Tail Risk Hedging - Graham Capital

1 Graham Capital ManagementResearch Note, October 2017 Tail Risk HedgingKshitij Prakash1 AbstractMany investors have significant long equity market exposure and seek effective portfolio protection. Several strategiesfor tail risk Hedging have been proposed to provide downside protection in equity market sell-offs, notably a) increasingfixed income allocation, b) buying protective puts through the sale of out-of-the-money calls (collars), c) Hedging usingVIX futures, and d) allocating to Managed Futures or other alternative risk premia strategies. In this paper we examinethe popular strategies for tail risk Hedging and highlight the cost-benefit of Risk; Hedging ; Diversification; Trend Following1 Quantitative Research Manager1. IntroductionIn statistics tails are defined as the extremes of a distribution( , those outcomes that have a small probability of occurring).

2 In finance the termtail eventstypically refers to infrequent, out-sized downside market moves such as those observed during the2008 financial crisis. There is no broadly accepted definitionof what constitutes a tail event, but consensus holds that we seemoves larger than those expected by financial models, approxi-mately every 3 5 years on average. In recent years equity marketshave soared and investors are increasingly looking to have a hedgeagainst their equity exposure. Because tail events are difficultto predict, and by their extreme nature can have a profound im-pact on a portfolio, protection from tail events can be a valuablecomponent of a diverse Risk HedgingEven supposedly diverse portfolios are often susceptible to sig-nificant risk associated with a sustained fall in equities , investors have used fixed income to offer someprotection during equity bear markets.

3 It has been observed thatequities and bonds show a high negative correlation during timesof exceedingly high volatility [Connolly et al. (2005)]. There-fore, increasing fixed income allocation in a portfolio has beenadvocated to help mitigate the downside exposure of equities intimes of high market risk. There are potential pitfalls inherent inthis strategy. For example, a classic 60-40 equities-bond portfolioeffectively equates to over a 90-10 allocation in terms of realizedrisk with equities dominating bonds. As a result, the protectionoffered by the fixed income allocation may be less than antici-pated. One way to address this is through the construction ofa risk-parity portfolio where equities and bonds have equal market participants use options to try to mitigate tailrisk. For example, a traditional Capital preservation strategy likeacollarworks by selling out of the money calls, and using thepremium to buy out of the money puts.

4 This effectively sets afloor and ceiling to potential profit and loss from movements ofthe underlying Futures provide another volatility-based indirect hedg-ing strategy. The VIX index tracks the volatility of S&P 500options and is commonly referred to as the fear gauge of equitymarkets. It is an aggregation of the implied volatilities of theputs and calls that expire approximately within a month s market sell-offs are typically accompanied by a spike inmarket volatility. For example, during the market uncertainty of2008, the VIX surged to historical highs over the course of twomonths as markets fell. By going long VIX futures contracts in anappropriate hedge ratio, one can hedge exposure to the underlyingequity Trading Advisors (CTAs) attempt to capturetrends in futures markets.

5 CTAs tend to have low correlationto equity assets, and as such they can be used to mitigate riskin an equity-dominant portfolio. The directional nature of suchfunds can potentially lead to high returns in times of market MethodologyIn this paper we will evaluate various tail risk Hedging strategiesto measure their effectiveness. The base comparison case is a60-40 portfolio with a 60% allocation to the S&P Total ReturnIndex (SPTR) and 40% allocation to the US Aggregate BondIndex (LBUSTRUU). The four strategies we consider : a portfolio having equal risk allocation toSPTR and LBUSTRUU instead of 60-40 allocation of : a portfolio replacing long exposure to S&P 500in the base portfolio with a 60% allocation to CLL Index(95-110 Collar) instead of Futures: a portfolio where we hedge 10% of bench-mark equity exposure at any given time by going long : a portfolio with a 20% allocation to the 20% volatility-targeted BarclayHedge CTA hedge ratio is calculated based on rolling beta of VIX Futures to S&P Risk Hedging 2/4S&P 500 Baseline 60-40 Risk-Parity Collar VIX CTAAvg Annual of $1$ $ $ $ $ 1.

