Sunday, June 14, 2015

Store of value

Two interesting posts about bitcoin by JP Koning (post 1, post 2) got me thinking about the function of money. Usually we say that money serves three functions: unit of account, medium of exchange, and store of value. But what does it mean to be a "store of value"? More specifically, what does it mean for a form of money to be a "good store of value," i.e., performing this function well?

Suppose, for simplicity's sake, that an asset's value (defined in consumption terms) follows a geometric Brownian motion with constant percentage volatility and drift. So it satisfies:

 dS_t = \mu S_t\,dt + \sigma S_t\,dW_t

Does "good store of value" mean that sigma, the volatility, is low? Or does it mean that mu, the drift, is high? Remember that in the short term, volatility dominates drift, while in the long term, drift dominates. Also remember that there should be a tradeoff between these two - assets with higher volatility will tend to have higher systematic risk, and thus will tend to have higher expected returns (drift). In other words, in general an asset can be either a good long-term store of value, or a good short-term store of value, but not both.

Stocks are a good example of an asset with high positive drift and high volatility. Their value bounces around a lot, but it tends to increase over time. If "store of value" means "value tends to rise over time", then stocks would be a very good candidate. Stocks are a good long-term store of value.

Fiat money with a 2%-inflation-targeting central bank is a good example of an asset with negative drift and low volatility. Over time, you can expect this currency to lose value, since there will tend to be about 2% inflation every year. But the value is highly predictable - it doesn't fluctuate very much at all from day to day. Fiat-money-with-2%-inflation-targeting is a good short-term store of value.

Looking out at the world, I see a whole lot of countries that use fiat money, with something like inflation targeting, as their medium of exchange (i.e., what they use to pay for stuff). And I see zero who use stocks as the medium of exchange, even though the technology now exists for us to make payments in stock shares quite easily (it's just the same as exchanging dollars electronically, really).

So I conclude that we want the medium of exchange - i.e., money - to be a good short-term store of value (i.e., to have low volatility), and that we don't need it to be a good long-term store of value (i.e., we don't care about its expected return).

Why is this the case?

It makes sense if you think about the way that we use money. People don't know exactly when they are going to need to spend money, or how much. If they keep their wealth in assets with high expected returns and high volatility - stocks, etc. - they run the risk of having to sell in a down market in order to pay for unexpected expenses. So it makes sense to keep some of their wealth in a low-volatility, low-expected-return asset like fiat-money-with-2%-inflation-targeting, in the expectation that they'll probably have to use it to pay for something. The low expected return - the fact that cash falls in value a little bit every year - doesn't matter so much, because you don't keep the cash around that long before you spend it.

(Note that this ignores correlations, but those won't end up mattering here.)

So this is why money should be a short-term store of value rather than a long-term store of value. This is why, as David Andolfatto pointed out, gold makes such a lousy form of money.

How about bitcoin? If it keeps experiencing high volatility, then it's not going to become the medium of exchange in the U.S. or other countries with inflation targets. But if volatility falls in consumption terms - in other words, if the bitcoin prices of goods and services become very stable - then bitcoin will have a good chance of becoming the medium of exchange.

One problem, though, is that there's a bit of a chicken-and-egg situation here. The more merchants use bitcoin, the less volatile its consumption value will probably be. But in order for merchants to use it, customers have to use it, and they'll only start using it if there's low volatility.

But if bitcoin eventually manages to solve this chicken-and-egg problem, its promoters hope that it will be able to offer about the same volatility as fiat money but with a higher expected return. That would make bitcoin dominate fiat money, and would kick fiat money right out of the universe of investible assets - or, more realistically, it would force central banks to adopt an inflation target lower than the rate at which bitcoin is mined. That, I think, is the hope of bitcoin enthusiasts who say that bitcoin will "compete with central banks."

So for bitcoin to become money, it has to figure out how to massively reduce the volatility of bitcoin prices of goods and services.


Eli Dourado has a good response. I think we agree on the volatility thing. I glossed over other kinds of transaction costs, which Koning addresses somewhat; on those matters, I'm pretty ignorant, so I will let Eli and JP work it out...

