# Analysis of Mark Spitznagel Tail Hedging, Part 2

Part 1

From what I can glean from the links provided in part 1, Universa allocates approximately 1% of its capital on OTM (out-of-money) S&P 500 puts that expire in 70-90 days and have a ‘delta’ of .01 (at-the-money puts typically have a delta of .50). These are puts that are struck at strike prices 30-35% below the present market price of the S&P 500 (which is why they have such a small delta) and are rolled over every 30 or so days. This means after 30 days the bought puts are sold and replaced with newer ones to keep the running time until expiration around 60-90 days for all the puts. The rest of the capital is invested in the S&P 500. Following this procedure purportedly allows investors to ‘capture the upside’ of the market but also ‘minimize the downside’, as per the video and Taleb’s posts.

Assume $200k of initial capital. The SPX index (a proxy for the S&P 500) is at 2150 as of 10/4/2016. The 1500 puts (30% out of money) that expire in 87 days are valued at 1.15 ($115 per contract). 1% of $200k means we have to buy 17 of these puts. All calculations are done with the erieri.com Black Scholes calculator. To calibrate the actual option prices with the results from the calculator, I used the following variables: volatility =.325 time= .24 of a year (about 85 days) Risk-Free Interest Rate: .01 Option Strike Price: 1500 The result is 1.12, which is close enough to the actual value of 1.15 (this means 18 contracts are purchased instead of 17) Unfortunately, Mark Spitznagel doesn’t say when it sells the puts (probably because that information is proprietary), but I will assume the puts are sold if the market falls at least 10%. If they are sold too soon, it defeats the purpose of having them as a hedging instrument. Wait too long and they may still expire worthless despite the market falling a lot. To simulate the passage of 30 days, I plug time = .16 into the calculator. Recalculating yields .19, for a loss of$93 per contract, or about $1,700 total for the month for all 18 contracts. For an entire year, assuring the market is flat and doesn’t crash, the total loss is around$20,000, or about 10% of the portfolio. This means the tail hedging portfolio will lag the S&P 500 by about 10% a year provided the market doesn’t crash. Consider the period between Jan 2003 to Jan 2007, in which there were no 10% crashes and the S&P 500 gained 60% (excluding dividends). The tail hedging portfolio wold have only gained 5%, which is pretty bad.

But what if the market crashes? Consider three recent sell-offs, denoted by (1),(2),(3), below:

Using historical option data simulated during the August 2015 crash, in which the S&P 500 fell 10% in a two-week period (1), the gains would have been anywhere from 30-50x, depending on the choice of strike per the method above. That means, assuming you sold the puts at the best price when the market was exactly down 10%, the $2,000 would have become$80,000. That makes up for four losing years. Again, that’s assuming you sell at the best time and price and don’t wait any longer, as the puts did eventually expire worthless.

I used Think or Swim to get the old put option data on SPY (an ETF proxy for S&P 500 that is 1/10 the value) before and after the August 2015 crash, as per the instruction above. As you can see, some of these tiny options gained 40x, so under some circumstances the potential profits are huge:

Sounds pretty good. So it must have worked equally well in Jan 2016 (2) when the market also fell 10%?

(here I’m using the SPX contract, which is 10x SPY)

Not quite. Actually, not even close. They only gained 3-4x, a far cry from 30-40x. What happened? The August 2015 crash pushed volatility very high, and for reasons that are mathematically too complicated to explain, significantly reducing the ‘explosiveness’ of the tiny puts. Second, the Jan 2016 crash was more protracted than the August 2015 crash (a month instead of a week). The hedge would have made $6,000, only enough to offset some of the 10% loss of the S&P 500 ($20,000 loss on the $200,000 portfolio), and this is assuming you don’t hold on to the puts any longer, because they too expired worthless. To give an example of why tail hedging usually doesn’t work that well under the vast majority of circumstances, consider the September 2016 ‘mini crash’ in which the S&P 500 fell 2.5% in a single day: On Sep. 8th, the day of the crash, the puts double in value, turning the$2,000 into $4,000. That isn’t enough, because the$200,000 lost $5,000, so you’re$3,000 short (assuming you sell the puts, but we cannot, because the 10% threshold hasn’t been triggered). But here is the worst part…on Sep. 26, the market is still 1.5% lower, but the puts have decayed so much that they have fallen from the purchase price, meaning you not only lost money on the S&P 500 but also lost money on the hedge, too. The hedge actually backfired.

Discussion

In conclusion, tail hedging, assuming perfect conditions, can yield enormous profits to compensate for many smaller losing trades, but in most instances it’s a significant drain if a crash does not occur under the optimal circumstances. Using Spitznagel’s OTM put strategy, unless the volatility before the crash if very low and or the crash is very deep and sudden, the returns will be insufficient as a hedge, and may actually cost money (meaning you lose on both the hedge and the decline of the underlying index, as I showed above).

The tail hedging method would have failed between 1990-1996, a period when volatility was very low but the market didn’t crash. It would have scored a win during the small crash of 1997, which was sudden, but volatility spiked afterward and would remain high until 2004. The high volatility during the late 90’s and 2000’s would have prevented the method (like we saw in Jan 2016 above) from scoring any big wins during the collapse of the dotcom bubble between 2000-2003. Although 911 would have yielded a good profit, the volatility preceding the attacks was still too high. It would have also failed during the 2003-2007 bull market.

Although tail hedging can yield abnormally high returns during crashes under perfect conditions, after factoring years of decay in the absence of crashes, the returns may be much worse than the S&P 500. The crash of 2008 was unique in that most of the losses occurred in just a few months (October and September), and the volatility was very low preceding the crash, but had 2008 crash either never happened or was more protracted (like the 2000-2003 bear market, which took three years to bottom instead of one), the returns using tail hedging would have been far worse.

Part of the appeal of tail hedging, despite worse returns, may have to do with two common cognitive biases: loss aversion (which means that a loss results in asymmetrically more discomfort than the pleasure from a gain) and recency bias (the tendency to overestimate the likelihood of rare events, because of a recent occurrence. The market crash and recession of 2008 is still fresh in people’s minds, but they don’t realize, historically speaking, that such events are very rare).

Often you hear the argument that tail hedging is profitable because stock returns don’t obey the normal distribution and therefore put options are ‘cheap’. This reasoning is wrong because put options have a very steep ‘skew’ that arises from a stochastic volatility model with ‘jumps’, a significantly more complicated model than the normal distribution model that underpins the Black Scholes equation. The skew is the result of crashes being priced in advanced into the puts, resulting in puts having much higher implied volatilities than predicted by Black Scholes. This is especially so after recent crashes, like I showed in Jan 2016 above. These expensive puts also decay very quickly, often producing rapid losses for anyone who buys them, and only very seldom producing a positive return for buyers. The overwhelming evidence suggests people overpay for put protection, not underpay.