6 Summary Table 1988-20173. DiscussionTable 1 compares the various Hedging strategies starting in benchmark 60-40 portfolio has a worst drawdown of to for the S&P 500, and an average annual returnof (historical drawdowns are plotted in Figure 1).In comparison, the risk-parity portfolio of stocks and bondshas the lowest drawdown but also reduces the average returns dueto much lower volatility of the fixed income allocation. It alsohas the highest Information Ratio (IR) among all the evaluatedhedging strategies. However, the high IR of risk-parity can in partbe explained by an unprecedented drop in bond yields over the 30year backtest period that is unlikely to be repeated in a rising rateenvironment. Increasing fixed income allocation to protect againstequity sell-offs only works under the assumption that equitiesand bonds maintain their negative correlation.

7 However, this hasnot been true historically for long periods of times [see GCMresearch note on equity-bond correlation]. Risk parity also makesuse of leverage to deliver higher volatility, which can exacerbatedrawdowns in periods of simultaneous bond and equity marketsell-offs. 50% 40% 30% 20% 10%0%199019952000200520102015 Drawdown %S&P 500 Baseline 60 40 Risk parityCollarVIXCTAF igure drawdowns of tail risk Hedging collar Hedging strategy has a similar IR as the 60-40 bench-mark portfolio and a significantly lower worst drawdown ; however, it results in significantly lower cumulative collars eliminates much of the potential upside fromequityrallies and this can be further compounded by the hightransaction costs associated with trading with VIX futures2looks superficially similar to thecollar Hedging strategy.

8 Compared to the benchmark portfolioit gives a lower IR albeit with a better drawdown profile. Someprotection is afforded by the negative correlation between VIX2 VIX Futures data available from 2004futuresand equities, but VIX futures are often in a state of con-tango and the negative roll yield associated with the hedge posi-tion can act as a drag on the CTA Hedging strategy exhibits higher cumulative wealthand IR than does the benchmark, along with an improved draw-down profile. Historically CTAs have performed well duringcrisis periods for equities as they can take short positions indownward trending markets. Unlike some of the other hedgingstrategies described here, CTAs can also see significant positivereturns when equity markets are doing well, and as a result areless likely to detract from performance during strong periods 2 examines the performance of tail risk Hedging strate-gies in the ten worst S&P 500 months.

9 We find that all of themoutperformed the 60-40 benchmark in every single instance.$5$10$1519901995200020052010201 5 Growth of $1S&P 500 Baseline 60 40 Risk parityCollarVIXCTAF igure growth of $1 invested in portfolios withdifferent tail risk Hedging cumulative growth of $1 in Figure 2 has the CTAhedged portfolio outperforming all other Hedging strategies bya wide margin. CTA allocation is able to deliver high volatilityin combination with uncorrelated alpha to give nearly the sametotal wealth as does the S&P 500. Direct Hedging using optionsdecisively gives the lowest returns out of all the strategies. Therisk-parity portfolio can t compensate enough for low volatilitywith its high IR and gives lower terminal wealth than does Risk Hedging 3/4S&P 500 Baseline 60-40 Risk-Parity Collar VIX CTAW orst ten S&P 500 2.

10 Tail risk Hedging strategies outperform Benchmark portfolio in worst S&P 500 months (1988-2017)4. ConclusionIn this paper we evaluated four tail risk Hedging strategies increasingfixed income allocation, direct Hedging using options,VIX Futures, and CTAs. Increasing fixed income allocationto form a risk-parity portfolio has historically achieved a veryhigh IR and good tail protection, but significantly lower terminalwealth. Volatility based Hedging strategies have lower IR thanbenchmark portfolio and realize lower volatility leading to lowercumulative growth. Finally we find that CTAs provide a highdegree of tail protection, with higher IR and similar volatility to a60-40 , Stivers, and Sun. Stock market uncertainty and thestock-bond return Journal of Financial and Quan-titative Analysis, 40(1):161 194, Risk Hedging 4/4 Legal DisclaimerTHIS DOCUMENT IS NOT A PRIVATE OFFERING MEMORANDUM AND DOES NOT CONSTITUTE AN OFFER TO SELL, NOR IS IT A SOLICITATION OFAN OFFER TO BUY, ANY SECURITY.