Hedging Against Black Swan Events: A Strategy That Pays Off In The Long Run

May 15, 2020 1:24 PM ETSPY, TAIL, VIXY, VXX33 Comments9 Likes
Enrique Zambrano profile picture
Enrique Zambrano
61 Followers

Summary

  • Deep out of the money (OTM) puts with short maturities are inexpensive and have a high appreciation potential, reason why they are ideal for hedging against tail risk.
  • We propose and test a hedging strategy using deep OTM put options on the SPY during the recent downturn.
  • In particular, 25%-30% OTM puts with four-months maturities are an efficient mechanism for protecting against these extreme events.
  • Options with these parameters are cheap enough to use over long time periods (more than 11 years) and will still outperform the benchmark after the downturn.

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The recent downturn in financial markets has brought back the debate of how to protect portfolios against Black Swan episodes. These unpredictable occurrences, which lead to a 25%+ market decline in a matter of hours or days, represent an important risk for investors. While it is true that these events happen once in a decade, the consequences of leaving portfolios unhedged could be devastating in terms of capital losses. In this sense, the main question is how to create strategies that effectively protect your portfolio with a relatively low cost (or for what it matters, opportunity cost).

There are several alternatives for hedging against these extreme events. First, you could keep enough treasuries in your portfolio. Also, buying volatility ETFs such as the ProShares VIX Short-Term Futures ETF (VIXY) or the iPath S&P 500 VIX Short-Term Futures ETN (VXX) could serve the purpose, or even others such as the Cambria ETF Trust - Cambria Tail Risk ETF (TAIL), which has been shown to be effective (as you can read here). Another alternative is protecting with puts. Finally, doing nothing at all and expecting a quick recovery is an option that investors could pursue. While the first alternatives involve different approaches and are subject to debate, the last entails an unavoidable truth: stocks may take a long time period to recover, resulting sometimes in catastrophic capital losses. The purpose of this article is to explain and test the use of deep out-of-the-money (OTM) put options as a hedge against tail risk.

These options are generally very inexpensive, reason why we could use them during long bull markets without incurring in important losses. Moreover, they have unpredictable sensitivities against changes in the stock price and volatility - that is, they have a high hedging potential in times of turmoil. This combination is certainly attractive for our purpose; therefore, we will design a strategy using deep OTM puts.

Building a hedging strategy with deep OTM puts

We must consider several factors in order to build a successful strategy with deep OTM puts. First, the choice of strike prices and expirations is essential since it will determine the cost and effectiveness in times of distress. Tail events happen once in a decade, reason why we need a strategy with relatively low cost and high hedging potential; otherwise, the losses associated with puts expiring worthless during bull markets would offset the gains during the panic. Second, given the options maturities, we must decide when to roll over the position; this will help us minimize the losses during bull markets. Third, we should determine the appropriate number of contracts, in other words, the percentage of protection for our portfolio.

In this article, we propose using options that expire in 4 to 6 months with relative strike prices between 70% and 75%. The rationale for this choice will become clear in the following sections. Additionally, we suggest rolling over the position when the options' remaining life is half the original maturity. This is a straightforward rule that will help minimize losses during bull markets, since options will not expire worthless. Also, we recommend hedging the entire portfolio - that is, buying one contract for each hundred shares in the portfolio.

We will explain the strategy's design considering a 4-months expiration and a 70% relative strike price (30% OTM options). We assume that the options' position is financed with borrowing (if needed). The procedure is as follows:

  1. On day 0, the investor buys 1,000 SPDR S&P 500 Trust ETF (SPY) shares at price P0. Simultaneously, he buys 10 contracts of the SPY put options expiring in 4 months, with strike price K such that K/P0=0.70 (the option is 30% OTM).
  2. On day 60, when the options' remaining life is half the original maturity, the investor sells his position in options and simultaneously buys 10 contracts of a new SPY put option expiring in 4 months, with a strike price K' such that K'/P60=0.70.
  3. Every two months the investor rolls his options position into new 4-months and 30% OTM contracts.

Our goal is to compare the strategy's performance with the unhedged portfolio - that is, a portfolio composed only by 1,000 SPY shares.

