Many investors have significant long equity market exposure and seek effective portfolio protection. Several strategies for tail risk hedging have been proposed to provide downside protection in equity market sell-offs, notably a) increasing fixed income allocation, b) buying protective puts through the sale of out-of-the-money calls (collars), c) hedging using VIX futures, and d) allocating to Managed Futures or other alternative risk premia strategies. In this paper, we examine the popular strategies for tail risk hedging and highlight the cost-benefits of each.
许多投资者都有很长的股票市场风险并寻求有效的投资组合保护 已经提出了几种尾部风险对冲策略，以提供股票市场抛售的下行保护，特别是a）增加固定收益分配，b）通过出售价外看涨期权（领子）购买保护性看跌期权，c ）使用VIX期货进行套期保值，以及d）分配管理期货或其他风险溢价策略。 在本文中，我们研究了尾部风险对冲的流行策略，并强调了每种策略的成本效益。
Keywords: Tail Risk; Hedging; Diversification; Trend Following
关键词：尾部风险;套期保值; 多样化; 趋势跟随
In statistics “tails” are defined as the extremes of distribution(i.e., those outcomes that have a small probability of occurring).In finance, the term tail events typically refer to infrequent, outsized downside market moves such as those observed during the 2008 financial crisis. There is no broadly accepted definition of what constitutes a tail event, but consensus holds that we see moves larger than those expected by financial models, approximately every 3–5 years on average. In recent years equity markets have soared and investors are increasingly looking to have a hedge against their equity exposure. Because tail events are difficult to predict, and by their extreme nature can have a profound impact on a portfolio, protection from tail events can be a valuable component of a diverse portfolio.
在统计中，“尾部”被定义为分布的极端（即那些发生概率很小的结果）。在金融领域，尾部事件一词通常指的是不常见的，超大的下行市场变动，例如2008年金融时期观察到的变化。 危机。 关于什么构成尾部事件没有广泛接受的定义，但一致认为我们认为变动大于金融模型预期的变动，大约平均每3 - 5年。 近年来，股票市场飙升，投资者越来越希望对冲其股票风险。 由于尾部事件很难预测，并且由于其极端性质会对投资组合产生深远影响，因此对尾部事件的保护可能是多样化投资组合的重要组成部分。
Tail Risk Hedging
Even supposedly diverse portfolios are often susceptible to the significant risk associated with a sustained fall in equities prices. Traditionally, investors have used the fixed income to offer some protection during equity bear markets. It has been observed that equities and bonds show a high negative correlation during times of exceedingly high volatility [Connolly et al. (2005)]. Therefore, increasing fixed income allocation in a portfolio has been advocated to help mitigate the downside exposure of equities in times of high market risk. There are potential pitfalls inherent in this strategy. For example, a classic 60-40 equities-bond portfolio effectively equates to over a 90-10 allocation in terms of realized risk with equities dominating bonds. As a result, the protection offered by the fixed income allocation may be less than anticipated. One way to address this is through the construction of a risk-parity portfolio where equities and bonds have equal risk allocations. Some market participants use options to try to mitigate tail risk.
即使是多样化的投资组合，也往往容易受到与股票价格持续下跌相关的重大风险的影响。传统上，投资者利用固定收益在股票熊市中提供一些保护。据观察，在波动性极高的时期，股票和债券显示出高度的负相关性[Connolly et al。 （2005）]。因此，提倡增加投资组合中的固定收益分配，以帮助减轻股市在高市场风险时的下行风险。这一战略存在潜在的陷阱。例如，一个典型的60-40股票债券投资组合实际上相当于在股票主导债券的已实现风险方面超过90-10。因此，固定收益分配提供的保护可能低于预期。解决这个问题的一种方法是建立风险平价投资组合，其中股票和债券具有相同的风险分配。一些市场参与者使用选项来尝试降低尾部风险。
For example, a traditional capital preservation strategy like a collar works by selling out of the money calls and using the premium to buy out of the money puts. This effectively sets a floor and ceiling to potential profit and loss from movements of the underlying asset.VIX Futures provide another volatility-based indirect hedging strategy. The VIX index tracks the volatility of S&P 500options and is commonly referred to as the “fear gauge” of equity markets. It is an aggregation of the implied volatilities of the puts and calls that expire approximately within a month’s time. Equity market sell-offs are typically accompanied by a spike in market volatility. For example, during the market uncertainty of2008, the VIX surged to historic highs over the course of two months as markets fell. By going long VIX futures contracts in an appropriate hedge ratio, one can hedge exposure to the underlying equity market. Commodity Trading Advisors (CTAs) attempt to capture trends in futures markets. CTAs tend to have a low correlation to equity assets, and as such, they can be used to mitigate risk in an equity-dominant portfolio. The directional nature of such funds can potentially lead to high returns in times of market stress.
