Volatility and Options Trading, Statistical Arbitrage in Volatility Space. Last Wednesday, the SP index went down by just The near inversion of the volatility term structure can also be seen on the VIX futures curve although to a lesser degree , as shown below.

The large changes in the spot and VIX futures were also reflected in the prices of VIX ETNs.

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We note that in normal times SVXY has a beta of about as referenced to SPY. To answer these questions, we first looked at the daily percentage changes of the VIX as a function of SPX returns. The Figure below plots the VIX changes v. Note that we plotted only days in which the underlying SPX decreased more than 1. The arrow points to the data point of last Wednesday. To quantify the probability, we counted the number of occurrences when the daily SPX returns are between The data set is from January to May 19 , and the total sample size is There are only 11 occurrences, which means that volatility spikes like the one of last Wednesday occurred only about 0.

So indeed, such an event is a rare occurrence. While accurate answers must await thorough research, based on other results not shown and anecdotal evidences we believe that the rise in the popularity of VIX ETNs, and the resulting exponential increase in short interest , has contributed greatly to the increase in the volatility of volatility.

We also note that from the Table above, out of the 11 occurrences, more than half 6 to be precise happened after , i. Position sizing and portfolio allocation have not received much attention in the options trading community. In this post we are going to apply a simple position sizing rule and see how it performs within the context of volatility trading. While this is a research venue that we would like to explore, we decided to start with a simpler approach.

We chose an algorithm that is intuitive enough for both quant and non-quant portfolio managers and traders. We utilize the market timing rule proposed by Faber [2] who applied it to different asset classes in the context of portfolio allocation.

The rule is as follows. This remarkably simple timing rule has been used successfully by Faber and others. The position is kept delta neutral, i.

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A short discussion on the rationale for choosing a market timing rule is in order here. Within the context of portfolio allocation, the 10M SMA rule is used for timing the direction of the market, i. Therefore, we thought that we could use a directional timing strategy to size an options portfolio despite the fact that their PnL drivers are different, at least theoretically. We tested the 2 strategies on SPY options from February to November Donninger, Timing the Tail-Risk-Protection of the SPY with VIX-Futures by a Hidden Markov Model.

Thomas, The Trend is Our Friend: Risk Parity, Momentum and Trend Following in Global Asset Allocation , Aug , https: The spot VIX index finished last Friday at The SKEW index is a good proxy for the cost of insurance and right now it appears to be expensive. A high reading of SKEW means investors are buying out of the money puts for protection. With the cost of insurance so high, is there a less expensive way for investors to hedge their portfolios?

One might think immediately of cross-asset hedging. However, if we use other underlying to hedge, we will then take on correlation basis risk and if not managed correctly, it can add risks to the portfolio instead of protecting it. In this post we examine different hedging strategies using instruments on the same underlying. We will use Monte Carlo MC simulation to accomplish our goal [1].

The parameters and assumptions of the MC simulation are as follows:. The asset is allowed to evolve freely in a risky world.

This would correspond to the portfolio of a Buy and Hold investor. We buy an at the money ATM put in order to hedge the downside. This strategy is the most common type of portfolio insurance. We buy an ATM put, but we then dynamically hedge it.

This means that we flatten out the delta at the end of every day. The GAMMA hedging strategy is not used frequently in the industry. The rationale for introducing it here is that given a high price of a put option, we will try to partially recoup its cost by actively scalping gamma, while we still benefit from the positive convexity of the option.

This means that in case of a market correction, the gamma will manufacture negative delta so that the hedging position can offset some of the loss in the equity portfolio. We use paths in our MC simulation. At the end of 1 year, we calculate the returns using a Reg-T account and determine its mean and variance.

The graph below shows the histogram of the returns for the NO HEDGE strategy,. Table below presents the expected returns, standard deviations and Value at Risks for the hedging strategies.

As it is observed from the table, hedging with a protective put PPUT reduces the risks. Standard deviation and VaR are reduced from 0. However, the expected return is also reduced, from 0.

This reduction is the cost of the insurance. Interestingly, hedging using gamma convexity GAMMA strategy provides some reduction in risks Standard deviation of 0.

In summary, GAMMA hedging is a strategy that is worth considering when designing a portfolio insurance scheme. However, results and the conclusion are consistent with our real world experience.

Last week the VIX index was more or less flat, the contango was favorable, and yet VIX ETF such as XIV, SVXY underperformed the market. In this post we will attempt to find an explanation. The forward volatility is calculated as follows,. Graph below shows the prices of VXX green and red bars and VIX April future yellow line for approximately the same period. Notice that their prices have increased since mid February, along with the forward volatility, while the spot VIX not shown has been more or less flat.

If you define the basis as VIX futures price-spot VIX , then you will observe that last week this basis widened despite the fact that time to maturity shortened. In summary, VIX futures and ETF traders should pay attention to forward volatilities, in addition to the spot VIX.

