MV=P…Que? Love and Circularity in the Time of Crypto

Authors: Anshuman Mehta and Brian Koralewski, General Partners, Austere Capital

The authors are principals of Austere Capital, a fundamentals-based hedge fund and venture capital firm. Request our previous research here.


The central thesis running through the crypto-currency space is an unhealthy obsession with supply-side scarcity.

The ultimate goal of creating digital-gold, a scarce resource, confers upon the holder riches beyond its ostensibly low intrinsic value. Much like the pale yellow physical-world counterpart is intrinsically useless but conferred value by social consensus. (Clearly, crypto-architects have visited India during ‘wedding season’!)

Accordingly, crypto-architects endow their creations with a limited or fixed supply schedule. When limited supply meets increasing demand, hodlers will become rich.

In this piece, we take a scalpel to this viewpoint’s core tenets:

  • Deflation is good -> Inflation is evil -> therefore price appreciation of supply-limited crypto-currencies is evidence of supremacy over and inevitable replacement of ‘fiat’
  • The monetarist equation M*V = P*Q is a great valuation tool for coins and tokens

Let’s begin at the beginning.

MV = PQ and the Gold Standard: A Brief History

M*V = P*Q, or the Quantity Theory of Money (also known as the Equation of Exchange) was originally formulated by the economist Irving Fisher in the early 1900s.

The equation scrutinized the relationship between

  • M — the monetary base
  • V — the velocity of money (or how many times a unit of currency is spent or used in a year)
  • P * Q — the output of the economy, as represented by the product of
  • nominal price level — P, and
  • the quantity of goods and services produced — Q
Figure 1. M*V = P*Q (Source: Austere Capital)

When Fisher first formulated the theory, the Federal Reserve had not yet been created and paper money was pegged to the amount of gold held.

This “Gold Standard” kept the economy in a low-growth mode since the flow of capital (e.g. investments in new businesses, lending etc.) was stifled by the available money supply, which in turn was capped by the quantity and growth rate of gold reserves. Gold reserves could only be increased at the rate at which they were physically mined out of the earth. The monetary base remained largely constant from one year to the next. Paper money was nominally “safe” but also scarce.

Gold-backed money was also susceptible to bank runs — in times of uncertainty, holders flocked to banks to exchange their paper money for an equivalent amount of gold. Indeed, the UK abandoned the gold peg in the 1930s following one such run that left it precariously short on the precious metal. This was one of the many occasions on which the UK abandoned the gold standard. Not much of a standard then.

Figure 2. Montagu Norman Telling the Gold Standard Where to Go

In the US, the Federal Reserve formally abandoned the gold standard once and for all in 1971, leading to the collapse of the Bretton-Woods Agreement in place since post-war 1945. The subsequent conversion to a free-floating “fiat” system backed by the “full faith and credit” of sovereign governments initiated a new form of Monetary Policy. The Federal Reserve was handed new statutory mandates, which included price stability and maximum employment and moderate long-term interest rates

This switch allowed for a speeding up of capital flow through the economy as investment and lending accelerated. It also provided Central Bankers with more tools to respond to the periodic recession or depression. When the GDP turned negative for two or more quarters (the definition of a recession), Central Bankers could ease the liquidity trap demand for safe assets by temporarily increasing the monetary base. This would have been impossible under the previous gold-backed system, where any increases in monetary base would need to be matched by an equivalent increase in the gold reserves.

Figure 3. “Redeemable in Gold on Demand” (Source: Wikipedia)

From Monetarism to Interest Rate Targeting to Monetarism

One drawback of Monetary Policy is the inability of Central Banks to influence monetary velocity V directly.

Since the collapse of Bretton Woods, Central Bankers realized that interest rate targeting via Open Market Operations (i.e. the buying and selling of government debt on the open market which increases/decreases the effective interest rates in the market) was a more effective policy tool than simply manipulating the Money Supply.

In the aftermath of the financial crisis of 2008–2009, even Open Market Operations provide insufficient to stop the rot. Faced with employment and structural solvency concerns, consumers and investors flocked to the best safe haven asset they knew — cash.