Tyler Cowen thinks Bitcoin's volatility is a bad sign for its chances of future adoption, because it reflects a consensus that Bitcoin will never really catch on. I disagree with Tyler. Suppose, for simplicity's sake, that milk was the only good that people consumed. And suppose that in the future, bitcoin becomes the universal medium of exchange, and that at that time the bitcoin price of milk is about the same as it is today. In this case, there is no benefit to buying a lot of bitcoin today, even if you know for certain that it's going to become universally adopted. Because the price of bitcoin is already "right", in consumption terms. Hoarding a bunch of bitcoin right now doesn't actually improve your tradeoff between future milk and present milk. So the lack of bitcoin speculation doesn't necessarily mean that people have decided that bitcoin is doomed. It could even mean the exact opposite.


  1. Anonymous1:21 AM

    "... assets with higher volatility will tend to have higher systematic risk, and thus will tend to have lower expected returns (drift)."

    Huh? I've always heard the opposite: high risk assets need to compensate through high return.

    1. Yep, typo. Thanks, fixed.

  2. "they run the risk of having to sell in a down market in order to pay for unexpected expenses"

    Does this actually make sense in a sufficiently emh/random walk world? The threat of actual inability to pay is still important, of course.

  3. > Does "good store of value" mean that sigma, the volatility, is low? Or does it mean that mu, the drift, is high? Remember that in the short term, volatility dominates drift, while in the long term, drift dominates.

    It seems clear to me that a "good store of value" has low volitility and drift near zero (neither strongly positive or negative"). The ideal store of value has mu=0=sigma. Having a positive drift makes something a good investment, but does not make it better at storing value.

    1. Remember, there's a tradeoff. Higher expected return also makes you accept higher risk. If we could choose both at once, imagine what a party that would be!!

    2. Yes I understand, I just think you should be a bit clearer about the logic. "Good store of value" = "vanishing mu and sigma" is a definition. When combined with the empirical fact that risk-adverse humans will bid on them, inducing a trade-off between expected returns and risk, this suggests (as you point out) you might see a separation into short-term stores of value, sigma=0, and long term stores of value, mu=0.

      However, having a single commodity that is a good long-term and short-term store of value is certainly possible so long as there are long-term investments with returns significantly higher than zero. This makes clear the possibility (which is obscured in your post) that if stocks are growing at 7% per year, then currency could have both sigma and mu very close to zero. The 2% depreciation of money due to inflation arises because of other monetary policy choices, not as an inexorable consequence of the fact that we want money to be a short-term store of value.

  4. Noah: When you say "good short-tern store of value," do you just mean "good medium of exchange?" If those are not the same thing, could you clarify?

    1. I'm trying to explain why I think the former implies the latter.

  5. "But if bitcoin eventually manages to solve this chicken-and-egg problem, its promoters hope that it will be able to offer about the same volatility as fiat money but with a higher expected return."

    That is a fundamental problem with bitcoins, basically its advocates want lower inflation or higher risk adjusted returns on their bitcoin than money in a world where money has already been destabilizing and chocking the economy by having _above_ market returns.

    The only way central banks are able to keep money stable even when keeping risk adjusted returns above market rates for stores of value is by having a formidable centralized power over the whole economy that allows it to shift value across money and other assets.

    "The more merchants use bitcoin, the less volatile its consumption value will probably be."

    This is not a given at all. If the currency's "long term drift" is sufficiently negative it is probably true. But a decentralized currency will always quickly become unstable if it is priced to be hoarded and I would say this problem would get worst as the currency becomes more popular because it would start to have influence on the aggregate, it would amplify price changes caused by even predictable shifts in demand.

    That is when people would want to save, when they would want to work now and spend later, they would accumulate currency instead of accumulating investments. But the investments are necessary for people to be able to increase consumption and reduce labor later.

    Investments are what causes increases in the future availability of stuff. If a currency accumulates idly independently of increases of the availability of things to buy, when it comes time to spend (eg. a large cohort of savers retire) you suddenly get all this cash chasing few goods. Without a powerful central authority to control prices, they will jump up.

    On a risk adjusted basis decentralized currencies will always have value equal or below market returns for stores of value, only governments have enough control to keep their currencies slightly above risk adjusted market returns (but they cause havoc in the economy when they do so).

