【深度期權】如何做空VIX？理想VS現實

THOU SHALL NOT SHORT THE VIX

關於VIX，大多數文章所展現的知識儲備並不夠，許多文章過多誇張做空VIX恐慌指數的潛在收益，這些文章無法展現VIX交易策略的深層風險。

Similarly, most investors are familiar with the VIX as it is frequently quoted in financial media, but few make the effort to understand how it is calculated. For the majority of speculators, it simply represents the fear index, which is not a particularly accurate nor useful interpretation.

類似地，大多數投資者都熟悉VIX恐慌指數，因為它在金融媒體中經常被引用，但很少有人努力了解它的計算方式。對於大多數投機者而言，它僅表示恐懼指數，這不是一種特別準確或有效的定義和解釋。

Given that the VIX has lately been trading at levels similar to those during the global financial crisis in 2008 to 2009, investors likely perceive the market sentiment to be at peak fear level. Some investors have noted that the VIX has mean-reverted quickly over time and are contemplating to short the index.

鑑於最近VIX的交易價格與2008年至2009年全球金融危機期間的水平相似，投資者可能會認為市場情緒處於恐慌情緒的最高水平。一些投資者指出，隨著時間的推移，VIX指數均值快速恢復，並正在考慮做空該指數。

這篇文章的核心在於把做空VIX（非常經典常見的套利策略）的潛在風險做個提示，讓投資者更加理性並且更加深度去理解VIX的原理以及機制。

IMPLIED VERSUS REALIZED VOLATILITY

隱含波動率和實際波動率的區別

The VIX measures the implied volatility of 30-day options on the S&P 500, although the actual calculation is quite complex. Implied volatility tends to be higher than realized volatility, which is called the variance risk and can be explained by investors paying a premium for options to hedge their portfolios. However, regardless of these well-known differences, the trends in both are almost identical.

儘管VIX的實際計算非常複雜，但VIX可以衡量標準普爾500指數30天期權的隱含波動率。隱含波動率往往高於實際波動率，這被稱為方差風險，可以用投資者為期權套期保值投資期權而支付溢價來解釋。但是，不管這些眾所周知的差異如何，兩者的趨勢幾乎相同。

In March 2020, the VIX reached an all-time high and breached the previous high from the global financial crisis. It seems that historically these peaks were rather sharp and implied volatility quickly returned to previous levels. In recent years this can be attributed to central banks responding swiftly to any market turmoil and actively supporting these markets via quantitative easing programs.

2020年3月，VIX達到歷史新高，並突破了全球金融危機造成的歷史新高。從歷史上看，這些高峰相當陡峭，隱含的波動性很快又回到了先前的水平。近年來，這可以歸因於各國央行對任何市場動盪迅速做出反應，並通過量化寬鬆計劃積極支持這些市場。

Source: CBOE, FactorResearch

THEORETICAL VIX TRADING STRATEGY

Most central banks are mandated to manage inflation, although the generation of investors that have started trading post-2008 might believe that avoiding stock markets from crashing is also core to policies. Modern central bankers have been challenged for caring too much on how stock markets are performing; however, they are under immense political pressure, especially the chairman of the US Federal Reserve given a rather vocal US president.

理論上的交易策略

大多數中央銀行被授權管理經濟中的通貨膨脹率，儘管在2008年後開始交易的一代投資者可能認為，避免股市崩盤也是政策的核心。現代中央銀行家因對股票市場表現過分關注而受到挑戰。但是，中央銀行家們承受著巨大的政治壓力，特別是美聯儲主席。

Naturally, investors can exploit this relationship by betting on volatility to mean-revert when trading at elevated levels.

自然地，投資者可以通過押注波動性來利用這種關係，以便在高水平交易時進行均值回歸。

A systematic, theoretical model would be to short the VIX when volatility is trading abnormally high compared to its recent history and exiting when mean-reversion set in, which can be measured with z-scores. The challenge in defining such a trading strategy is the number of assumptions required. We need to define entry and exit z-scores, the lookback periods, trading costs, implementation, among others.

