Can volatility indices provide useful signals on the “underlying” market? We tried to figure it out analysing some relations between the VIX and other indices provided by the Chicago Board Options Exchange. The VIX index, which is derived from prices of a basket of out-of-the-money options on the S&P500, represents a measure of the S&P500 expected volatility over the next 30-day period. On a similar fashion, one can calculate expected volatilities for different maturities. In fact, the CBOE has introduced in the last few years three more indices: the VXST (9-day), VXV (3-month), VXMT (6-month). If we look at the volatility term structure, it usually displays an upward slope during periods of low realized volatility; this means that when the market is calm, investors expect volatility to rise in the future. On the contrary, during market turmoils, short-term expected volatility, which is greatly sensible to shocks, tends to spike more than the long-term one. Therefore, the term structure becomes downward sloping as investors expect the market to stabilise in the future. In our opinion, analysing some relations between the four volatility indices might provide good market timing signals on the S&P500. In particular, we focused our attention on the VIX/VXV ratio. The aforementioned behaviour of the term structure indicates that we will observe a ratio higher than 1 during market downturns. Furthermore, as the chart clearly shows, the ratio tends to peak in conjunction of market bottoms.

We tried to exploit this relationship building a trading strategy that buys the S&P500 when the VIX/VXV ratio spikes. The first step was to define what a peak is, because of course it is impossible to know ex-ante when the ratio is going to reverse. Thus, we built Bollinger Bands (i.e., a moving channel where the upper and lower bound are defined respectively as the ratio’s moving average plus or minus a multiple of its standard deviation), in order to define relative “highness” and “lowness” of the ratio. When the VIX/VXV ratio exceeds the upper bound, the strategy buys the S&P500 and it closes the position as the ratio goes back into the channel.

In order to assess the performance of the strategy, we use S&P 500, VIX and VXV daily closing levels from July, 2006 to November, 2015. Such a time horizon has two principal advantages: first, it is sufficiently large to claim that our results are consistent; second, it covers full business cycle, which is very important in backtesting long-only strategy. Our strategy has two key inputs: the lookback period, i.e. the period, during which we estimate the moving average and moving standard deviation, and the threshold level (the multiple of moving standard deviation), which we use as a proxy to determine when the ratio peaks out. One more input is the lag between lookback period and making the trading decision, i.e. determining how long ago the lookback period ends in the past. For instance, if we assume that the lag is equal to one, we compare today’s ratio with its moving average, calculated for several days in the past up to (and including) yesterday. In our research, we find that the results for lags equal to one and to zero are close to each other, both performing well, while other lag inputs perform much worse. Taking into account the speed of modern market transactions, we consider the strategy with lag equal to zero to be as viable, as the ones with lag equal to one and more. Finally, we take into consideration the transaction costs, associated with the strategy, however, since SPX futures tend to be very liquid, transaction costs generally amount to infinitesimal values. We estimate transaction costs to be at 0.05%.

Now we pass to the actual results of our backtesting. We present one realization of the strategy below, in comparison with SPX chart. It is for Z-score threshold of 1.5 and for lookback period of 20 days. This realization has annualized post-transaction costs Sharpe ratio, based on returns on each transaction, of around 1, while SPX disposes of Sharpe ratio of only 0.34. It is to be mentioned that there are other combinations of lookback and Z-score, which yield to much higher Sharpe ratios, sometimes of around 4-5 post-transaction costs, but generally the transaction number is not sufficient to state that the performance is supposed to be consistent. Therefore, in order not to fall victims of data-snooping bias, we prefer relatively less profitable, but more consistent strategy.

Here, we do not focus our attention on the leverage issues, even though it should be mentioned that leverage opportunities are especially attractive for our strategy: the trading portfolio may be divided into two sections, one of which may be invested into SPX futures in accordance with the trading signal and the other may be hold in cash or other low-risky instruments. Thus, we can get a variety of leverage levels at almost no additional costs, just using the fact that futures by their nature provide the investor with leverage. Employing leverage financing makes a lot of sense: the higher is the Sharpe ratio of the strategy, the less risky is leveraging it. Therefore, even though cumulative returns of the strategy are not too much higher than of S&P index, it might be leveraged such that it yields times more than the index, while being exposed to the same level of risk.

Besides the review of our strategy, we decided to compare it to another VIX-linked strategy that is quite well known: long SPX, when VIX, instead of VIX/VXV ratio, peaks out. In fact, such a strategy performed very well during the financial crisis, but recently it is doing much worse, than it used to. The relative performance of the strategies is summarised at the chart. One more point to be stressed is that, for the VIX strategy, we did not take into consideration transaction costs, so in fact its performance is supposed to be worse.

To sum up, the ratio of different volatilities indices appears to contain some very interesting buy signals for the broad market index. The backtesting of the trading strategies, based on such signals, yields into highly profitable strategies, which tend to outperform the market and which can be efficiently leveraged. There is no doubts that the strategy presented in the article may be further enhanced and become even more profitable but, even in its basic form, it is of much interest and provides the incentive for further research.

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## 1 Comment

## Best Fiend · 24 November 2015 at 20:17

Avtor pidr, infa 100%.