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What is volatility trading?
In this post I would like to discuss a practical approach to implement the delta-hedging for volatility trading strategies. Keep on Reading!
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In my last post I have discussed the growing popularity and demand for strategies investing in the volatility risk-premia. One of the recurring questions that arises when I discuss this topic is whether it makes sense to allocate to these strategies in a low volatility regime. In this post I will present evidence that the current level of the implied volatility serves as a weak predictor for the performance of a short volatility strategy. Instead, the two factors are significant to explain and predict the performance of the short volatility strategy: first, the realized volatility of the VIX and, second, the roll yield associated with the term structure of the VIX futures.
In my experience, I find that the two factors are significant to explain and predict the performance of the short volatility strategy:
These two factors can explain up to 60-70% of returns on the short volatility strategy. What is most relevant for quantitative strategies is that these two factors can be predicted indead:
We see that, while the level of the VIX has been indeed very low and well below its in-sample average for the past two years, the volatility of VIX daily returns was actually higher than the in-sample average. Short volatility strategies and, in particular, the strategy selling the VIX futures have been highly profitable over the last two years because of the roll yield that was higher than the average. Finally, the roll yield is somewhat correlated with the realized volatility of the VIX with the Spearman rank correlation of 38%.
Figure 1. The VIX at the month start
Figure 2. The realized volatility of the VIX
Figure 3. The average monthly roll cost of the VIX futures
In my analysis, I apply the time series of the four strategies summarised in Table 1:
Table 1. Considered strategies
Strategy name | Bloomberg ID | Inception Date | # months |
S&P500 Total Return | SPXT Index | 04-Jan-1988 | 356 |
S&P500 Put Write | PUT Index | 30-Jun-1986 | 375 |
Short VIX futures | SPVXSPI Index | 20-Dec-2005 | 141 |
Dynamic VIX futures | Proprietary Back-test | 20-Dec-2005 | 141 |
Figure 4 displays the realized performance of the strategies since the inception. It is remarkable that the Put Write strategy has generated total returns comparable to the total return on the S&P500 index yet with smaller volatility and drawdowns. The strategy shorting the VIX futures has had a stellar performance over the past two years, but it went through an intolerable drawdown of -92% during the financial crisis in 2008. The dynamic strategy applies quantitative rules to switch between short, long, and neutral exposure, which enables it to perform in all market conditions.
Figure 4. Performance of 1$ NAV since strategy exception
The goal of my analysis is to attribute realized monthly returns on the four strategies to particular market regimes as defined by historical values of explanatory variables. Monthly returns on each of the strategy are split into the four buckets using the values of the three conditioning variables:
The four buckets are defined by the quantiles of the conditioning variables so that these buckets correspond to the four states of the conditioning variable from the low regime to the extreme regime:
Table 2 and Figure 5 report and illustrate the quantiles of the explanatory variables and the associated regimes. The regime-conditional monthly returns indicate the strategy sensitivity to the given regime of the explanatory variable.
Table 2. In-sample quantiles of the explanatory variables and inferred regimes.
Frequency | Regime | VIX at the month start | VIX monthly realized volatility | Vix futures roll yield |
25% | Low regime | … < 14% | … < 71% | … < -9% |
25% | Medium regime | 14%< … < 18% | 71%< … < 87% | -9%< … < -6% |
25% | High regime | 18%< … < 23% | 87%< … < 111% | -6%< … < -3% |
25% | Extreme regime | …> 23% | …> 111% | …> -3% |
Figure 5. Quantiles of explanatory variables
For each strategy I compute monthly returns and then assign these returns to the four buckets using the value of the explanatory variable observed in the given month and its bucketing quantiles.
