The conventional wisdom is that put options are too expensive to use as “tail risk” insurance against extreme losses in equities. But reports earlier this year of their spectacular success in a fund advised by Nassim Nicholas Taleb prompted me to evaluate whether investors should use them.

After the S&P 500 index dived by 34% from February 19 to March 23, stories emerged of spectacular returns for so-called tail risk or “Black Swan” funds. The Financial Times reported that Universa Investments, advised by Black Swan author Nassim Taleb, “made a return for investors of more than 4,000 percent this year.” There ensued a Twitter battle between Taleb and Cliff Asness of hedge fund AQR, precipitated by AQR’s issue of – as Taleb tweeted – “2 flawed reports saying tail risk hedging doesn’t work.” Asness, of course, tweeted back in insulting Twitterdom fashion.

The evidence, however, shows that Taleb was right and Asness was wrong.

How to measure the performance of tail risk strategies

We don’t know the fine details of Universa’s strategies, but we can reasonably infer that they involve purchase of deep-out-of-the-money put options on an equity index. Their purpose is to buy a form of insurance that pays off if the market drops. Thus, they hedge against market declines.

As such, the performance of these funds should not be measured on the tail risk funds in isolation. They are clearly meant to enhance the performance of a whole portfolio of which they are only a part.

Thus, measuring return on investment the way the Financial Times reported doesn’t make sense, as former risk manager Aaron Brown pointed out in a May 29 Bloomberg article. “Suppose you pay $100 per month for homeowner’s insurance on a house valued at $250,000,” he says. If, one fine month, your house burns down you will receive $250,000 – a one-month return, it would seem, of 249,900% on your monthly premium of $100.

This isn’t very meaningful. First of all, in the same month, you lost $250,000 on your house that burned down. The two should be considered in combination, not in isolation – the negative value of your lost house and the positive value of your insurance payoff.

Also, it’s most certainly not the return you get in the long run. To calculate that, you have to take into account all the monthly premiums you paid over the years, not just the premium in the month you got a payoff.

Part of the value of insurance is that it enables a positive form of moral hazard. If you have insurance, you can take more risk. If you couldn’t get homeowner’s insurance, you might have to be satisfied with a less valuable house, so that if it burns down you won’t lose as much.

By the same token, if you would otherwise reduce the risk of your portfolio by allocating to a 60/40 stock/bond mix, adding a tail risk strategy to mitigate the downside risk may make you feel comfortable investing 100 percent in equities instead. This is one of the chief benefits touted by the managers of tail risk funds.

A tail risk strategy, unlike a 60/40 mix, produces returns that are not symmetric. They curtail the downside but do not curtail the upside in a symmetric fashion. Therefore, conventional ways of measuring risk-adjusted return – such as a Sharpe ratio – do not apply well to the measurement of tail risk performance.