一個系統的理論模型是在波動率與其最近的歷史記錄相比異常高時賣空VIX，並在設置均值回歸時退出，這可以用z-score 來衡量。定義這種交易策略的挑戰是所需的假設數量。我們需要定義進入和退出z-score，回溯期，交易成本，實施等。

We need to be cautious of overfitting and create two simple scenarios where we only vary the lookback period. The entry z-score is set at 4, which results in only a few trades each year, exit z-score at 0, and we trade on signals delayed by one day. The aim is to take advantage of the short-term mean-reversion characteristics of the VIX.

我們需要對過度擬合保持謹慎，並創建兩個僅更改回溯期的簡單方案。入場的z-score設置為4，這導致每年僅進行少量交易，出場z-score 設置為0，我們對延遲一天的信號進行交易。目的是利用VIX的短期均值回复特性。

We observe that both scenarios had roughly similar performance profiles in the period between 1993 and 2020, but also some major divergences. The most significant one was in February 2018, when the VIX increased by more than 100% on a single day when stock markets declined due to the concern of the US Federal Reserve raising interest rates. The scenario with the shorter lookback wiped out all previous gains accumulated since 1993, while the scenario with the longer lookback gained as the short position was entered a few days later.

我們觀察到，在1993年至2020年期間，這兩種方案的績效概況大致相似，但也存在一些重大差異。最重要的一次是在2018年2月，當美國聯邦儲備委員會（Federal Reserve，簡稱：美聯儲）提高利率引起股市下跌時，VIX在一天之內就上漲了100％以上。回溯時間短的情況消除了自1993年以來的所有先前收益，而回撤時間較長的情況是幾天后進入空頭頭寸而獲得的。

The sensitivity of these two relatively simple scenarios to the lookback period highlights the challenge of dealing with the VIX as a time series. It also highlights the risk of shorting a financial instrument can double its value on a single day, which is highly unlikely for almost all assets, except for stocks that are being acquired. There are worse events for humanity than a pandemic, e.g. a small asteroid on a collision course with earth or a minor alien invasion.

這兩個相對簡單的場景對回溯期的敏感性突出了將VIX作為時間序列處理的挑戰。它還強調了做空金融工具一天之內其價值可能翻倍的風險，這幾乎對所有資產都不太可能發生，除了被收購的股票。對於人類來說，比大流行還更糟糕的事件，例如 與地球碰撞或外星人輕微入侵的小行星。

Source: CBOE, FactorResearch

THEORY VS. REALITY

Even if a talented quantitative developer could identify a robust model to profitably exploit the mean-reversion characteristics of the VIX, there are some arguments why this might not be a sensible strategy for the majority of investors.

VIX交易的理論與現實

即使有才華的量化開發人員可以找到可靠的模型來盈利地利用VIX的均值回歸特徵，也有一些爭論為什麼這對於大多數投資者而言可能不是明智的策略。

Behavioral Aspects

Implementing a short-volatility trading strategy will require investors to act when stock markets are typically in turmoil. There have been times when volatility was high and stock markets performed well, e.g. during the boom in technology stocks in 1999, but mostly volatility increases when stocks are declining.

交易行為方面

實施短期波動性交易策略將要求投資者在股市通常處於動盪時採取行動。有時候，波動性很高，股票市場表現良好，例如 在1999年科技股的繁榮時期，但當股票下跌時，波動率大多增加。

Given the positive relationship between volatility and negative stock market returns on average, implementing such a strategy requires investors to allocate capital when they would be experiencing a significant loss on their equity portfolio, which is emotionally challenging for most investors.

考慮到波動率與平均負股票收益率之間存在正相關關係，實施這樣的策略要求投資者在股票投資遭受重大損失時分配資金，這對大多數投資者而言是具有挑戰性的。

Furthermore, volatility clusters and often lingers at elevated levels. Historically, this would have led to significant drawdowns in such a trading strategy. Few investors have the stamina to adhere to a strategy that frequently features drawdowns larger than 50%.