Forward and spot volatilities often move together, but they diverge from time to time. The divergence is a source of risk as well as opportunity. In previous blog posts, we explored the possibility of using various volatility indices in designing market timing systems for trading VIX-related ETFs.

The system logic relies mostly on the persistent risk premia in the options market. Recall that there are 3 major types of risk premium:. A summary of the systems developed based on the first 2 risk premia was published in this post.

In this article, we will attempt to build a trading system based on the third type of risk premium: As a measure of the volatility skew, we use the CBOE SKEW index. According to the CBOE website, the SKEW index is calculated as follows,.

SKEW typically ranges from to One can estimate these probabilities from the value of SKEW. We observe that this system does not perform well as the other 2 systems [1]. Hence using the volatility skew as a timing mechanism is not as accurate as other volatility indices.

In summary, the system based on the CBOE SKEW is not as robust as the VRP and RY systems. Therefore we will not add it to our existing portfolio of trading strategies. The article refers to a well-known phenomenon that under normal market conditions, the VIX and SP indices are negatively correlated, i.

In this post we revisit the relationship between the SP and VIX indices and attempt to quantify their dislocation. We first investigate the correlation between the SP daily returns and change in the VIX index [1].

The graph below depicts the daily changes in VIX as a function of SP daily returns from to We observe that there is a high degree of correlation between the daily SP returns and daily changes in the VIX. We calculated the correlation and it is To do so, we calculated the residuals. The graph below shows the residuals from January to December Under normal market conditions, the residuals are small, reflecting the fact that SPX and VIX are highly and negatively correlated, and they often move in lockstep.

However, under a market stress or nervous condition, SPX and VIX can get out of line and the residuals become large. Table below summarizes the results. The dislocation occurs not infrequently. Most of the time this kind of divergence is unpredictable. It can lead to a marked-to-market loss which can force the trader out of his position and realize the loss.

VIX Options and Futures

So the key in managing an options portfolio is to construct positions such that if a divergence occurs, then the loss is limited and within the allowable limit. In this post, however, we choose to use the change in the VIX as measured by daily point difference. We do so because the change in VIX can be related directly to Vega PnL of an options portfolio.

Therefore, we applied linear regression to the whole data set from to For more accurate hedges, traders should use shorter time periods with frequent recalibration.

In previous posts, we presented 2 volatility trading strategies: In this post we present a detailed comparison of these 2 strategies and analyze their recent performance.

The first strategy VRP is based on the volatility risk premium. The trading rules are as follows [1]:. The trading rules are as follows:. Table below presents the backtested results from January to December But the percentage return of each trade remains the same. We observe that RY produced less trades, has a lower annualized return, but less drawdown than VRP. The graph below depicts the portfolio equities for the 2 strategies.

It is seen from the graph that VRP suffered a big loss during the selloff of Aug , while RY performed much better. In the next section we will investigate the reasons behind the drawdown.

The graph below depicts the day HV of SP blue solid line , its 5-day moving average blue dashed line , the VIX index red solid line and its 5-day moving average red dashed line during July and August As we can see, an entry signal to go short was generated on July 21 red arrow. The trade stayed short until an exit signal was triggered on Aug 31 blue arrow.

The system exited the trade with a large loss. The reason why the system stayed in the trade while SP was going down is that during that period, the VIX was always higher than 5D MA of 10D HV. This means that 10D HV was not a good approximate for the actual volatility during this highly volatile period. Recall that the expectation value of the future realized volatility is not observable.

This drawdown provides a clear example that estimating actual volatility is not a trivial task. By contrast, the RY strategy was more responsive to the change in market condition. It went long during the Aug selloff blue arrow in the graph below and exited the trade with a gain. The responsiveness is due to the fact that both VIX and VXV used to generate trading signals are observable. In summary, we prefer the RY strategy because of its responsiveness and lower drawdown.

Both variables used in this strategy are observable. The VRP, despite being based on a good ground, suffers from a drawback that one of its variables is not observable.

To improve it, one should come up with a better estimate for the expectation value of the future realized volatility. This task is, however, not trivial. Last month was particularly favorable for short volatility strategies. In this post, we will investigate the reasons behind it. First, the main PnL driver of a delta neutral, short gamma and short vega strategy is the spread between the implied volatility IV and the subsequently realized volatility RV of returns. Trading strategies such as long butterfly is profitable when, during the life of the position, RV is low compared to IV.

The graph below shows the difference between IV and RV for SP during the last 5 months. Note that RV is shifted by 1 month, so that IV-RV presents accurately the spread between the implied volatility and the volatility realized during the following month.

Hence short volatility strategies were generally profitable during October. The second reason for the profitability is more subtle. The graph below shows the IV-RV spreads in function of monthly returns. As we can see, there is a high degree of correlation between IV-RV and the monthly returns. In fact, we calculated the correlation for the last 10 years and it is 0.