    The main benefit of cryptocurrencies replacing government money (which is probably not sufficient to outweigh their problems), is actually that they have the exact opposite behaviour than what their proponents think they have and want, that they could never, on a risk adjusted basis, keep their value as well as government money. But since people and banks would have fewer incentives to hoard them than overvalued government money and more incentives to invest instead, they might stay out of the way of the private economy and allow the world to stay closer to full employment.

  6. I would personally not define "store of value" as a GBM on an underlying S itself. I would define store of value as a GBM on the *spread* between the asset value S(t) and the consumption basket. One could also argue that in the GBM above,dW is highly correlated with the consumption basket, but that is not exactly the same thing.

    Something more along the lines of:
    dS = a (mu(C)-S)dt + s dW ("Vaskicek" model see here:

    Asset value drifts towards the mean value of the consumption basket mu(C). A good store of value would have large a (speed at which the asset value reverts) and small sigma s.

    1. I would define store of value as a GBM on the *spread* between the asset value S(t) and the consumption basket.

      Defined in what units?

    2. The units would be the unit of account.

    3. Why would you define "value" as this spread, instead of just using the value of the consumption basket as the units of measurement for the value of the asset?

    4. ahh, I see, you are defining S in consumption terms, I missed that.

    5. Yeah. That will still be a bit different from what you do, which will have a barrier in it.

    6. Barrier? Hmm, I do not think so but maybe it means something different to me.

      A bit different because the value of the asset is allowed to drift from the value of consumption for a short time, but gets pulled back. This is more like the *long term* store of value in your post. This is also closer to the case mu=0 in your GBM above.

      I guess thinking this through, I am arguing for the long term store of value, but allowing the short term value to wiggle more.

      In your model above, you ask: "does it mean that mu, the drift, is high?" I would have thought mu=0. Why would we allow a good store of value to drift too far from the value of consumption? If people are only holding money long enough to pay for things, it is not so much a store of value, it's a medium of exchange.

  7. Noah, I get the impression you've just discovered Keynesian liquidity theory. In a standard presentation, the alternative to money would be bonds, not stocks.

    The chicken and egg thing with bitcoin is also recognized at the international level with hard and soft currencies. Incidentally, bitcoin supply is not elastic, so it would have to support a payment superstructure the way base money does currently. Otherwise it remains a parallel currency. Is there a general theory of parallel currencies? It's an important practical concept (e.g. Greece).

  8. Everyone wants what they can't have. So what else is new?

  9. Great post, I think we're pretty much on the same page. FWIW, if I had to choose a comic book character to illustrate the post, it'd be this

  10. I think JP nails the consumer angle pretty well. Bitcoin is stagnating, even as VC funding for infrastructure has increased and the names of investors have gotten bigger (eg GS, CME). Some hope is being put on the ever-pending launch of the Winklevii ETF. But it's pretty clear that without some major new influx of investment in coin itself, the pending halving of mining rewards about a year from now is going to crush the mining industry.

    1. The other big reason BC doesn't compete with debit and credit cards that JP doesn't mention is that debit and credit cards have security features and the possibility of chargebacks. A bitcoin wallet couldn't add those without having to charge similar transaction fees to debit and credit cards.

  11. Yeah, no. The "store" part is propaganda. Otherwise mints are literally creating warehouses of flat-screen TVs and such. There is no "storage" in any real sense of that word. Heck, you can't even eat the stuff. Maybe burn the paper stuff for heat. The value that is "stored" is like those "nominal values" of 1/20 cent disclaimed on store coupons.

    Don't get me wrong, money is a very very good thing. But if you want stored value, buy a house, or a business, or a shed.

  12. I don't think receding volatility would even help all that much. Here's why:

    As long as people have the option of using national currencies electronically (and we are already far along in this direction) instead of bit coin, there is little incentive for regular consumers to invest in a currency that's not backed by anything. Even if it ever overcomes the short run volatility issue, you still need a whole bunch of people to accept the risk of converting their liquid cash into a parallel currency that carries no guaranty of fungibility.

    There is cognitive aspect to why people hold certain currencies that's sometimes taken for granted. For example, people hold US cash not simply because it's a store of value (of course, that's a big part of it) but also because there exists a solid network of other users. At the very least, they 'know' that they can use it to buy things in many different places. We are not all exporters, or central bankers, or multinational corporations. We don't have long-term hedging and reserve currency strategies; we don't think about trade invoicing. But we know that people use US dollars, or Euros, and we don't care why. At the most basic level, we know that this currency is tied to the US economy. Gold is a poor counterexample: it predates modern monetary policy and, really, national sovereignty in its present form.

