Bitcoin as a call option

Welcome back. It must have been a good day Tuesday, virus-wise: the cruise lines and the airlines led the market. Perhaps it was the news that the Moderna vaccine works well in teens. Whatever it was, good. Summer starts this weekend. Meanwhile, there is a certain vexed topic I cannot seem to get away from . . .

Two more points about bitcoin and then I’ll stop, I promise 

Readers may remember my argument last week that it helps to think of bitcoin as equity in a company whose only asset is a promising but unproven technology. The technology is a new form of money. Lots of people have agreed or disagreed with the notion that bitcoin technology is unproven, but if you can accept that idea, the argument can be improved upon.

Peter Atwater, president of Financial Insyghts and sometime contributor to the FT, has pointed out that my argument can be taken a step further, by thinking of bitcoin as a call option on a company with an unproven technology. What’s the difference? The call option better captures the volatility and sentiment that characterises bitcoin trading. Atwater points to this chart of call option volume in the big, hyped-up tech stocks (blue line):

Now look at a chart of bitcoin:

That blue line up top does look a fair bit like the yellow one below. Here is Atwater: 

“The correlation isn’t a perfect fit. The 2018 call option volume follows Bitcoin Bubble 1.0 rather than being coincident with it, but the more recent parallel is both striking and apt. 

“Excited retail stock investors are always last to the party and when they enter the room, they look for the fastest way to get drunk. They reach for the most leverage they can, believing that prices only go up. Call options provide the perfect tequila shot. Cryptocurrencies now serve the same role, only with price volatility that is 10 times that of stocks . . .

“ . . . call options are always the very last stop of the bull train.”

I think Atwater is right that part of the reason that bitcoin is popular now is its immense volatility. But there is of course the possibility that this call option will pay out big in the end, because the underlying technology could turn out to work.

In this context, a reader pointed out to me another good feature of the bitcoin-as-equity idea: companies with uncertain growth prospects actually should have surprisingly high values (as bitcoin does) according to the most canonical of valuation approaches — the dividend discount model (do you feel this getting geeky? You should be).

A paper written some years ago by Lubos Pastor and Pietro Veronesi argued that the Nasdaq bubble of the late 1990s was not as bubbly as many think. This is because the growth prospects of tech companies were then highly uncertain, and such companies actually should have high valuations. This is not intuitive, so I got Professor Pastor on the phone at the University of Chicago and he walked me through the argument. 

Under the dividend growth model, the value of an asset increases with the growth rate of its dividends (the model can be applied to companies that don’t pay dividends by substituting, say, growth in equity value for dividend growth). But, crucially, value does not increase in a linear relationship with growth — price accelerates as growth goes up. Why? Because of compounding. Just as, with a debt that is not paid regularly, interest accrues on interest, growth accrues on growth. 

Here is the punchline: between a stock that is expected to grow 20 per cent, and a stock that is expected to grow either 10 per cent or 30 per cent with equal probabilities, the latter is worth more, because the price curve is convex (feel the geekiness coursing through you!). 

Here is a graph (which may look suspiciously like I banged it out in two minutes using Microsoft Word):

Notice the convex orange line, where growth rates meet valuations. The stock marked with the blue star, which might grow fast or grow slow, has a higher valuation than the middling-growth stock marked with a red diamond. This despite having the same average expected growth rate, because of the compounding potential of the higher of its two possible growth rates.

Back to bitcoin, at last: my view is that, like an option on an unproven but promising tech company, it is either worth a whole lot more than it is now — or nothing at all. But such things are and should be worth quite a lot. As Pastor put it to me: “Lottery tickets on growth are very valuable.” 

Armstrong screws up some easy math 

In the section about cold calling yesterday, I made a dumb math mistake, implying that a cold caller had to make 10,000 calls in a day to make a sale. That would be impossible. I meant 1,000 calls, which you could make in a (very long) day, on the (correct) assumption that the great majority of the calls are just seconds long (ie, “click”).

One good read

My colleague John Plender is worth reading on any topic. His analysis about threats to the reserve status of the US dollar is no exception. We’ve all read a million columns about the death of the dollar over the years, and it lives on. But John argues convincingly that, at least at the margin, things are shifting.

robert.armstrong@ft.com