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Can a Value Investor Buy a Bitcoin?

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Why Bank of America's "maximum fair value" formula is illogical, and how one might analyze the future potential of Bitcoin instead.

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Two bubbles found they had rainbows on their curves. They flickered out saying: "It was worth being a bubble, just to have held that rainbow thirty seconds."
--Carl Sandburg

Bank of America (NYSE:BAC) made the news recently for initiating analyst coverage of bitcoins with a "maximum fair value" of $1,300. That figure is the result of a formula that takes the 10 variables below:

Bitcoin_Amount = Number of bitcoins in existence now

Global_GDP = Global GDP

Gold_Amount = Total value of gold bars, coins, and ETFs in private hands

Gold_Price = price per troy ounce of gold

Market_Cap = Average stock market capitalization of Western Union, MoneyGram and Euronet

Silver_Price = price per troy ounce of silver

US_Cash = US household checking deposits and cash

US_Consumption = US personal consumption expenditures

US_eSales = US 2012 business to consumer e-commerce sales

US_GDP = US GDP

And plugs them into the following formula:

[US_Cash * US_eSales * Global_GDP * 10% / (US_Consumption * US_GDP)
+ Market_Cap
+ Gold_Amount * Silver_Price / Gold_Price] / Bitcoin_Amount

There is a lot to make fun of here, and I will mostly resist. This is intended to be a serious column about the value of bitcoins, not a specific criticism of this report. However the quant in me has to mention that plugging a bunch of numbers (including a shamelessly arbitrary 10%) into a made-up formula is not quantitative finance, and it would be foolish to put any credence at all - much less buy or sell a bitcoin - on the result. I suspect it's no coincidence that the author came up with a price 20% above the market price at the time of his writing, as suspiciously many equity analysts manage to do. Even if the price tumbles the next day, you can't look too foolish, since the price did get within 20% of your target; if the price goes up, you were directionally correct; and if the price stays about the same, you were about right. The target is high enough to justify buy recommendations from your sales force, but not so high as to be a strong argument against sell recommendations.

The formula doesn't make sense for other reasons. It mixes numbers totaled over the year 2012 with ones averaged over 2003 to 2012 with discounted future values with numbers from the day of writing, and suggests the result is valid for the future. It implies an inverse relation between bitcoin and gold prices, and a positive relation between bitcoin prices and the amount of traditional cash people hold; both of these appear contrary to common sense. There is no economic analysis, no backtest, no validation; nothing that a serious person would use before betting her own money.

On the other hand, I give credit to Vadim Iaralov, the report's author, for trying to measure things that are usually relegated to angels-on-the-head-of-a-pin semantic bickering. It's worth picking through his specific mistakes, not because we are going to come up with a better price for bitcoins, but because it illustrates the important practical questions any investor has to think about before deciding to buy or not to buy bitcoins.

Let's start with the most tangible part of the formula, the average market capitalization of three money transfer companies. The logic is that the bitcoin represents an alternative way to transfer money, so its value should be related to the value of these companies.

The trouble is that the market capitalization of the companies represents the market's risk-adjusted net present value of future expected cash flows. What matters for bitcoin value is how much people are willing to pay for money transfer services, that is, the revenues of these companies, not their cash flows. And that revenue does not represent the value of a bitcoin. Instead it is related to how much people would pay to use a bitcoin for a year (assuming we use annual revenues of the companies).

The total revenue of non-bank money transfer companies was about $10 billion last year, but this represents the tip of the iceberg. Bitcoin could replace a lot of bank money transfers, plus a lot of undocumented money transfers (like carrying cash across borders, or doing reciprocal transactions), plus greatly expand the amount of money transfer that takes place. Moreover, the revenue figures for the companies don't include lots of fees and taxes people pay, plus the cost of delays and uncertainties. I don't think it's unreasonable to guess that people would pay $100 billion per year for money transfer services that could be provided by bitcoin.

How does this relate to the value of a bitcoin? Aside from some start-up effort, the main cost of using bitcoins is the chance that you're holding them when they become worthless. Suppose you think the chance of that happening in the next year is 10%. Then the total stock of bitcoins can be worth $1 trillion, which represents an expected cost to bitcoin users of $100 billion per year. You can get much higher numbers for bitcoin value if you add in other uses for bitcoins, such as consumer and business transactions. Or if you prefer you can get a much lower value if you assume lower market penetration, competition from traditional and new entities, government discouragement, breakdown of the bitcoin community and infrastructure, technical weakness found in the process, or other problems. It's important to understand, however, that bitcoins can be worth quite a lot of money today even if everyone is sure they will eventually become worthless, as long as there is a significant probability of transactional value being delivered before the crash.

This is an upper limit, not a floor. If the price of bitcoins gets too high, the expected loss from holding them gets too great, and people will seek cheaper ways of transferring money. People may individually try to get around the problem by holding bitcoins for shorter periods of time, but since the total supply is fixed, that cannot reduce the total cost. On the other hand, if the price of bitcoins gets too low, there would be no force pushing the price back up. There is no reason for people to voluntarily decide to pay more for using the coins.