The Fed and other central banks around the world began a wholesale experiment of “Quantitative Easing”, aggressively purchasing primary and secondary issuance of Govt.-issued bonds to counteract a contracting money velocity V by increasing monetary base M.

At one point, the Fed was purchasing $80B worth of asset purchases per month. This is also what’s known as Central Bank money printing, loathed by libertarians and fiscal hawks worldwide. Ironically they’d prefer to fix M but to their liking.

MV = PQ, Price Stability and Inflation

Back to M*V=P*Q for a moment.

The equation still has its utility, helping central bankers determine an optimal monetary base M required to maintain a stable and growing GDP P*Q, a calculation especially important after the constraints of gold-peg had been abolished.

Velocity V on the other hand was almost an afterthought, the multiplier they derived by dividing P*Q by M.

Once calculated, we could assume V to be constant in the short run thereby illuminating other relationships. For example, with a constant V, money base M is [directly proportional to] P*Q. In the short-run, as M increases, GDP increases. Not bad to give the economy and markets a fillip, almost like a shot of pure oxygen helps an ailing patient recover.

But Q, or the production capacity of the economy is a structural constraint and increases at a very slow pace. Beyond these constraints, increasing M only serves to increase price levels P — i.e. inflation or worse, hyper-inflation.

Figure 4. Keeping V constant, M is proportional to P * Q (Source: Austere Capital)

Therefore, money supply M can be used to influence price inflation, increasing or decreasing it to maintain price stability. In this way, Central Banks give investors and consumers comfort about the future of the economy, incentivizing investments and consumptions and keeping the economic engine going.

MV = PQ and A Misplaced Lust for Deflation

A major argument for the supremacy of crypto-currencies — at least viewed by the most libertarian or crypto-anarchist factions — is their fixed supply, or “deflationary” nature. This scarcity coincides with (and therefore causes?) price appreciation against a benchmark, usually the USD.

Point proved, case closed, we’re all Bitcoiners now. Right?

Not quite. Deflationary currencies work horribly in real world — essentially, the gold standard all over again. A deflationary environment encourages hoarding of cash, as it will be worth more tomorrow than it is today. This hoarding is magnified in economic downturns, gives rise to deflationary spirals.

Figure 5. A Deflationary Spiral is Bad for Everyone (Source: Innovative Advisory Group)

One could even theorize that in an all-crypto-currency world, with no Central Banks, there’d be no one to provide much needed liquidity injections during times of throttled capital flow. With velocity rapidly descending towards zero, CryptoLandia would swiftly and pro-cyclically descend into a prolonged and catastrophic recessions.

So whilst parabolically rising crypto-currency prices are great when viewed from a fiat-currency investment perspective, they’d be terrible for the residents of CryptoLandia. Except perhaps the top 1% of Crypto owners who’d be sitting pretty, enjoying the increased spending power of their air-dropped haul.

Perhaps explaining the early adopter’s love for deflationary crypto-currencies?

Figure 6. This Guy Loves Deflation (Source: Remy and Reason TV)

MV = PQ can be Circular

MV = PQ equation is what’s called an identity equation — an equation created such that both sides are always equal. In this case, sum of all purchases in an economy ought to be equal the sum of all sales. M*V represents the former, or the number of times money is ‘spent’. P*Q represents the latter, or the sum of all production sold.

We need to be cautious in using MV = PQ free of the original context and constraints. The equation can be circular, as the terms aren’t exactly independent of the other.

For example, the St Louis Fed data shows V = (P*Q) / M falling drastically during the last crisis. We know that over this period GDP severely contracted, reducing the numerator. But also know that M was dramatically expanded in response, increasing the denominator.

Figure 7. Expansion of the Monetary Base (Source: St. Louis Fed)

So did V contract because consumers hoarded cash and businesses delayed investment decisions? Or was it because the evil Central Bankers increased M even as the P*Q fell?

