How frequent are Black Swan Events (defined as monthly declines of 20 percent or more) in financial markets? The answer to the question is important for investors who want to perform a cost-benefit analysis on the Black Swan Exchange-Traded Funds that were launched by Horizons ETFs recently. The cost side of the equation is clear: a portfolio that buys puts as protection against market crashes will lag the long-only portfolio by the net cost of the puts.

The marketing material put out by Horizons gives some idea of the magnitude of the gains that put options can provide in the event of a market decline. Horizons says that a hypothetical portfolio with a Black Swan overlay is expected to increase in value by 13 percent when the underlying market declines by 30 percent. That sounds enticing but how often do these events occur?

Based on S&P 500 index rolling month returns, Horizons ETFs says that Black Swan events are far more frequent than one would expect: 25 declines of 20 percent or more over the past 50+ years. Therefore, concludes Horizons (see table in this page), a Black Swan overlay would deliver protection from market crashes approximately every two years.

It is hard to find justification for Horizons conclusions in S&P 500 daily closing prices going back to 1950 available on Yahoo! Finance. It is true that if one looks at rolling monthly returns there were 25 instances of declines of 20 percent or more. However, rolling monthly returns vastly overestimates the number of serious declines. To see why, imagine that the S&P 500 is at 1200 for 19 days, plunges to 900 (a 25 percent decline) and stays at that level for another 19 days. If one looked at rolling monthly returns (Day 1 to Day 20, Day 2 to Day 21, … , Day 20 to Day 39) one would conclude that there were 20 Black Swan Events in that 39 day period! But, in reality there was exactly 1 Black Swan Event that an investor could have profited from: the crash on Day 20.

It turns out Black Swan events were extremely rare. In the S&P 500 data since 1950, there are only three Black Swan events (declines of 20 percent or more): 1987, 2008 and 2009. Surprisingly, (at least for me), the market declines of 2000-02, even in the immediate aftermath of the terrorist attacks of 9/11, the markets did not decline more than 20 percent.

It is hard to draw conclusions about how frequently Black Swans events occur from the limited data set that we have. An investor starting out in 1950 would have endured 37 years (!) of under performance waiting for her put option strategy to pay off. But, assuming Black Swan protection works as advertised, it would have paid off twice in the span of 2 years in 2008 and 2009.

This article has 7 comments

  1. I think you meant buy puts in the first paragraph (vs sell).

  2. Cc Nice job analyzing this and helping people avoid this crap.

  3. I’m still trying to wrap my mind around how the black swan option strategy works. If there are rolling daily sets of options, then there are 20 or so sets of put options open at any given time. Then it seems that we should think of each set of options covering about 5% of the portfolio. If a given event only causes, say, 7 rolling periods to see a 20% or larger drop, then doesn’t that mean that we only get the black swan portfolio boost on about 35% (7/20) of the portfolio?

  4. @Michael: From the holdings summary of the ETFs, it appears that the options strategy is fairly straight-forward (it is actively managed, so perhaps the actual strategy may be very different). As of May 31, 2012 the sub-advisor has invested approx. 0.45% of the portfolio in put options. The ETF is currently long S&P500 July 2012 puts at a strike price of 1,000. The ETF is short S&P 500 July 2012 puts at a strike price of 800. That’s why I don’t think it is reasonable to conclude how often this strategy will pay off based on rolling monthly returns.

    http://profile.horizonsetfs.com/fundprofile_hap.aspx?f=HUS.U&c=&lang=en

    The fund overview page notes that the put options are expected to pay off when monthly declines exceed 20%. Assuming, the puts expire worthless at other times and assuming 0.45% to be cost of premiums every couple of months, the ETF should incur costs of 5% every year. That seems fairly steep if Black Swan events are far rarer than every two years that Horizons seems to suggest.

    http://www.horizonsetfs.com/pub/en/etfs/?etf=HUS.U&r=o

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