If you are a bitcoin optimist, it is no trouble to come up with assumptions that justify very high ceilings for bitcoin prices. In a world with $50 trillion of end-consumer transactions (and many business transactions as well) and $15 trillion of cash (of one sort or another), it's not unreasonable to think people would be willing to pay $1 trillion for bitcoin services. You might think the market opinion of the chance of bitcoin collapse was 5% per year, or even lower. Even with the full 21 million bitcoins issued, that's still a price per coin of about $1 million. Yes, it's more than the sum of all the money in the world today, but that's no contradiction; a better money could lead to more total holdings.

Remember, however, there is nothing to push bitcoins up this high, just no reason that people would stop using them even if prices got that high. On the other hand, if you are a bitcoin pessimist, you might think there's a limit on the order of $5 billion of what people would pay for bitcoin services, given possible legal problems, no barriers to competition, and other issues. You might think there's a 40% chance of bitcoins collapsing over the next year. In that case, bitcoins are now about at their ceiling price, and have nowhere to go but down, unless there is a speculative bubble.

To think about a floor, look at the first term in the formula, the one with US_Cash and eCommerce sales in it. It divides cash held by total expenditures (it calls this the velocity of money, but it is actually the inverse of velocity) to decide consumers hold $4 in cash for every $100 they spend every year. It then estimates how much people would spend in bitcoin transactions (10% of US eCommerce sales grossed up to a global total by GDP ratio). Multiply those two numbers and you get the value of bitcoins consumers will hold.

That's a bad way to estimate things because the value of bitcoins people will hold is determined by the cost and convenience of holding them; and these are different from cash. Moreover the amount of purchases people will make with bitcoins is also a function of cost and convenience. Finally, most of the cash people hold is not for transactional convenience.

Despite the numerical problems, there is a valid logical point here. The value of bitcoins is related to the value of transactional balances people want to hold in bitcoins, which in turn is related to what people are willing to pay for transactional services.

To put a number on this, I would look first to the experience at Silk Road, the only large-scale, diversified, successful marketplace based on bitcoins (since shut down by the US government). One of the things that irritates me about economics is that none of the many papers on bitcoins, including this research note, included any empirical research. I have been interested in bitcoins and other alternative currencies for many years. I've used bitcoins, and spoken to as wide of a variety of users, investors, and entrepreneurs as I can. My admittedly anecdotal estimate is that Silk Road regulars held bitcoins equal to about 25% of annual transactions. There were reasons for that which I will not go into here, except to say that some of them apply to mainstream uses of bitcoins as well, and make it likely that regular bitcoin users will maintain much higher ratios of holding to transactions than is typical for government-money users. This is in fact empirically true of the mainstream bitcoin users I know personally.

This sets a floor because as the price of bitcoins declines, people are unable to keep large enough balances for transactional convenience. They buy more bitcoins, and the price goes up. Note that this price increase does not discourage use of bitcoins. Transactional users are holding exactly the same value as before the increase. If anything, they have a warm feeling due to the profits they make on their bitcoin holdings. That's why this does not set a ceiling on bitcoin prices. Speculators can bid the price of bitcoins up to the moon, transaction users will cheerfully sell them the bitcoins to do it, as transaction users adjust their holdings to constant purchasing power. On the way back down, transaction users will less cheerfully buy the bitcoins back. The volatility benefits transaction users net, but it might discourage use, especially for transaction users who jump in when bitcoins are hot and get out when bitcoins go south.

The third term in the Bank of America formula is intended to account for net demand by financial holders. Forget the silver-adjusted gold stocks nonsense, the right way to think about this is with the Capital Asset Pricing Model. There are states of the world in which bitcoins are very valuable and most other financial assets are not. One scenario might be called "weak governments," similar to the world in the 1970s. Currencies inflate, government debt devalues, economies stagnate, demand for commodities falls. Trade barriers and regulations proliferate, sporadic efforts are made to expropriate wealth, but the will to enforce laws is lacking. In particular, there is not the will to crack down on bitcoin use, nor the energy to start wars.

These conditions have always led to the use of ad hoc and alternative currencies, and bitcoins are far more efficient than historical examples, plus they would have the advantage of an established track record. People might choose to hold significant fractions of their wealth in bitcoins. At that time it's reasonable to assume bitcoin prices would be pushed up to the ceiling where they are too high to support money transfers and real use of bitcoins declines. There's no guarantee that the price would stop at the ceiling, bitcoin prices could do what gold did and decouple completely from any transactional use. But that would bring us out of the realm of rational economic calculation.

If you're willing to specify a few future scenarios including this one, and assign probabilities, you could in principle estimate an optimal portfolio holding of bitcoins, which you could then convert to a valuation. Assuming that value fell below the ceiling from the first analysis and above the floor from the second, it would give you a reasonable target value for bitcoins, plus an educated guess at how bitcoins should correlate with other financial assets. Of course, adding the ceiling to the floor to the portfolio value, as Bank of America did, makes no sense at all.

After all that, what do I think bitcoins are worth? I won't answer that, but I will say there is enough potential for significant economic value and that bitcoins are not a bubble. No doubt many people are buying them because the price has gone up, and there will be a period of high volatility. At the end of that period, I'm betting that the final bitcoin price will be much less than its peak price. But I see some reasonable possibility that bitcoins settle down to a value stable enough to use, and that use takes off, and value goes well above current prices. I don't say bitcoins are a good investment, but I do say they're not a crazy one.
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