Or, even more nonsensically, a greater-than-proportionate reduction in Mthan the P*Q contraction would at least numerically restore V. By this measure, should the Fed have actually contracted monetary base by hiking rates and withdrawing stimulus?

We say again — applying this equation free and clear of its original context and constraints can yield frankly ridiculous results.

How MV=PQ Works in the Real World

Let’s go back to our old friends, the Nigerians, who we first met in our analysis of Stellar and XLM.

The Nigerian monetary base is NGN 11T and its annual GDP is c. NGN 18T. Applying our equation, this yields to a velocity V of 1.7.

Now let’s assume that the Nigerian economy starts to slow down. Corporate and personal bankruptcies defaults increase, and the banks’ ability to lend is impaired. There’s bad news on the TV, sentiment generally worsens and instead of talking of the next bubble, Nigerians find themselves talking of the next crash. Families and investors start to conserve cash, reduce spending and postpone purchases. Previously referred to as the ‘liquidity trap’, this reduces Velocity V, because investors and consumers become naturally cautious.

A slowing economy is bad because it leads to vicious circles. Fearing the future, investors and consumers postpone purchase and investment decisions. Factories shut down, workers get laid off leading to unemployment, further suppressing demand. The economy contracts and becomes moribund.

This is why most central banks have a price stability mandate — keep inflation at a steady track at or around 2% for most developed economies.

In our example, when Nigerian economy slows, the central bank can do one of two things.

It can lower the interest rates and introduce fiscal stimulus, cutting taxes and embarking on public investment programs to stimulate the economy. The Nigerian central bank interest rate is around 14%. By lowering rates, the Nigerian CB encourages savers to spend because they don’t get much return on their bank deposits. It also induces risk taking because opportunity cost of capital, much like the actual borrowing cost, is lowered.

This approach has its limits though. You could only reduce rates to 0% (or so we thought before the crisis. There have been some notable examples of ‘mildly’ negative interest rates since.)

The second approach is a Quantitate Easing or QE program. QE has twin effects of reducing the government interest rate curve, the bedrock off which all assets in the economy are priced, and removing government bonds from the supply of investible assets in the economy.

But why do all of this? Isn’t some correction good?

Yes — some cooling of an overheated economy is good, via what’s called a soft-landing or a managed reduction of inflation.

Figure 8. The Chinese Soft Landing of 2012-Present (Source: CCN)

But go too far and the economy can plunge into a deflationary spiral, a terrifying prospect. Let’s take a simple example — say the prices of new refrigerators are falling in Nairobi, week on week. Rational consumers will postpone their purchase of a new fridge, expecting lower prices in the future.

On an aggregate level, this causes demand for fridges to go down. Fridge manufacturers are stuck with costly excess inventory and cut back on manufacturing. They impose layoffs, increasing unemployment amongst fridge plant workers. Fridge workers in turn reduce their willingness to make discretionary purchases, for example buying cars. This further suppresses aggregate demand, now hitting car manufacturers and their employees.

Corporate failures mount, it becomes hard to earn revenue to pay off debts and the economy keeps contracting in a vicious cycle.

A deflationary spiral must be avoided at all costs.

So, when our Nigerian friends are faced with a slowing economy, they try to maintain price stability by temporarily increasing M. In the short-run at least, this should have the impact of counteracting the slowing money circulation velocity V, and maintaining price stability (P*Q).

With some luck, they are able to mitigate the impact of a slowdown.

Do the Printing Presses Stay On?

In theory, when the economy recovers and confidence returns, velocity Vshould recover to pre-crisis levels.

At such a time, QE can be reversed. If it continues abated, i.e. M remains elevated, then either Q or P, or a combination of both, will increase to balance the equation.

While increased money supply M generally incentivizes investment, and we’d expect production capacity Q to show some increase, this is a structural change and it takes time. The more likely impact is a rapid increase in P, or hyperinflation, a prospect the libertarians and monetarists have been warning us of since the onset of QE.