Figure 6 illustrates the average monthly returns on strategies conditional on the VIX at the month start. I present the annualized monthly returns, which are obtained by multiplying the monthly return by 12, not geometric or compounded returns. Because of the volatility drag, the annual compounded return is 23% on the short VIX strategy compared to the annualized monthly average return of 42%. For simplicity of reporting and analysis, I resort to annualized monthly returns. The unconditional returns are obtained as the average of the whole sample without conditioning with the average of the regime conditional returns equal to the unconditional return. The reported performances must be interpreted as relative measures.
We see that monthly returns on the S&P 500 index and the Put Write index are not dependent on the VIX at month start. The short VIX strategy and the dynamic strategy perform better in the regime with high VIX. However, the risk adjusted returns adjusted by the volatility and measured by the Sharpe ratios do not differ significantly across different regimes because, in the regime wihh high VIX, the strategies also produce higher volatility of the realized performance.
Figure 6. Average annualized monthly returns conditional on the VIX at the month start
Figure 7 reports the average monthly returns conditional on the realized volatility of the VIX.
We see that the realized volatility of the VIX or, in other words, the realized volatility of the volatility produces much stronger explanatory power than the VIX itself. In particular, the S&P 500 index, the Put Write and short VIX strategies all produce negative average returns only in the regime with the extreme volatility of the volatility while the highest returns and risk-adjusted ratios are achieved in the regime with the low realized volatility of the VIX.
The dynamic VIX strategy applies the forecast of the expected realized volatility of the VIX as a one of the risk-control parameters so that, as a result, it is able to avoid losses in the regime of extreme realized volatility.
Figure 7. Average annualized monthly returns conditional on the monthly realized volatility of the VIX
Figure 8 reports average monthly returns conditional on the VIX futures roll yields. Similarly to the realized volatility of the VIX, VIX roll yields provide a strong explanatory power on all strategies. I recall that the Spearman rank correlation between the realized volatility and roll yields is 38% in-sample, so both variables provide distinct insight.
We see that all four strategies achieve the best returns as well as risk-adjusted ratios when the roll yields are below the median. The dynamic strategy is using the roll yields as one of the risk-control parameters and attempts to avoid concentrated trading for regimes with low roll yields so that it tend to produce slightly negative performance in the regimes with low roll yields.
Figure 8. Average annualized monthly returns conditional on the monthly average roll yields on the VIX futures
I conditioned the monthly performance of volatility trading strategies on the key observable variables including the VIX at the month start, the monthly realized volatility of returns on the VIX, and the average roll yields on VIX futures. I showed that the conditional performances and the risk-adjusted performances on all strategies do little depend on the VIX level. Instead, the realized volatility of the VIX and the roll yields on the VIX futures provide significantly stronger explanatory power.
Figure 9 illustrates the explanatory power R^2 of the regression of monthly returns on the strategies using the monthly realized volatility of the VIX and monthly VIX futures roll yields as explanatory variables.
Figure 9. Explanatory power of the regression of monthly returns with the realized volatility and the roll yield as predictors conditional on the VIX as the start of the month
We see that for the strategy shorting the VIX futures, the explanatory power of this regression is very strong at about 60% across all regimes of the VIX. Moreover, the explanatory power does not depend on the VIX regimes.
To conclude, I can answer the question about shorting volatility in the regime with the low implied volatility in the following way:
While the volatility strategies shorting the implied volatility produce better risk-adjusted returns in periods with higher levels of the implied volatility, the realized volatility of the VIX and the roll costs on the VIX futures play much stronger explanatory role in predicting the future performance of volatility strategies. The ability to quantify and forecast these variables is far more important for a dynamic quantitative strategy than choosing an appropriate level of the implied volatility for timing entry and exit points.