This means that when IV-RV is high, SP usually trends up. However, when the market trends, the cost of hedging in order to keep the position delta neutral is high. By contrast, even though IV-RV was high in October, the market moved in a range, thus helping us to minimize our hedging costs. This factor therefore contributed to the profitability of short volatility strategies.

In summary, October was favorable for short volatility strategies due to the high IV-RV spread and the range bound nature of the market. In previous 2 articles , we explored a volatility trading strategy based on the volatility risk premium VRP.

The strategy performed well up until August , and then it suffered a big loss during the August selloff. In this article, we explore another volatility trading strategy, also discussed in Ref [1].

This strategy is based on the volatility term structure [2]. It is well known that volatilities exhibit a term structure which is similar to the yield curve in the interest rate market.

The picture below depicts the volatility term structure for SP as at August 31 [3]. Most of the time the term structure is in contango. This means that the back months have higher implied volatilities than the front months.

However, during a market stress, the volatility term structure curve usually inverts. In this case we say that the volatility term structure curve is in backwardation a similar phenomenon exists in the interest rate market which is called inversion of the yield curve. Specifically, we go long if the volatility term structure is in backwardation and go short otherwise.

To measure the slope of the term structure, we use the VIX and VXV volatility indices which represent the 1M and 3M implied volatilities of SP respectively. In the next installment we will compare the 2 strategies, volatility risk premium and roll yield, in details. The strategy discussed in this post, however, is not meant to exploit the term structure risk premium. It uses the term structure as a timing mechanism. Therefore, it is theoretically different from the term structure of spot volatilities which are calculated from SP options.

Practically speaking, the 2 volatility term structures are highly correlated, and we use the futures curve in this article for illustration purposes. Last year, we presented backtested results for a VXX trading strategy. In short, the trading rules are as follows:. The strategy performed well in backtest. In this follow-up post, we look at how it has performed since last year.

The Table below summarizes the results. However, it suffered a big loss during August. The graph below shows the portfolio equity since last August. Large losses are typical of short volatility strategies. An interesting observation is that after the large drawdown, the strategy has recovered, as depicted by the upward trending equity line after August.

This is usually the case for short volatility strategies. Despite the big loss, the overall return not shown is still positive. This means that the strategy has a positive expectancy. Drawdown can be minimized by using a correct position size, stop losses, and a good portfolio allocation scheme. Another solution is to construct limited-loss positions using VXX options. Skip to content Relative Value Arbitrage Volatility and Options Trading, Statistical Arbitrage in Volatility Space. Is Volatility of Volatility Increasing?

VIX futures as at May 16 blue line and May 17 black line. So was the spike in volatility normal and what happened exactly? Daily VIX changes v.

Table below presents the dates and VIX changes on those 11 occurrences. Within the context of volatility trading, we compare 2 option strategies 1- NoTiming: Strategy NoTiming 10M-SMA Number of Trades 81 Percent Winners 0. CBOE SKEW index as at close of March 17, The parameters and assumptions of the MC simulation are as follows: The graph below shows the histogram of the returns for the NO HEDGE strategy, Return histogram for the NO HEDGE strategy Table below presents the expected returns, standard deviations and Value at Risks for the hedging strategies.

Strategies Expected return Standard Deviation Value at Risk NO HEDGE 0. Footnotes [1] We note that the simulations were performed under idealistic assumptions, some are advantageous, and some are disadvantageous compared to a real life situation. VXX green and red bars and VIX April future yellow line prices If you define the basis as VIX futures price-spot VIX , then you will observe that last week this basis widened despite the fact that time to maturity shortened.

Recall that there are 3 major types of risk premium: Daily point change in VIX v. SP return We observe that there is a high degree of correlation between the daily SP returns and daily changes in the VIX.

Volatility trading strategies In previous posts, we presented 2 volatility trading strategies: The trading rules are as follows [1]: The trading rules are as follows: But the percentage return of each trade remains the same RY VRP Initial capital Ending capital Portfolio equity for the VRP and RY strategies It is seen from the graph that VRP suffered a big loss during the selloff of Aug , while RY performed much better.

Performance during August The graph below depicts the day HV of SP blue solid line , its 5-day moving average blue dashed line , the VIX index red solid line and its 5-day moving average red dashed line during July and August References [1] T Cooper, Easy Volatility Investing, SSRN , IV-RV spreads of SP The second reason for the profitability is more subtle.

SP monthly returns This means that when IV-RV is high, SP usually trends up. SP Volatility Term Structure at Aug 31 Most of the time the term structure is in contango. There are 2 interesting observations This strategy did not suffer a large loss like the VRP strategy during the August selloff of last year Long volatility trades are profitable In the next installment we will compare the 2 strategies, volatility risk premium and roll yield, in details.

In short, the trading rules are as follows: The Table below summarizes the results All trades Long trades Short trades Initial capital Ending capital Bars Held 15 9. VRP volatility trading strategy Large losses are typical of short volatility strategies. Page 1 Page 2 Page 3 Next page. Get new posts by email. Relative Value Arbitrage Proudly powered by WordPress.