It is important to note that V cannot be measured directly with ease. So as GDP growth recovers, the Central Banks will likely reduce M and observe the impact on the GDP, therefore deriving V. If required, they would then reduce M some more and repeat the observation process. This is because V is not an objective statistic that can be easily measured — it must be derived for GDP growth rate with a given growth in money supply M.

Let’s MV=PQ the Crypto Way

It’s clear then that M*V = P*Q is complicated interplay of monetary base, the GDP and the economic incentives of investors, savers and consumers. But to understand how this equation is applied to crypto valuation, we have to unlearn all the intricate economic relationships we covered above.

In the crypto-interpretation, MV=PQ has been variously used to determine token target price, market size, ‘market cap’, even d’app or protocol network valuations.

In his seminal piece, Chris Burniske built a model for token valuation using an elegant framework of a distributed network with a native token.

The underlying assumption was that the revenues generated each year by a network or protocol are ‘earned’ by token holders by selling their tokens to protocol customers. In other words, a future expectation of USD-denominated income P*Q is divided by the ‘token base’ M circulating V times through the system. The result is a target price, effectively the exchange rate of the crypto-currency, back into USD.

This is extremely disingenuous.

The first problem is that estimating revenue or P*Q of a crypto-network is hard, because well, there are none. (And before you say “But trading…”, trading revenues from price appreciation do not count as these rely on a constant Ponzi-like admission of new entrants returning capital to departing holders).

Next, the author(s) confessed to estimating V in order to complete the equation. Unlike our previous economic examples where velocity V was a derived multiplier to make the equation between M and P*Q balance, here it is an active ingredient that is estimated and input to derive M.

An arbitrary assumption of V, made with no regard to the token model or economic incentives of token holders, has since become the norm in this kind of analysis.

And then there is this.

The MV = PQ Circularity

In order to determine a token’s USD price target, we need to estimate P*Q in USD terms. This logically makes sense — after all most goods and services are still priced in ‘fiat’ will continue to do so for a long time. US-based or USD-based customers will conduct price equivalence analyses against competitors in USD. Commercial transactions will take place in USD, and market size is measured in USD terms.

The right side of the equation M*V = P*Q is therefore in USD.

This is an extremely important determination, and leads to a discovery that causes the whole experiment to unravel.

Let’s go back to our friends in Nigeria.

The economy in Nigeria is denominated in Nigerian Naira. M and P*Q are both similarly denominated in Naira. V then is the velocity with which the Naira circulates in the Nigerian economy.

Notice something?

In the Nigerian MV = PQ, all these terms are denominated in the currency of the network — NGN. What we do not do, what we cannot do, is use MV= PQ to determine the target price for NGN in USD i.e. the NGN/USD FX rate.

But somehow, the authors of most M*V = P*Q crypto pieces are able to do so with ease. So what gives?

Let’s look again at the linked piece again — the author assumes that his startup captures a certain market share of global market, equivalent to a certain USD amount.

Ah ha — we have already assumed USD-denominated revenues for the network.

But the proposed protocol has its own native token, much like Bitcoin or Filecoin or any similar other. To use the network, one must purchase the token. And to buy the token, you must sell USD at the prevalent … trading price or exchange rate.

We spy circularity here.

How so? A distributed network is expected to generate USD revenues by buying and selling tokens at the traded token/USD price all year long. The crypto M*V = P*Q equation turns right around and uses this very USD revenue figure to try to determine a target token/USD price.

No bueno.

Does this circularity show up when using real-world examples? Let’s explore.

Keeping TRAC of Your Origin (Trails)

OriginTrail is an early stage distributed ledger supply chain startup with its own token, TRAC. In order to use their ledger, whether to write to it or acquire supply chain data from a provider, a user needs to own the TRAC token.

Let’s assume you need 1 TRAC to buy 1MB of data. And there’s demand for 100MB of data globally per year.

So what is Origin Trail’s revenue (P*Q) per year?

P*Q = 100 MB * 1 = 100 … but 100 what?

