Part II. The Parabolic Supertrend in Bitcoin— FCV and the Bitcoin Trifecta

More nuts and bolts on valuing Bitcoin

Prateek Goorha
Apr 29, 2018 · 8 min read

In my previous post on this topic, I described what I felt to be a useful imagery to have in mind when examining Parabolic Trav’s supertrend chart, which looks like this figure.

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Figure 1: The Bitcoin Supertrend (courtesy: Parabolic Trav)

If you haven’t read it, a quick summary of that previous article is that I proposed the imagery of bacterial growth. The three phases of bacterial growth, repeatedly sequenced together, mimics the Bitcoin supertrend. There is a lag phase, during which the bacteria are acclimatizing to the conditions in a Petri dish; an exponential phase, where the bacteria are growing through rapid, exponential multiplication, and phase of stagnation, where the bacteria exhaust the resources in the Petri dish and cannot grow any further. Left in that state, the fourth phase of retardation would then ensue. However, if more resources are provided, say by way of a larger Petri dish, the process continues anew. The parallel to the Bitcoin supertrend are easy to imagine.

Since that view may sit as somewhat too deterministic, in this post, I want to provide some of the nuts and bolts, and explore some other features of the Bitcoin ecosystem that Parabolic Trav and I have been exploring.

A recap on liquidity preference

The opportunity cost of holding money is, of course, determined by the real rate of interest that we have access to for a given quantity of our money. Usually this is the risk-free rate of interest, such as the Federal Funds Rate in the US. As the opportunity cost of holding money increases, our liquidity preference contracts, and so does our desire to carry money.

Now, it is, of course, rather insular to think that our liquidity preference is some easily describable static concept with close correspondence to the risk-free rate. This is because, as consumers, we have access to a vast range of interest-bearing assets, differing in their risk-return profiles. As we move our money around from one asset to another, the risk premium, our risk-preferences, our time-preferences, our ability to minimize tax-burdens, and a host of other aspects, all interact to determine our liquidity preference.

What is important here, however, is just that our short-run elasticity of demand for liquidity is pretty low. We tend not to be in a position to adjust our liquidity preferences rapidly in the short run, based on all the various factors that affect the opportunity cost of money. Expenditure patterns, commitments and essential needs serve to lock us into a narrow range of liquidity preference. In the longer-term, however, we tend to have a much more elastic response for liquidity. Expenditure patterns can be adjusted and the costs incurred in undertaking such adjustments can be defrayed over a longer span of time.

FCV

That these really are two separate aspects of the phenomenon becomes clearer when we consider the two aspects of what determines the rate at which we might convert fiat money into bitcoin, or what Parabolic Trav and I have previously called the Fiat Conversion Velocity:

1. When we see bitcoin as money, the Fiat Conversion Velocity (FCV-BM) is modulated by a relative rate, which is to say, a consumer’s liquidity preference is split across two, admittedly intersecting, economies — the incumbent economy and a smaller incipient cryptoeconomy. This relative rate is simply expressed as:

q=(Liquidity Preference in bitcoin)/(Liquidity Preference in fiat).

Note that the equation for q suggests that FCV-BM would be especially sensitive to the risk-adjusted relative rates of return. This suggests an income effect, generated purely from substitutions of consumption away from the cash-based traditional economy to the bitcoin-based cryptoeconomy, and vice versa.

2. When we see bitcoin as an asset, a liquidity preference for bitcoin alone becomes largely a meaningless concept. Expenditures are undertaken exclusively in fiat currency. The Fiat Conversion Velocity (FCV-BA) in this case is relevant directly, insofar as it is a precondition to buying the asset itself.

r=(Value retention in bitcoin)/(Value retention in fiat).

This equation, by contrast, suggests a pure wealth effect from bitcoin, with no reference to consumption substitutions across underlying economies.

In sum then, we have,

FCV=f(FCV-BM,FCV-BA,e)

FCV=f(q,r,e), where e is an exogenous shock; dFCV/dq>0; dFCV/dr>0

That FCV is conditioned by exogenous infrastructural effects, economy-wide shocks and random noise in the information on bitcoin is made plain by the effects on FCV from adverse news events or exchanges that get overwhelmed by demand and begin creating serious bottlenecks for consumers. The effect on volume is clearly indicative.

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Figure 2: The lack of volume in Q1, 2018. (courtesy: Parabolic Trav)

Some, usually ‘maximalists’, would argue that we can simply lose the distinction between FCV-BM and FCV-BA for a variety of reasons. Others, ‘cryptopluralists’ usually, tend to argue that the avenues for spending bitcoin as money are limited and that there are a host of regulatory and taxation issues that complicate the assessment of a liquidity preference in bitcoin. Besides, several use cases are beyond the reach of Bitcoin. And, so, what matters is only the FCV-BA.

