Journal Of Indexes: Tails, You Lose

May 14, 2014

The anatomy and usage of a tail-hedging index.

HedgeFundIndexationAndReplication

[This article originally appeared in the May/June 2014 issue of the Journal of Indexes.]

 

The three-year period defined by the start of the credit crisis in 2008, the intervening “flash crash,” and the subsidence of the sovereign debt crisis in 2011 marked one of the most volatile regimes in market history. Of particular note were the successive waves of “tail events,” market dislocations deemed a priori to be statistically improbable. Although differing in both intensity and duration, these events, collectively known as “fat-tail events” or “black swans,” precipitated abrupt and immense drawdowns as stock prices unraveled from company and macroeconomic fundamentals.

Why Hedge Tails?

As an example of the potential impact of tail events upon a market portfolio, consider the magnitude of the drawdowns experienced during the heart of the credit crisis in 2008. As seen in Figure 1, under the assumptions of normality embedded into modern portfolio theory, it is anticipated that over the course of a trading career, one would observe at most one one-day drawdown in excess of 4 standard deviations (i.e., 5+ percent). Yet as shown in Figure 2, during the four-month period from August to December 2008, the market experienced 10 such declines—negating six years of equity growth in the span of four months. On the surface, therefore, the most obvious and oft-cited reason to hedge against tail events is to mitigate the severity of market drawdowns.

Risk Parity

Risk Parity

A more subtle and arguably more important benefit of a tail hedge, however, is that it addresses the most disruptive feature of a tail shock—specifically, the impact-associated market distortions that often accompany tail events. These market distortions undermine 1) the underlying principles of financial valuation—causing a departure of asset prices from their “fair” values; and 2) the stabilizing assumptions of portfolio construction, including:

  • Breakdown in portfolio diversification (via correlation)
  • Negative feedback loops (via volatility clustering)
  • Beta instability (via cross-asset contagion)
  • Discontinuous trading

Volatility Buffer
Often during these events in which in-house volatility-based risk limits are suddenly breached, portfolio managers (“PMs”) and traders are forced to sell out of tactically unattractive but strategically desirable positions. Tail hedges can provide a volatility buffer to mitigate the need to exit these positions or to lessen the impact of increased volatility.

Credit Reserve
It is somewhat ironic that downside tail events also provide the best opportunity to outperform. In fact, some of the greatest equity-market outperformances (i.e., upside tail shocks) followed immediately on the heels of the market’s sharpest sell-offs. Take, for example, the crash of 1987, in which the market collapsed 23 percent over the course of one day but recouped the bulk of the losses over the course of the next two days. A good way to recover returns lost due to a tail shock is therefore to invest during times of market duress. However, in many cases, trader positions are often drastically pared down as the aforementioned risk limits are breached. An important function of tail hedges is therefore to provide a source of funding that accrues as the market is in decline and that can then be used to lever into a long position to allow the portfolio to more quickly recover.

 

 

Algorithmic (Signals-Based) Tail Hedging

The primary challenge during the current low-volatility environment, however, is that the cost of static, “always on,” tail insurance is often expensive to hold. Accordingly, if a tail event fails to materialize, the buyer of a systematic tail strategy risks significantly underperforming his unhedged peers. To moderate the cost of carry, hedgers often shift toward dynamic tail-risk strategies during times of market stability.

Over the last few years, a vast number of dynamic strategies in the form of algorithmic indexes1 have been designed to profit from the realization of tail events and offered as a hedging product to end investors. Algorithmic indexes (aka “algos”) are liquid, transparent and easily investable through delta-one wrappers such as swaps, notes or more advanced products involving the use of derivatives and/or leverage in order to produce a highly asymmetrical payoff.

Algorithmic Tail-Risk Construction

As of the time of writing, the marketplace currently has more than 200 active tail-risk algorithmic products spanning five asset classes. However, due to the leverage to downside shocks and the greater liquidity offered by equity volatility products in times of market distress, the majority of algo products invest in equity volatility. Figure 3 provides a cross section of Credit Suisse’s more popular tail-hedging algos (by notional invested), their asset class exposure and a short description of the trading rules.

Algorithmic tail-risk construction generally follows a five-step process:

  1. Tail definition
  2. Benchmark selection
  3. Trigger design
  4. Simulation
  5. Test of efficacy
Figure 1
For a larger view, please click on the image above.

 

In the following pages, we will use the development of our Equity Dynamic Tail Hedge Index (Ticker: DYTL) as a case study to illustrate the process of constructing a tail-risk algorithm.

Step 1: Tail Definition
The obvious first step to developing a tail-risk algo is to first define what is meant by “tail.” Given the breadth of investment styles, the definition of the term “tail-risk” itself (and therefore the solution) may vary greatly among investment professionals. Take for example, the flash crash, in which the market plummeted 10 percent during the course of one hour and then recovered 8 percent during the next hour to finish down 2 percent for the day. For an investor such as a high-frequency trader or an active delta-hedger who was actively trading during that period and therefore realized profit and loss (“P&L”) during those volatile two hours of the day, such an event may in fact qualify as a tail event. However, if one were a “low-frequency,” long-term investor such as a pension fund that did not trade during that day, then a tail event may refer to a protracted deterioration in one’s portfolio caused by a breakdown of the core investment strategy. For the purposes of this case study, we will define a tail risk as a sizable abrupt market decline that triggers a persistent volatility regime shift from a low- to high-volatility environment.