100 TRAC.

And what if TRACs were sold an average price of $1 through the year? Now we can calculate Origin Trail network’s USD revenues.

P*Q in USD = 100 MB * 1 TRAC/MB * $1/TRAC = $100

Great, we have our USD revenue but guess what — the process of earning this USD denominated revenue already baked in the the implicit ‘target price’ for TRAC. The most important ingredient in determining TRAC token price, the USD-denominated P*Q, already factors in an actual exchange price for TRAC/USD at which it was earned.

This is an important result, and it holds good even for the likes of BTC. The conclusion is inescapable. M*V = P*Q simply cannot be used to calculate the target price a crypto currency.

Comparing Crypto-Networks using MV=PQ

Ah, you say, but we conduct comparative analyses of national GDPs in USD terms all the time. Perhaps there is a way to compare ‘cryptocurrency economies’, or decentralized networks, similarly?

All we’d need to do is calculate P*Q strictly in the native token terms, and then convert it to USD at a year-end traded price.

Ne c’est pas?

The answer sadly is still non — since the P*Q side of the equation is initially denominated in fiat terms.

The utility of the network or protocol will always be measured in an off-chain medium-of-exchange (likely the fiat currency of the country in which the service is rendered). Networks will always capture market value in fiat terms, and the token price will be largely irrelevant to the price customers are willing to pay for the service.

It’s no surprise then that crypto-architects allow for tokens to be sub-divisible into many quadrillion smaller units to enable this ease of real-world use.

Use-Case for MV = PQ in Crypto Valuation

So, can we use M*V = P*Q for anything at all within the spectrum of cryptocurrency valuation?

Well, no, not in terms of valuation.

We theorize that a startup’s ability to influence the token base M based on observed velocity V can help it manage the actual price paid by end users of its service. Clever protocol design can allow the network to self-release or burn tokens as necessary.

Clever crypto-architects can also monitor the health of a functioning distributed network by keeping tabs on velocity V. Low velocity, whether by design or misaligned investor, participant and customer incentives, may push up token prices but render the networks commercially unviable.

These are still rather difficult calculations since token velocity, based as it is on projected user adoption and token holder incentives, cannot be known ahead of time.

Additionally, a more interesting question arises:

The more “successful” a crypto-network becomes — i.e. the more user-traction it receives — the more the token appreciates in value, paradoxically incentivizing speculators and hodl’ers to hoard it rather than its intended use in the decentralized platform.

Arguably, the success of a decentralized network then works against its future success.

The counter against this is to price services not in token terms, but in fiat currency. At that point, we question the very need for a token — why not sell the services in fiat?

This circularity doesn’t manifest itself more explicitly for tokens like Bitcoin. We believe this is because Bitcoin has a tradable screen price that is completely de-linked from its intrinsic value as a transmission mechanism. Other factors at play, such as speculation or evasion, push up the price of BTC beyond what is justifiable from an economic standpoint.

We also note that optimal token velocity is rarely addressed in white papers — Basic Attention Token (BAT) formally addresses this in theirs. Their contention is that, based on natural supply/demand dynamics between token users and hodl-ers, an optimal token velocity is ensured. Hence, when the token becomes more profitable to hodl rather than use, users will switch to a cheaper network that provides a similar service, causing the former token’s value to decline, which will make the network cheaper to use again, and so on.

Some others, like Factom and BlockEx’s DAXT platform, utilize a specific token-burning mechanism in order to ensure an optimal balance between token hodl-ing and use.

Conclusion

And so, we find yet that another popular tool for determining crypto-currency valuation is fundamentally flawed.

MV = PQ is a fine approach to monetary theory, but within the context of its derivation and limits to its use.

Applying MV = PQ to crypto-currencies might yield numbers in the same order of magnitude as on-screen trading prices. But that’s down to a careful selection of the inputs or mere happenstance than any intellectual rigor. It is akin to observing two bananas, ten oranges and five apples on a table, and suggesting that (Apples = Oranges / Bananas). Mathematically correct but not scientifically sound.

And that’s not how we like them apples.


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