# Introduction

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.

# Explanatory factors for return attribution of short volatility strategies

In my experience, I find that the two factors are significant to explain and predict the performance of the short volatility strategy:

- The realized volatility of the VIX or, in other words, the realized volatility of the implied volatility. This factor is related to the realized volatility of the short volatility strategy and, as a result, it measures the realized risk of the volatility strategy.
- The roll yield of the VIX futures curve or, alternatively, the cost of carrying the long option position. This factor is related to the expected profitability of the short volatility strategy that either sells options or VIX futures. The VIX futures curve is typically in the contango with the upward sloping term structure. The contango effect is caused by the cost of carry of a long option position.

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:

- On the one hand, both the volatility and the realized volatility of the volatility exhibits the clustering effect, when the periods of high volatility and high realized volatility tend to be followed by the periods with high volatility. On the other hand, the volatility exhibits the mean-reversion effect over the longer time frames, when the volatility tends to mean-revert from the regime with the high volatility to the regime with the low volatility. Figure 1 illustrates the time series of the VIX and Figure 2 displayes the realized volatility of the VIX, which is computed as the realized volatility of daily log-returns on the VIX.
- The roll yield on the VIX future is also characterised by mean-reverting dynamics with about 80% of observations being negative when the futures curve is in the contango. Figure 3 displays the time series of the average monthly roll yield. The average monthly roll yield on the VIX futures computed as the spread between the first and the second month futures divided by the price of the constant maturity one month future.

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

# Methodology

## Investment strategies

In my analysis, I apply the time series of the four strategies summarised in Table 1:

- The total return strategy on the S&P 500 which serves as an equity benchmark for short volatility strategies.
- The CBOE put write strategy which sells at-the-money put options on the S&P 500 index quarterly. This strategy is computed by the CBOE and dates back to year 1986.
- The strategy shorting one month constant maturity futures on the VIX. The strategy is computed by Bloomberg and it dates back to year 2005. The exchange traded product that replicates this strategy started to trade in 2011 with the ticker XIV.
- The dynamic VIX strategy which trades in the one month constant maturity futures on the VIX both on the short and long side using signals generated by a proprietary model. This quantitative strategy employs the two key factors considered here for the signal generation. Presented is the back-tested performance on this strategy.

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

## Conditioning of monthly returns

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:

- VIX at the month start;
- Realized volatility of daily returns on the VIX in the given month;
- The average monthly roll yield on the VIX futures computed as the spread between the first and the second month futures divided by the price of the constant maturity one month future.

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:

- [0-25%] quantile is the low regime;
- [25-50%] quantile is the medium regime;
- [50-75%] quantile is the high regime;
- [75-100%] quantile is 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

# Analysis of regime conditional performance

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.

## Returns conditional on the VIX at month start

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

## Returns conditional on the monthly realized volatility of the VIX

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

## Returns conditional on the VIX futures roll

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

# Concluding remarks

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.*