Bitcoin is now 44 percent off its intraday high of $266.
But that’s part of the point, isn’t it? (Have we ever posted on the two envelopes problem? I think so but I can’t find it through search.) Imagine you hold a currency which, over the next period will either double or halve in value. The expected return of such a Bitcoin is in fact (0.5 x .5) + (0.5 x 2) = 1.25.
What a good deal that is! Holding a single Bitcoin — a very volatile Bitcoin that is — seems like a lot of fun. It’s unlikely that simple risk aversion will take away the expected gain there.
Does this not mean that exchange rate variability is desirable per se, a kind of automatic utility machine? The party holding the other currency reaps a comparable gain from the ex ante volatility.
Fischer Black was obsessed with this problem for a few years, though I don’t think he ever quite nailed it. The mathematics behind Jensen’s Inequality are relevant here, but again that’s not the same as an explanation of the puzzle. My preferred path is to start with the Sumnerian “never reason from a price change” insight, but in any case this is a good brain teaser for your evening.