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Hedging the Lower Tail Risk

What I learned from Robert Waldmann: Almost no professional portfolio manager worries about the lower tail, because if you are in the lower tail the whole world has gone to hell in a handbasket and people have other, more important things to worry about than whether one's portfolio manager had appropriately hedged whatever risk is now roosting on the roof.

Felix Salmon disagrees:

RGE - Economonitor: Brad DeLong responds to my entry on Bob Rubin thusly:

The lower tail--both in its economic and political aspects--is still ferocious and scary. But it is still the lower tail. And I can understand why finance professionals would rather not price it at all than price it into their forecasts and so run a high probability of lagging their peers' performance.

He has a point: If there's a 90% probability of the market going up by 15% and a 10% probability of the market going down by 60%, how do you position yourself? You want to be long, even on the balance of probabilities. So in practice you simply do what you would have done if the lower tail didn't exist. But of course today's markets have more options than simply long/short.

Specifically, it's possible to hedge against a large downside risk by buying long-dated, far-out-of-the-money put options which cost almost nothing using Black-Scholes but which act as a very good hedge against lower-tail events. Such positions don't even need to be a dead loss if the lower-tail event doesn't happen, since even an increase in the perceived probability of such an event is likely to drive their price higher.

What's more, DeLong seems to be saying ("it is still the lower tail") that scary events like the ones Rubin was talking about ("nuclear proliferation, Islamic radicalism, the endgame in Iraq, instability in countries that mean a great deal to us in the Middle East, what's going to happen in Pakistan, and many other issues as well") are still low probability. Many geopolitical strategists might disagree, in which case it might make sense simply on the balance of probabilities to position oneself defensively.

It is the case that the cost of buying the long-dated out-of-the-money put options is a constant drag on one's performance in those high-probability states of the world in which you don't wind up in the lower tail. But Felix has a good point: in a world of derivatives, you buy puts if you think that the market will raise its estimate of the chance of a lower-tail event. And you do so even if you think the lower tail remains very unlikely.