The strategy in practice

We will test the strategy's performance using historical prices between 12/18/2017 and 04/17/2020. Although the period is short, it comprises subperiods that could help us draw meaningful conclusions: in 2018 the market moved sideways and ended with some losses, in 2019 the market posted big gains, and in the first part of 2020 it suffered sharp declines. Data was retrieved from Bloomberg.

Since our primary concern are the costs and their potential impact over the strategy's long run performance, we first present the average expenses. In order to properly compare the numbers, costs must be presented in a yearly basis. We achieve this by multiplying the cost for 10 contracts with the rollover frequency during a year. For instance, 4-months expirations roll over six times a year, while 6-months and 1-year roll four and two times, respectively. Results are displayed in table 1.

Table 1: Annualized costs of the strategy with different parameters

Expiration

Statistics

30% OTM

25% OTM

20% OTM

15% OTM

1 year

Average cost for 10 contracts (USD)

4,260

6,400

8,800

12,440

Average net cost for 10 contracts (USD)

3,540

5,353

6,927

9,820

Average cost (%)

1.55%

2.33%

3.18%

4.51%

6 months

Average cost for 10 contracts (USD)

2,996

4,782

7,547

11,631

Average net cost for 10 contracts (USD)

2,457

3,949

6,137

9,309

Average cost (%)

1.08%

1.73%

2.71%

4.18%

4 months

Average cost for 10 contracts (USD)

2,207

3,463

5,790

9,917

Average net cost for 10 contracts (USD)

1,555

2,285

3,758

6,420

Average cost (%)

0.78%

1.22%

2.03%

3.48%

Source: Created by author using data from Bloomberg.

*Net cost is calculated as the difference between the buying price and the selling price of the options. The average excludes the periods in which the strategy yielded gains (puts were sold at a higher price).**Average cost (%) is the average cost for contracts divided by the value of 1000 SPY shares at the time of buying the option, multiplied by the rollover frequency during a year.

From table 1, we can observe that 15%-20% OTM puts are too costly. Their gain in value in times of distress does not offset the losses incurred when the markets are going up. Paying more than 2% of your SPY portfolio every year is not appropriate since the probability of sharp downturns is quite small; these events merely happen once in a decade. The same argument applies for 1-year expirations. In this sense, we discard all the strategies involving either 15-20% OTM options or 1-year maturities, which leaves us with 4m - 6m expirations and 25% - 30% OTM options.

In order to get an idea of the strategies' performance across time, we show both the absolute and relative differences of the hedged portfolios against the benchmark in the following charts.

Chart 1: Absolute differences between strategies and the unhedged portfolio

Source: Created by author using data from Bloomberg.

Chart 2: Relative differences between strategies and the unhedged portfolio

Source: Created by author using data from Bloomberg.

First, we must highlight that all strategies outperformed the benchmark in the selected time period. However, this must be analyzed cautiously. The weight of the recent downturn inside a 3-year sample is artificially high. We should consider the costs of implementing the strategy over a longer time horizon, since tail events rarely occur. We will get back to this in a moment.

As we can observe, the 4-months strategies have a greater hedging potential. The maximum differences against the benchmark are around 25,000 dollars (11% in relative terms) for the 30% OTM options and 35,000 dollars (15% in relative terms) for the 25% OTM puts, while the maximum differences for the 6-month expirations reduce to 20,000 dollars (8%) and 25,000 dollars (11%), respectively. This comes for three reasons: 4-months options are cheaper; they are more sensitive to changes in the underlying variables; and the implied volatility curve tends to invert in times of panic (implied volatility becomes higher for closer months). In this sense, the strategies with 4-months expirations seems to be the most appropriate.

Even though the 4-months strategies have a higher hedging potential, it is worth noticing that the 6-months strategies showed better results at the end of the sample. This is explained by a matter of the strategy's timing: the options were rolled over towards the 09/20/2020 maturity on 03/20/2020, just the day before the market bottomed and with volatility almost at its maximum. This generated a high profit in cash which was then dragged until the end of the sample, while the 4-months strategies didn't roll over and started to reduce their relative gains as the market partially recovered and puts saw a decrease in their value. However, this situation may serve as an example of the potential outcome of actively managing the hedge.

