sense to me. But this goes both ways: the dollar is highly volatile in terms of a diversified index of companies. The only thing that breaks the symmetry is relative price stickiness of many consumer goods and wages. But if wages and consumer goods were priced in a stock market index, then this index would appear stable and the dollar would seem unstable. Is this a problem for your argument?

1. This article may help.
2. Kind of. If we become philosophical, the mere pass of time involves a risk, and we could think of the "risk-free return" as the premium paid to hedge it.
3. The important volatility measure for a currency is about minimizing the uncertainty of nominal income. Nearly 90% of all international loans are denominated in dollars and not in S&P 500 shares or bitcoin for a reason. Price stickiness will not allow to multiply your real income by 10x only because you denominated your prices in bitcoin and it spiked, the same way you cannot expect prices to remain stable in a country with an hyperinflating currency, even if everything is denominated in that currency. Nominal rigidities have a very limited effect.

That article doesn't suggest that increasing labor reduces productivity. It reduces the marginal productivity of labor of course, but not the total productivity (e.g. GDP), so I'm still having trouble with your first point.

Total factor productivity is a scale factor that reflects the portion of output growth that is not accounted for by changes in the capital and labor inputs. It is mainly a reflection of technological change. I think you are confusing output with productivity.

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A couple of reactions:

1. On fiat money: “Volatility represents a holding cost that will offset any expected return remaining after all other costs are discounted, but the holding costs of an asset that does not provide any positive returns do not necessarily originate from the uncertainty of its future value.” What is the “holding cost” of a fiat currency? What is its “expected return”? It seems like holding cost is a negative expected return in this case, no? I’m a bit confused by the distinction between holding cost and expected return in the case of a fiat currency, and why this results in lower volatility.

2. On short-term volatility >= long-term volatility: “An asset with an uncertain long term value cannot be stable in the short term, as it does not give the possibility for intertemporal arbitrage to provide liquidity and prevent short-term fluctuations.” This is the second thing I’m not sure I understand. Can you unpack this a bit more? Why can’t an asset with an uncertain long-term value provide liquidity during short-term fluctuations? First, what kind of fluctuations are we talking about? Fluctuations in the demand of this uncertain asset? Can’t substitutes provide short-term liquidity to accommodate those short-term fluctuations in demand? Why is that impossible? Can you walk me through the arbitrage you have in mind?

3. On bitcoin price growth suppression: “Attempting to stabilise its [Bitcoin’s] value is not an economically rational mean-reversion strategy […], it would imply issuing an ever-increasing amount of bitcoin denominated IOUs […] to suppress its price growth trend perpetually, which is an irrational enterprise doomed to failure.” I agree with this but I don’t think anyone is proposing to suppress bitcoin’s price growth perpetually, only in the short-run.

4. Volatility vs autocorrelation: Let’s say I agree with you that there is a floor on volatility for bitcoin. What are your thoughts on autocorrelation, which some argue is a different lens on the usefulness of an asset as money? An autocorrelated time series of price leads to more uncertainty of the price level in the long run if you make mistakes in the anticipation of the price changes. This offers a different angle on the comparison between bitcoin and fiat: bitcoin may be more volatile but it is less autocorrelated. Maybe trading higher volatility for lower autocorrelation is desirable for long-term contracting?

1. An ideal money would have no holding cost or provide any return beyond those justified by productivity growth. The cost of holding a fiat currency balance (like the ones we have now) would be its devaluation and the uncertainty of its value relative to the mentioned ideal. Fiat currencies rarely provide a positive expected return, just a convenience yield matching the holding cost.
2. Unless the supply of an asset can increase, issuing substitutes implies shorting it naked. This is a non-ergodic strategy and very different from issuing gold substitutes when its price rises, which can be backed by future gold production and hence an ergodic strategy.
3. If you cannot suppress price growth perpetually, suppressing it in the sort run is economically impossible. It is like giving money away for free.
4. I'm not familiar with this argument, sorry.

From my points 1, 2, and 3:

1. Pay attention to the difference between predictable vs. unpredictable returns. I was making the narrow point that in expectation and in equilibrium, you'd expect the return to be 1/discount_rate, which is the risk-free rate.

2. I'm not sure how useful it is to define away the subjective discount factor and treat it all as risk. Are people indifferent between a guaranteed 1 util today and a guaranteed 1 util in one year? Also not sure if this changes my interpretation of your argument or not.

3. This point is circular, so I don't see how it proves anything about a hypothetical world where we used S&P or Bitcoin as money. If we denominated salaries in S&P shares, there would also be no uncertainty in nominal income.