此外，波動性集群並經常徘徊在較高水平。從歷史上看，這將導致這種交易策略的大幅縮水。很少有投資者有毅力堅持採用通常虧損額大於50％的策略。

Source: CBOE, FactorResearch

Long-Term Perspective on Volatility

VIX data is only available from the CBOE from 1993 onward, which provides slightly less than 30 years of data. During this period the VIX only breached 50 twice, in 2008 when Lehman Brothers declared bankruptcy and in 2020 during the Coronavirus crisis. We observe that during this observation period the VIX always quickly mean-reverted to levels below 20.

波動性的長期觀點

僅從1993年起，CBOE才提供VIX數據，該數據提供不到30年的數據。在此期間，VIX僅在2008年雷曼兄弟宣布破產和2020年冠狀病毒危機期間兩次突破50。

我們觀察到，在此觀察期內，VIX總是迅速均值回復到20以下的水平。

However, we can use realized volatility as a proxy for implied volatility and extend the observation period to cover 90 years of financial history. We observe that during the Great Depression in the 1930s volatility remained at abnormally high levels for years, which would have made a short-volatility mean-reversion strategy unattractive.

``但是，我們可以使用已實現的波動率作為隱含波動率的替代指標，並將觀察期延長至涵蓋90年的財務歷史。我們觀察到，在1930年代的大蕭條時期，波動率多年來一直保持在異常高的水平，這將使短期波動率均值回复策略失去吸引力。

A few years ago it would have been easy to argue that volatility will not remain at elevated levels for long periods of time given experienced central bankers that studied financial history with the intent of avoiding past monetary mistakes, such as those made during the Great Depression.

幾年前，如果有經驗的中央銀行研究金融歷史的目的是為了避免過去的貨幣政策上的錯誤，例如大蕭條期間犯下的錯誤，那麼很容易就可以說，波動率不會長期保持在較高水平。

However, central banks globally have already used up most classic tools of their arsenal and are forced to devise new ones. There is a risk that these are or will become ineffective and volatility to remain high for years, much like in the past.

但是，全球中央銀行已經用盡了其武器庫中最經典的工具，並被迫設計新工具。就像過去一樣，這些風險可能會或將變得無效，並且波動性會持續多年。

Source: Kenneth R. French Data Library, FactorResearch

Practical Considerations

Even if an investor could stomach allocating capital when volatility is high and live through the painful drawdowns, then he would struggle to implement the short-volatility mean-reversion strategy as the VIX is not a tradable index. There are VIX futures and options, but these come with their own intricacies like roll yield and time decay.

交易VIX的實用思考

即使投資者在波動率很高時可以忍受分配資金並度過痛苦的虧損期，但由於VIX並非可交易指數，他仍將難以實施短期波動率均值回歸策略。有VIX期貨和期權，但它們都有其自身的複雜性，例如滾動收益率和時間衰減。

Asset managers have launched various products related to the VIX over the years, but none replicate it precisely. Shorting volatility was a popular strategy post the global financial crisis given the frequent central bank interventions that created the buy-the-dip mentality. However, occasionally volatility spiked and led to the implosion of some short-volatility products like XIV in February 2018.

多年來，資產經理已經推出了與VIX相關的各種產品，但沒有一個能夠精確複製它。考慮到中央銀行的頻繁干預產生了買入買入的心態，在全球金融危機之後，做空波動是一種流行的策略。但是，波動率偶爾會飆升並導致一些短期波動性產品（如XIV）在2018年2月爆掉(發行商無法兌現義務，違約）。

The most popular product for shorting volatility available today is ProShares’ Short VIX Short-Term Futures ETF (SVXY), which provides inverse exposure to short-term VIX futures and has approximately $650 million in assets under management. Although the ETF was not liquidated in 2018, it suffered a drawdown of more than 90%. After this, SVXY reduced its leverage to 0.5, but rebalances daily like most inverse ETFs, which can erode value quickly given negative compounding. As an alternative, investors could also short the iPath Series B S&P 500 VIX Short Term Futures ETN (VXX) that provides long exposure to short-term VIX futures.