 

 

Step 2: Benchmark Selection
The second step is to create a “naive” or systematic hedging benchmark index (the benchmark) using a plain-vanilla options strategy to gauge the relative performance of the tail-hedging strategy. In our example, our benchmark is designed as follows:

  • Strategy: Every month, on each listed expiry date, we execute a rolling strategy whereupon we purchase new S&P and EuroStoxx 50 90 percent strike put options with a two-month expiry. At any time, we would therefore have four options in the portfolio with maturities equal to front-month and back-month expiries. All options are let to run until they expire.
  • The notional of the purchased options is equal to one-fourth of the mark-to-market value of the benchmark on that same day in order to match exposures.
  • Performance calculation: The benchmark is calculated in USD. Payoffs or premiums are paid in and out of a synthetic USD cash account earning the federal funds rate.

The simulated history of the benchmark is shown in Figure 4. We also show the cumulative P&L of the S&P 500 Index and the cumulative P&L of the S&P with a one-to-one overlay of the benchmark as a hedge.

Figure 4 demonstrates the conundrum faced by many systematic plain-vanilla hedging strategies:

When a tail event does materialize, such a strategy can successfully cushion the initial blow of a tail event. In our example, for $100 invested in the portfolio in April 2008, the hedging strategy would have saved the investor up to $20 by November 2008. However, if a tail event does not materialize, it also shows how the long-term running cost (the carry) of the strategy may gradually eat up the accrued hedging benefits.

Risk Parity

This then illustrates the disadvantage of a static tail-hedge strategy: By systematically investing in the same notional, it tends to be under-invested in the period leading up to the shock, causing the investor to be under-hedged, and it tends to be over-invested immediately after the tail event when the price of options is high and the risks have dissipated, resulting in higher performance drag.

Step 3: Choice Of A Tail-Hedging Strategy
Rather than the benchmark and its short-delta/long-volatility bias, we prefer a cleaner tail-hedging strategy that aims to isolate the volatility component typical of tail events.

The underlying fundamental strategy of the Equity Tail Hedge S&P Index can be broken down into five steps:

  1. The algorithm completes a monthly sale of vanilla ratio-put spreads on the underlying equity index consisting of:
    • short a number of three-month 95 percent puts
    • long a number of three-month 80 percent puts
  2. The quantity of puts is chosen such that each leg generates a profit/loss of 1% of the strategy notional (i.e. 1 percent vega exposure) per point change in the underlying index volatility. The position thus naturally adapts to the prevailing level of equity volatility. Specifically, during times of low volatility, when options’ vega is low, the quantity of options needed to generate 1 volatility point increases, resulting in higher exposure to a tail event before it has happened. Likewise, when a tail event has occurred and equity volatility and options’ vega are high, the quantity of options needed to generate 1 volatility point is lower, and the strategy naturally deleverages itself at each reset. The ratio of 95 percent puts to 80 percent puts has a historical average of 1-to-3.15.
  3. The position is delta-hedged. (Once the directional component of the position is removed via delta-hedging, what remains is pure exposure to volatility at each strike, thus resulting in a long skew exposure.)
  4. The puts are unwound a day before expiration to avoid expiration-day effects and are rolled on a monthly basis.
  5. Any cash balance accrues at the relevant rate.

 

 

Step 4: Trigger Mechanism
To enhance the performance of the basic “benchmark” tail hedge, we thus introduce the use of a timing indicator or trigger mechanism. The objective in employing a trigger mechanism is to decrease the weighting (and therefore the cost) of the downside hedge in times of quiet markets and to ratchet up exposure in anticipation of a tail event. In our example, we discuss the use of two triggers taken from two asset classes: 1) equity volatility skew; and 2) CDS spreads from the fixed-income markets in the construction of the Credit Suisse Equity Dynamic Tail Hedge Index.

Signal 1 – Skew: Implied equity-market skew is defined as the difference between implied volatility for lower strike options (typically put options purchased for protection) and implied volatility for higher strike options (typically call options purchased for leveraged upside exposure). Historically, during severe market downturns, implied equity-market skew has increased significantly (Figure 5), confirming our choice of equity skew as the primary source of tail protection in Step 3. This may be explained by an increase in demand for downside protection, pushing up implied volatility levels for lower strike levels.

Risk Parity

The indicator analyzes the historical distribution of the three-month 80-100 skew on the underlying equity index over the last three months. If the skew level is significantly above the mean, the signal for a distressed market is activated. This indicator has been historically reactive to market events signaling the beginning of a tail episode.