Artur Sepp works as a Quantitative Strategist at the Swiss wealth management company Julius Baer in Zurich. His focus is on quantitative models for systematic trading strategies, risk-based asset allocation, and volatility trading. Prior to that, Artur worked as a front office quant in equity and credit at Bank of America, Merrill Lynch and Bear Stearns in New York and London with emphasis on volatility modelling and multi- and cross-asset derivatives valuation, trading and risk-managing. His research area and expertise are on econometric data analysis, machine learning, and computational methods with their applications for quantitative trading strategies, asset allocation and wealth management. Artur has a PhD in Statistics focused on stopping time problems of jump-diffusion processes, an MSc in Industrial Engineering from Northwestern University in Chicago, and a BA in Mathematical Economics. Artur has published several research articles on quantitative finance in leading journals and he is known for his contributions to stochastic volatility and credit risk modelling. He is a member of the editorial board of the Journal of Computational Finance. Artur keeps a regular blog on quant finance and trading at http://www.artursepp.com.
The views and analysis presented in this article are those of the author alone and do not represent any of the views of his employer. This article does not constitute an investment advice.
I present a few systematic strategies for investing into volatility risk-premia and illustrate their back-tested performance. I apply the four factor Fama-French-Carhart model to attribute monthly returns on volatility strategies to returns on the style factors. I show that all strategies have insignificant exposure to the style factors, while the exposure to the market factor becomes insignificant when strategies are equipped with statistical filtering and delta-hedging. I show that, by allocating 10% of portfolio funds to these strategies within equity and fixed-income benchmarked portfolios, investors can boost the alpha by 1% and increase the Sharpe ratio by 10%-20%.
It is becoming acknowledged that volatility strategies should constitute an integral part of allocation to alternatives in portfolios of institutional and HNW investors. Indeed, both the academic and the practical experience indicate that volatility strategies produce robust risk-adjusted long-term performance, when properly designed and executed.
The growing investors’ demand for transparent solutions has been recently met by algorithmic strategies and exchange-traded funds offered by major institutions. These algorithmic strategies provide multiple solutions to invest and allocate to volatility strategies in a direct and transparent way. Yet, investors and allocators must make the ultimate decision about selecting and allocating to appropriate investment solutions.
Importantly, investors need to carefully consider the following aspects by allocating to volatility strategies:
In this note, I will describe a quantitative approach along with back-test simulations to answer these questions to make the allocation decision. I will present a few examples and draw interesting conclusions.
I will only consider the volatility carry strategies which involve selling and shorting the volatility to capture the volatility risk-premia. I will deal with products linked to the volatility of the S&P 500 index given its depth and liquidity and will consider the three algorithmic strategies.
In table 1, I provide some details about these strategies.
Table 1. The description of the algorithmic strategies
Asset | Implemen-tation | Source of Profit | Source of Loss | Pro | Cons |
Put | Sell ATM puts | Put Premium | Realized negative performance of the S&P 500 index | Simple play on volatility premium | Significant delta exposure |
Strangle | Sell 20-delta puts and calls | Put and call premiums | Realized negative and positive price performance beyond one standard deviation | i) Delta-neutral at the inception
ii) Exposure to skew and convexity risk-premiums |
Disproportionately sensitive to tail events |
VIX | Sell 1^{st} and 2^{nd} month VIX futures | Contago premium | Positive performance of the VIX | Simple play on volatility term premium | i) Dependent on contago / backwardation
ii) Significant beta to the S&P 500 index in tail events |
The key attribute of these strategies is the source of the profit-and-loss.
Compared to other asset classes, volatility strategies tend to exhibit higher drawdowns relative to their historical volatilities and strongly negative skewness of realized returns. As a result, implementation of these strategies requires the design of the systematic hedging algorithms.
For each asset, I will consider the following hedging approaches:
3a. Filter+Hedge: the strategy applies the filter as described above. If the roll passes the filter, the strategy will sell options and implement the delta-hedging strategy upto the option expiry. The delta-hedging strategy is only applied for the PUT and Strangle strategies which involve trading in options directly and have well-defined delta exposure.
3b. Filter+ Long/Short: this strategy applies only for the VIX strategy. First the strategy applies the filter and, dependent on the signal strength, it enters either short (when the VIX futures term structure is in contago) or long positions (when the VIX futures are in backwardation).