    Just look at the IMF's Special Drawing Rights. Few people know this, but this quasi-currency unit has existed for decades and we're still not past the point where it's a significant reserve currency, despite various national and international efforts to get the momentum going. I was at a small private conference 5 years ago, where a senior IMF economist told me that within 10 years we would get enough critical mass for SDRs to really compete with the dollar for international reserve status. Does anyone have numbers on how the SDR is doing on this front? Can't imagine much has changed, and in this case we're not even talking about a replacement to territorial currencies but simply a basket thereof.

    So, unless someone can outline a plausible, long term vision of an erosion of how global economic integration (or something else) will create enough incentive for bitcoin to reach critical mass, I just don't see this happening.

    Really, I think the only way to solve the chicken and egg thing is for some (powerful and big) country to basically adopt it as a medium of exchange. And why would they do that, when they can (eventually) just fully digitize their own currency?

    If people are reluctant to even give us physical cash (and they are), what chance does bitcoin have?

    My bet is on bitcoin being regulated and traced by all the major economies before it gets the critical mass it needs. And then, it will lose the one attribute that makes it more attractive than national currencies: anonymity. Once it loses that, I bet people's wouldn't even trade their Russian rubles for it, let alone their US dollars or their RMB.

  13. Noah,

    Nicely said. There is something else to consider, something a little more subtle. I would argue that even if the purchasing power of a money was relatively stable over time, that it may nevertheless be very sensitive to large, infrequent, and unexpected shocks to the demand for money.

    So, suppose that we see a stable value (low volatility) in BTC. Does this imply it is is "stable?" My answer is no. It's purchasing power might still be subject to a dramatic increase during a financial crisis (as people flock to the safety of BTC). In a world where contracts are denominated in nominal terms, the implied deflation would wreak havoc on the economy.

  14. For personal fetishistic reasons, I'm going to comment on this without using the word "money".

    The short- versus long-term volatility point is a good one. But to consider from a different angle:

    1. How volatile is the unit of account (e.g. The Dollar) relative to a basket of goods. (In your words, how volatile is its consumption value?)

    2. How volatile is a given asset's price, relative to the unit of account?

    A key virtue of currency-like assets (especially physical fiat currency, but also deposits in stable, fiat-backstopped banks, etc.) is that is that their Volatility #2 is (historically) perfectly zero.

    A dollar bill is always worth a dollar. A whole category of volatility is magically eradicated from the fretful holder's anxious mind. There's utility in that alone.

    Then there's #1, of course (inflation), which is a form of drift. (If it's rapid hyperinflation, is it still drift?) But that underlies and affects all owned assets, like the current beneath a boat race.

    This fetish arises (and the true purpose of this comment emerges) because 1. economists don't have a goddam definition of "money" that they've agreed on (physics without a definition of energy?), and 2. "medium of account" is incoherent gobbledygook, conceptually. (What is a "medium" of account? Accounting ledger pages? Quicken bits and bytes?) "Unit" of account, please...

    Thanks for listening... ;-)

  15. To be honest I cannot see any way how bitcoin can ever be better than fiat money in the store of value function. The key part is that bitcoin is electronical, so it competes with electronic money. So whatever drift the bitcoin has can be compensated by interest on electornical money. Or in short it does not matter if we have money with no supply and positive 2% drift (stemming from long term real growth) or if we have money which supply increases 4% but with with 4% interest resulting in 2% inflation. In both cases holding money results in an interest rate that is determined by long term growth drift of an economy.

    If bitcoin replaces fiat money it will be for other reasons: less payment regulation, easier use etc. Which is paradoxically one of the main drivers behind volatility of bitcoin as it is the thing that can make bitcoin sucesful.

    1. On the second thought, scratch the "it does not matter" becuase it does matter if we use money that experiences positive inflation or if we use delation money. It matters for business cycle and any sane government should do something about it due to money illusion. So bitcoin probably never will be medium of account, which is what is important when it comes to moneyness.