Signal 2 – CDS Spreads: The indicator is linked to the five-year CDS spread of companies for the relevant underlying equity market. If the CDS index is significantly above the mean, the signal for a distressed market is activated. If the CDS index is significantly below the mean, the signal for a distressed market is deactivated. Otherwise, the signal remains unchanged. The indicator captures medium-term risk and is reactive to changes in the macro environment.

The signals just discussed trigger allocations by the Credit Suisse Equity Dynamic Tail Hedge Index to the Credit Suisse Equity Tail Hedge Index, which in turn is long equity-market skew.

To drive the allocation between cash and the index, the two signals are run daily:

  • If one of the signals is switched ON, 50 percent of the exposure is allocated to the CS Equity Tail Hedge S&P Index, the index described at Step 3.
  • If both signals are ON, 100 percent is allocated to the hedge index. If neither of the signals is ON, 100 percent is invested in cash (U.S. federal funds rate or EONIA).

Historically, at least one of the signals has been ON for 31 percent of the time period. Typically, a distressed macro environment would first activate the CDS signal, indicating that the likelihood of a tail event has increased. The skew signal would activate when the market crisis gains momentum and equity skew breaks out of range.

This exact methodology is also applied using the Euro Stoxx 50 as an underlying, where the child index (Credit Suisse Equity Dynamic Tail Index) allocates to the parent index (Credit Suisse Equity Tail Hedge Index), based on Euro Stoxx 50 skew and European CDS prices.

 

 

Step 5: Simulation
In general, our simulation for the CS Equity Dynamic Tail Hedge Index embodied the two traits we felt were desirable in a tail-hedging algo, delivering outsized returns during periods of market crisis, and efficiently reducing the effect of negative carry over stable market periods via the dynamic signals (Figure 6).

Risk Parity

An important consideration is that tail-risk strategies that incorporate some element of market timing, regardless of whether it is actively determined by a PM or signal-based, face the very real risk that a hedge may not be in place when it is needed. One must therefore evaluate the benefit of reducing carry costs in times of stable markets versus the risk of potentially missing the event because the signals have been “switched off.”

The final step to the process of algo construction is therefore to conduct an additional test of efficacy above and beyond the basic simulation in order to determine 1) whether the inclusion of the proposed signals provide adequate cost reduction to compensate for the risk of the hedge being “deactivated” during the days leading up to a tail event; and 2) how the chosen algo stacks up against the nondynamic version.

Step 6: Additional Tests of Efficacy
The primary criteria we use to evaluate the efficacy of tail-risk algos is to compare the tail-to-carry ratio of each strategy with one another. The tail-to-carry ratio is computed by dividing the average performance during tail events by the negative annualized carry. The metric essentially conveys how many years of negative carry can be paid for by one single tail event. The higher the ratio, the more efficient the hedge.

In our first example, we test the efficacy of our signal overlay, by comparing our signal-based Dynamic Tail S&P Strategy index (DTSP) to its unconstrained parent strategy, the Tail Hedge S&P Index (TLSP), which is 100 percent invested at all times.

Figure 7 compares the performance of DTSP versus TLSP from 2008 to 2014. At first glance, one might conclude the unconstrained “always on” strategy is superior given that DTSP provided comparable returns to TLSP during the Lehman collapse and the emergence of the Greek sovereign crisis in 2008 and 2010, but as shown in Figure 8, because the CDS signal activated late into the tail strategy in summer 2011, DTSP underperformed. Note, however, that during periods of market stability, DTSP reduced the cost of carry on average by a factor of 4.5, producing a higher and therefore efficient tail-to-carry ratio.

Risk Parity

Risk Parity

 

 

Concluding Remarks

Perhaps an ironic aspect of tail events is that it is not the expected or foreseeable events (aka the known unknowns) that cause the greatest market upheavals, but rather the events from left field (the unknown unknowns). More often than not, true tail events often 1) have little or no historical precedent; and 2) are difficult to anticipate a priori. Backtesting, by contrast, is by definition a backward-looking process that optimizes “to fight the war.” As a result, hedging strategies that are designed for a specific event or asset class that have been responsible for tails in the past may be optically attractive from a backtesting perspective but may not necessarily outperform if a future tail event is greatly dissimilar to prior shocks.

Nonetheless, dynamic tail-hedge strategies in the form of algorithmic indexes can provide a liquid, transparent and easily investable solution to mitigate the impact of a “fat tail” or black swan market event. In conclusion, the volatility buffer provided by a tail hedge not only serves to reduce the downswing in overall portfolio performance, but also could allow a credit reserve to put money to work after market shock. A systematic tail hedge that also avoids a heavy cost-of-carry can keep PMs off the sidelines during the very time they should be the most active in navigating periods of market duress.

Endnote
1 Algorithmic indexes are rules-based, systematic investment strategies that are created to be transparent, liquid and investable. These indexes can, in turn, be packaged into structured notes, OTC swaps and options, and even funds. Algorithmic indexes differ from “trading algorithms” which typically focus on the execution of stocks and baskets of stocks.

 

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