In table 2, I present the summary of the nine strategies. For the ease of visualization, I will use red color for strategies with no hedge, blue color for the strategies with the statistical filter,and green color for strategies with the filter and hedge.
Table 2. Characteristics of the hedging strategies
Strategy name | Underlying | Statistical Filter? | Delta-Hedged? | Long/Short? |
Put | S&P 500 ATM Put | No | No | Short |
Strangle | S&P 500 OTM Put and Call | No | No | Short |
VIX | 1st and 2nd month Vix future | No | No | Short |
Put+Filter | S&P 500 ATM Put | Yes | No | Short |
Strangle+Filter | S&P 500 OTM Put and Call | Yes | No | Short |
VIX+Filter | 1st and 2nd month Vix future | Yes | No | Short |
Put+Filter
+Hedge |
S&P 500 ATM Put | Yes | Yes | Short |
Strangle+Filter
+Hedge |
S&P 500 OTM Put and Call | Yes | Yes | Short |
VIX+Filter
+Long/Short |
1st and 2nd month Vix future | Yes | No | Long/Short |
To align the risk-profile of each strategy and make meaningful comparisons, I will apply the volatility targeting with the annual volatility target set to 10%.
The volatility targeting is implemented in the two steps:
I use the period from January 2005 to September 2017 (the VIX futures trading started in October 2005). As the benchmarks, I use the three assets:
The realized total performance of the benchmarks includes dividends distributed by these ETFs.
In table 3, I show the back-tested performance of the volatility strategies. Figure 1 illustrates the Sharpe ratio vs the maximum drawdown. Figure 2 illustrates the strategy alpha vs beta. The alpha and beta are estimated by regressing the monthly performance of the strategy explained by the monthly performance of the S&P 500 index. The monthly alpha from the regression is annualized. Table 4 reports the realized correlation matrix of monthly returns on these strategies.
Table 3. The back-tested performance of volatility strategies from 2005 to September 2017
Notations: Return is the total annualized return. Vol is the volatility of monthly returns. Sharpe is the Sharpe ratio using monthly volatility. Skewness and Kurtosis are the skewness and excess kurtosis of monthly returns, respectively. Max DD and Max DD recovery are the maximum drawdown and days to recover from it, respectively. Alpha and Beta are the coefficients of the regression of monthly returns on the strategy against the monthly returns on the S&P 500 index; the reported alpha is the annualized.
Figure 1. Backtested Sharpe ratio vs max drawdown
Figure 2. Strategy alpha vs beta computed by regressing monthly performance of the strategy explained by the monthly performance of the S&P 500 index.
Table 4. The correlation matrix of realized monthly returns.
Vanilla strategies produce Sharp ratio comparable to the S&P 500 index but with smaller drawdowns. They have beta about 0.5 to the performance of the S&P 500 beta and insignificant alpha. They are also strongly correlated among each other with average correlation of 0.7.
The strategies with filter improve the Sharpe ratio twofold and reduce the drawdown by about 50%. They also produce a smaller beta of about 0.2 to the S&P 500 index with statistically significant alpha. Their average pair-wise correlation is about 0.5 indicating that opportunities and signals are relatively correlated.
The strategies with the filter and delta-hedging produce the strongest risk adjusted performance with very small beta and significant alpha. Their pairwise correlation is 0.25 indicating a potential diversification benefit by allocating to the basket of these strategies. The VIX strategy with Long/Short exposures has actually produced the negative correlation and betas to all three benchmarks, so that it can serve as a good diversifier for equity portfolios.
I apply the four factor Fama-French-Carhart model to relate monthly returns on the strategies into the monthly returns on the market factor (MRK), the size factor (SML), the book-to-market value factor (HML), and momentum factor (UMD). I use the AQR data for monthly returns on the factors estimated using US stocks.