In this paper, we will evaluate various tail risk hedging strategies to measure their effectiveness. The base comparison case is a 60-40 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 are
1. Risk-Parity: a portfolio having equal risk allocation to SPTR and LBUSTRUU instead of 60-40 allocation of capital.
2. Collars: a portfolio replacing long exposure to S&P 500in the base portfolio with a 60% allocation to CLL Index(95-110 Collar) instead of SPTR.
3. VIX Futures: a portfolio where we hedge 10% of benchmark equity exposure at any given time by going long VIX futures.1
4. CTA: a portfolio with a 20% allocation to the 20% volatility targeted Barclay Hedge CTA Index.
4. CTA：对20％波动率分配20％的投资组合，目标是Barclay Hedge CTA指数。
1A hedge ratio is calculated based on rolling beta of VIX Futures to S&P 500.
Table 1 compares the various hedging strategies starting in 1988. The benchmark 60-40 portfolio has a worst drawdown of 31.4%compared to 50.9% for the S&P 500, and an average annual return of 9.2% (historical drawdowns are plotted in Figure 1).In comparison, the risk-parity portfolio of stocks and bonds has the lowest drawdown but also reduces the average returns due to the much lower volatility of the fixed income allocation. It also has the highest Information Ratio (IR) among all the evaluate hedging strategies. However, the high IR of risk-parity can in part be explained by an unprecedented drop in bond yields over the 30year backtest period that is unlikely to be repeated in a rising rate environment. Increasing fixed income allocation to protect against equity sell-offs only works under the assumption that equities and bonds maintain their negative correlation. However, this has not been true historically for long periods of times [see GCMresearch note on equity-bond correlation]. Risk parity also makes use of leverage to deliver higher volatility, which can exacerbate drawdowns in periods of simultaneous bond and equity market sell-offs.
Figure 1. Historical drawdowns of tail risk hedging strategies. A collar hedging strategy has a similar IR as the 60-40 benchmark portfolio and a significantly lower worst drawdown of 20.8%; however, it results in significantly lower cumulative wealth. Buying collars eliminate much of the potential upside from equity rallies and this can be further compounded by the high transaction costs associated with trading options. Hedging with VIX futures2looks superficially similar to the collar hedging strategy. Compared to the benchmark portfolio it gives a lower IR albeit with a better drawdown profile. Some protection is afforded by the negative correlation between VIX futures and equities, but VIX futures are often in a state of contango and the negative roll yield associated with the hedge position can act as a drag on the portfolio. The CTA hedging strategy exhibits higher cumulative wealth and IR than does the benchmark, along with an improved drawdown profile. Historically CTAs have performed well during crisis periods for equities as they can take short positions in downward trending markets. Unlike some of the other hedging strategies described here, CTAs can also see significant positive returns when equity markets are doing well, and as a result, are less likely to detract from performance during strong periods for equities.
Table 2 examines the performance of tail risk hedging strategies in the ten worst S&P 500 months. We find that all of them outperformed the 60-40 benchmark in every single instance.
Charting cumulative growth of $1 in Figure 2 has the CTAhedged portfolio outperforming all other hedging strategies by a wide margin. CTA allocation is able to deliver high volatility in combination with uncorrelated alpha to give nearly the same total wealth as does the S&P 500. Direct hedging using options decisively gives the lowest returns out of all the strategies. The risk-parity portfolio can’t compensate enough for low volatility with its high IR and gives lower terminal wealth than does the benchmark
In this paper we evaluated four tail risk hedging strategies –increasing fixed income allocation, direct hedging using options, VIX Futures, and CTAs. Increasing fixed income allocation to form a risk-parity portfolio has historically achieved a very high IR and good tail protection, but significantly lower terminal wealth. Volatility based hedging strategies have lower IR than the benchmark portfolio and realize lower volatility leading to lower cumulative growth. Finally, we find that CTAs provide a high-degree of tail protection, with higher IR and similar volatility to a60-40 benchmark.
在本文中，我们评估了四种尾部风险对冲策略 - 增加固定收益分配，使用期权直接对冲，VIX期货和CTA。增加固定收益分配以形成风险平价投资组合历史上已经实现了非常高的IR和良好的尾部保护，但终端财富显着降低。基于波动率的对冲策略比基准投资组合具有更低的IR，并且实现更低的波动率，从而导致更低的累积增长。 最后，我们发现CTA提供高度的尾部保护，具有更高的IR和类似的波动性，达到60-40基准。
Connolly, Stivers, and Sun. Stock market uncertainty and the stock-bond return relation. The Journal of Financial and Quantitative Analysis, 40(1):161–194, 2005.