Whatever your particular persuasion, I think that ignoring the difference laid out above would make for a rather facile viewpoint. Indeed, bitcoin’s use case as a global form of money remains open in the short-term and a hallmark prospect for its future. Besides, the number of places where bitcoin can be used as money is not only growing, but growing in an interesting manner. As the number of business, such as BitPay and Cash, continue deploying the infrastructure for the payment by and acceptance of bitcoin in a user-friendly manner with low transactions costs, a broader swathe of merchants all over the world become more willing to accept bitcoin.

So, FCV-BM is a function of an infrastructural effect, just as FCV-BA is pre-conditioned on the infrastructure provided by exchanges.

Note further, that the infrastructural effect highlights the strong endogeneity between the two concepts of FCV. My liquidity preference for bitcoin increases as your liquidity preference for it increases provided we are both consumers in a broader market that is itself exhibiting an increasing q. This co-dependence is arguably smaller in scale for r, modulated through a smaller set of financial markets, but it remains relevant there as well.

The Bitcoin Trifecta

Effect 1: Sarnoff value

The Sarnoff value in a network describes a linear relationship between the number of participants in the network and its value. The law comes from, David Sarnoff, a pioneer of radio broadcasting. His concern was, therefore, in the willingness of a consumer to participate in the network in order to value the network; communication between listeners was largely irrelevant. Bitcoin, as a money and as an asset has aspects of this personal value. As such, we could use Sarnoff’s law to write that the aspect of the value of Bitcoin, as proxied by the price of bitcoin btc, being proportional to the number of participants in the Bitcoin network, N:

btc=a.N

We should expect this effect to operates differently over shorter periods of time than it does for longer periods. The constant of proportionality in this effect can be seen as a function of the relative liquidity preference, q . For relatively shorter periods a is a more inflexible driver, since it depends on the short-term degree of inelasticity in the demand for money, as discussed above.

Effect 2: Metcalfe value

The Metcalfe value of the network is proportional to the square of the number of participants within it. This is broadly acknowledged to be a primary driver for btc, as it is premised on the interaction effects between network participants (consumers, developers, merchants, etc.). Naturally, this effect is most relevant for bitcoin as money, and its impact on btc is modulated by the ability to convert from fiat into bitcoin, so that one may begin participating across the network.

btc=b.N^2

Effect 3: Ecosystem infrastructural value

The idea here is to identify distinct types of infrastructural investments that are necessary in the Bitcoin network ecosystem. There are, of course, several such broad types, besides the most obvious ones pertaining to energy-efficient mining, ASIC R&D, establishment of exchanges in new markets, and educating regulators and erecting compliance procedures. Say that there are I such types of infrastructure groups within the ecosystem comprised of its N participants, such that I(N). Now, we can see that at any point in time in the network there might be any of the 2^I possible grouping of those types of infrastructures in place, not counting the two extremes. One such extreme involves none of the I in place, or a total destruction of the ecosystem, and the other involves some steady state where all of them have been erected. For all other periods of ecosystem development, the system is in flux. Occasionally, the vast parts of the infrastructure — in some country, say — might be uprooted by virtue of some adverse circumstance, such as an adverse regulatory ruling on tax compliance or a noxious actor trying to sabotage Bitcoin from within. So, the relationship to btc this gives us is:

btc=c.2^(I),

where c can be both positive as well as negative, based on our discussion.

So, the overall value of bitcoin can be given by this trifecta equation:

btc=a.N+b.N^2+c.2^(I)

TL;DR

btc=Sarnoff value + Metcalfe value + Ecosystem infrastructural value

The overall modulation for the strength of each effect on bitcoin can be understood by examining the idea of a Fiat Conversion Velocity, which, in turn, depends on two aspects of bitcoin: relative liquidity preference and relative value retention. While there is endogeneity in this relationship, it is helpful to keep the distinction in mind to sort out ancillary effects, such as those of interest rates, stock markets, financial intermediation, general consumer sentiment and so forth.

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Prateek Goorha

Written by

Social scientist interested in the economics of innovation. Part-time author. Full-time blockchain explorer.

Coinmonks

Coinmonks

Coinmonks is a non-profit Crypto educational publication. Follow us on Twitter @coinmonks Our other project — https://coincodecap.com

Prateek Goorha

Written by

Social scientist interested in the economics of innovation. Part-time author. Full-time blockchain explorer.

Coinmonks

Coinmonks

Coinmonks is a non-profit Crypto educational publication. Follow us on Twitter @coinmonks Our other project — https://coincodecap.com

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