Table 5 reports the estimated coefficients of the 4-factor model. We see that all strategies have insignificant exposures to the style factors. Only the put strategy has a significant exposure to the momentum factor, which is intuitive. The exposure to the market factor is significant for vanilla strategies, while it reduces considerably for the strategies with the filter. The strategies with the delta-hedge have insignificant exposure to the market factor.
Table 5. Estimated exposures to Fama-French-Carhart 4-factor model using monthly returns from 2005 to September 2017
Notations: Alpha is the annualized alpha, MRK is the beta to the market factor, SMB is the beta to the capitalization factor (small minus big), HML is the beta to the book-to price value factor (high minus low), is the beta to the momentum factor (up minus down). R^2 is the explanatory power of the regression. The value of the t-statistics is provided in the parentheses. Significant estimates are marked with *.
Now I consider the impact of the volatility strategies on the portfolio level. Again, I use the three benchmarks. For each of the tree benchmarks, I assume that 10% of the total funds are allocating to any of the 9 strategies separately with monthly rebalancing.
I define the alpha as the regression of the monthly performance of the 90%/10% portfolio invested in the benchmark and the volatility strategy, respectively, explained by the monthly performance of the respective benchmark. The annualized alpha of this regression indicates the marginal contribution of the volatility strategy to generation of the alpha for the benchmarked portfolio.
Figure 3 shows the contribution to the portfolio alpha. Figure 4 shows the % increase in the Sharpe ratio of the 90%/10% portfolio invested 90% in the benchmark and 10% in the strategy against vs 100% portfolio wholly invested in the benchmark.
Figure 3. Contribution to the portfolio alpha for thee benchmarks
Figure 4. % Increase in the Sharpe ratio of the 90%/10% portfolio invested 90% in the benchmark and 10% in the strategy against vs 100% portfolio wholly invested in the benchmark.
Vanilla strategies have a small risk-adjusted contribution to portfolio benchmarked to the S&P 500 index or 50/50 portfolios. However, they do produce significant contribution to portfolios benchmarked to UST bonds. This is because they have equity overlay with helps to off-set the rates risk in bullish market conditions.
The strategies with the filter produce significant contribution to portfolios benchmarked to the S&P 500 index. Furthermore, they improve the risk-adjusted contribution to fixed-income portfolios by reducing the downside of the equity overlay.
The strategies with the filter and delta-hedge have a mixed contribution: the put strategy has a stronger correlation to the S&P 500 in tail events so its marginal contribution is relatively modest. Both Strangle and VIX strategies has a significant improvement of the risk-profile for all of the three benchmarks.
Well-designed algorithmic strategies provide transparent solutions for investing to volatility risk-premia. The risk profile and delta exposures must be explained to investors and tailored to their portfolios and benchmarks. The volatility strategies with statistical filtering can be applied as overlays in fixed-income portfolios. The delta-hedged option strategies and long-short VIX futures strategies can be applied as absolute return strategies in allocations to alternatives.
Artur Sepp works as a Quantitative Strategist at the Swiss wealth management company Julius Baer in Zurich. His focus is on quantitative models for systematic trading strategies, risk-based asset allocation, and volatility trading. Prior to that, Artur worked as a front office quant in equity and credit at Bank of America, Merrill Lynch and Bear Stearns in New York and London with emphasis on volatility modelling and multi- and cross-asset derivatives valuation, trading and risk-managing. His research area and expertise are on econometric data analysis, machine learning, and computational methods with their applications for quantitative trading strategies, asset allocation and wealth management. Artur has a PhD in Statistics focused on stopping time problems of jump-diffusion processes, an MSc in Industrial Engineering from Northwestern University in Chicago, and a BA in Mathematical Economics. Artur has published several research articles on quantitative finance in leading journals and he is known for his contributions to stochastic volatility and credit risk modelling. He is a member of the editorial board of the Journal of Computational Finance. Artur keeps a regular blog on quant finance and trading at http://www.artursepp.com.
The views and analysis presented in this article are those of the author alone and do not represent any of the views of his employer. This article does not constitute an investment advice.
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