當今市場上最流行的做空波動性產品是ProShares的ShortVIX短期期貨ETF（SVXY），該產品對短期VIX期貨提供反向敞口，管理的資產約為6.5億美元。儘管ETF在2018年未清算，但其縮水率超過90％。此後，SVXY將槓桿率降低至0.5，但與大多數反向ETF一樣，每天進行重新平衡，在負複合收益的情況下，它們可以迅速侵蝕價值。作為替代方案，投資者也可以做空iPath系列B標普500 VIX短期期貨ETN（VXX），該期貨提供了對VIX短期期貨的多頭敞口。

However, comparing SVXY or a short position in VXX to theoretically shorting the VIX highlights vastly different performance. The VIX declined from 2011 to 2019, but exhibited negative skewness given explosive increases and slower declines. Due to compounding, this results in a highly negative performance when calculating a theoretical short position in the VIX. In contrast, SVXY generated high returns since 2011, but with extreme drawdowns that destroyed almost all previous gains.

但是，將SVXY或VXX中的空頭頭寸與理論上將VIX賣空的情況進行比較，可以發現性能差異很大。從2011年到2019年，VIX有所下降，但由於爆炸性增長和下降速度較慢，因此呈現出負偏度。由於復合，當計算VIX中的理論空頭頭寸時，這會導致高度負面的表現。相比之下，SVXY自2011年以來產生了高額回報，但虧損嚴重，幾乎破壞了之前的所有收益。

Investors using the VIX as a time series when creating volatility trading strategies need to be aware that the available investment products will behave significantly differently to the index.

投資者在製定波動率交易策略時使用VIX作為時間序列，需要意識到可用的這類的投資產品的行為以及獲利將與VIX指數走勢大不相同。

Especially inverse ETFs should be viewed with caution as they provide the desired short exposure on a daily basis, but given the mechanics of compounding that does not equate to a similar performance over longer time periods.

尤其要注意反向ETF，因為它們每天都會提供所需的空頭頭寸，但是鑑於復合機制並不等同於較長時期內的類似表現。

Source: CBOE, FactorResearch

FURTHER THOUGHTS

Analyzing the VIX is insightful for investors as it encourages them to consider the impact of a change in volatility on their portfolios. Unfortunately, most asset classes and strategies are directionally short volatility. Developed and emerging market equities, corporate and high yield bonds, private equity, venture capital, and most other assets benefit from a benign market environment. None of these increase in value when the global economy is heading into recession, which tends to reflect in rising correlations in crisis periods.

進一步思考

對VIX進行分析的投資者本身很有洞察力，因為它鼓勵投資者考慮波動率變化對其投資組合的影響。

不幸的是，大多數資產類別和策略在方向上都是短期波動性。發達市場和新興市場股票，公司債券和高收益債券，私募股權，風險投資以及大多數其他資產都受益於良性的市場環境。當全球經濟陷入衰退時，這些價值都沒有增加，而這往往反映在危機時期的相關性上升。

Few asset classes or strategies benefit when volatility is increasing or elevated, although these tend to generate the largest diversification benefits and are therefore highly valuable for any asset allocation framework, even if only as a satellite position. Unfortunately, these are typically difficult to hold for investors as they do not behave like the rest of the portfolio in normal times and are therefore constantly challenged. As usual, the enemy is us.

當波動率增加或升高時，很少有資產類別或策略會受益，儘管這些資產類別或策略往往會產生最大的多元化收益，因此，即使僅作為附屬資產，也對任何資產分配框架都具有很高的價值。不幸的是，對於投資者而言，這些通常很難持有，因為它們在正常時期的表現不像其他投資組合那樣，因此不斷受到挑戰。像往常一樣，然而真正的敵人就是我們。