The importance of actively managing the strategy

Rounding it up, strategies with 4-months expirations and deep OTM puts have both low cost and high hedging potential. Nevertheless, as we can see in the charts above, they can lose their gains quickly if the market recovers. Here relies the importance of actively managing the options. The investor could choose to roll over the position or even just sell the hedge when volatility is remarkably high, thereby locking in a profit and avoiding a potential depreciation of the options when the market rebounds. Perhaps setting an implied volatility target (say a VIX value over 50) could help with the decision. Although selling when volatility reaches its maximum is just a matter of luck, volatility can remain high for days and even weeks, giving enough opportunities before reverting towards its mean.

Let's suppose that an active investor sells the options when the VIX is over 50, precisely between 03/09/20 and 04/02/2020. That leaves 19 trading days (almost 4 entire weeks) to execute the trade. Considering the average prices during the period, the proceeds from the sale for the 4m - 30% OTM and 4m - 25% OTM options would have been 18,195 and 26,053 dollars, respectively. Subtracting the accumulated costs from the preceding years means that the strategies would have earned 15,385 and 21,743 dollars more than the benchmark over the whole period, respectively. This is illustrated in the following chart.

Chart 3: Performance of the actively managed strategies vs. benchmark

This difference is not negligible. Assuming that previous years are like 2019, it means that we could have run the 30% OTM strategy for an additional 9,89 years before the tail event (roughly 11,89 years in total, considering 2018 and 2019) and the return would have been similar to the unhedged portfolio. For the 25% OTM strategy, the statistic is approximately 9,52 additional years. In other words, if we had started the strategy just after the 2008 financial crisis, it would have outperformed the benchmark after the 2020 downturn. Moreover, if we add some minor downturns in the way (let's be clear, not all years are like 2019 during a bull market), we could probably apply the strategy for a longer period. Yes, of course, we are not considering the time value of money, but for illustrating purposes it suffices.

Although these numbers represent the additional years necessary for both portfolios having the same return, one thing is clear: the hedged portfolios would have outperformed the benchmark during the entire period on a risk-adjusted basis. Volatility is lower for the hedged portfolios since put options have a strong negative correlation with its underlying stock price. All else equal, a decrease (increase) in the stock price means an increase (decrease) in put prices. Likewise, a surge in volatility, often associated with plunges in the market, causes put prices to climb. For these reasons, the hedge effectively reduces the portfolio's variability.

In this sense, the results suggest that using deep out of the money options with relatively short expirations are an efficient mechanism for hedging against tail risk. They appreciate substantially in times of turmoil while they cost little during bull markets, thus serving their purpose. We can use the strategy for long time periods, and it will outperform the benchmark on a risk-adjusted basis. Between all possibilities, options 25%-30% OTM combined with 4-months maturities seem to work best, although 6-months expirations could also fulfill the mission.

Conclusions

In this article, we presented a hedging strategy that pays off in the long run. Although the exercise conducted is far from rigorous, we were able to retrieve some meaningful conclusions. The proposed strategy has a low cost and works great in times of turmoil, thus functioning as an efficient hedging technique against tail risk. We can use it for a relatively long bull market (more than 11 years) and it will still pay off when the downturn comes. Moreover, it will outperform the unhedged portfolio on a risk-adjusted basis, given its ability to reduce the portfolio's variance. Finally, even though we used a SPY portfolio, the strategy can be easily extended for any stock portfolio, since these extreme events affect the broad market in a similar manner (at least in first instances).

The use of options as a hedge can sometimes be confusing, but we have presented here a simple method. Nonetheless, the strategy can be improved in several ways. For instance, we could consider varying the percentage of the portfolio that would be hedged, or perhaps distributing the expirations throughout the entire year, or even combining several maturities. Finding the optimum parameters would certainly enhance the strategy's performance.

Lastly, we must emphasize the limitations of our strategy. It requires an active management in order to work efficiently. However, the proposed rule of selling the options when the VIX is over 50 seems as an appropriate alternative: it gives enough opportunities to close the position with sufficient profits. Altogether, the strategy described in this article represents an effective hedge against tail risk. Moreover, it pays off in the long run. We strongly recommend protecting your portfolios with 25%-30% OTM puts and 4-months expirations.

This article was written by

Enrique Zambrano profile picture
61 Followers
Economist and Mathematician. Professor at Universidad Metropolitana in Caracas, Venezuela. Interested in options, futures, risk management, econometrics and simulations.
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Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

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