## Understanding volatility term structure

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**Predicting economic disasters?**

To understand volatility term structure, one must first choose a volatility model. Current volatility models focus on the stochastic volatilities and jumps, but lack the necessary connection with the state of the macro economy. Investors and advisors need a new model on volatility that can provide greater insight into changes in the real economy.

One option is the Regime Switching Rare Disaster Model, proposed in the recent research paper “Asset Pricing Implications of Volatility Term Structure Risk.” The proposed model connects the slope of volatility term structure with the length of potential economic disasters.

That is to say, a downward-sloping VIX term structure today predicts small chance of a long (severe) disaster in the near future, but an upward-sloping VIX term structure predicts small chance of a short disaster in the near future.

**Benefiting from a new model **

Volatility term structure can offer a number of insights that other, more traditional models may not. For instance, it may offer greater insights and understanding about the timing of the market. The model suggests a changing regime once the VIX term structure changes from upward sloping to downward sloping. It can also be used as an important signal for market timing.

The other takeaway from the model is that it can be used for constructing trading strategies that earn this VIX term structure risk premium. The “risk premium” is the extra return investors require by taking more risks. Based on the “Regime Switching Rare Disaster Model,” a visible change of VIX term structure can reflect a change of risk. By taking this risk, the investor is compensated by a higher return, thus earning a VIX term structure risk premium. More simply, by taking risks on VIX term structure, one can expect to achieve higher returns than when one is not taking these risks.

Following are two strategies that can be used to take advantage of the VIX term structure risk premium.

**Time series VIX futures strategy**

The VIX futures term structure tends to be in contango; thus, the investor in a long futures position pays a negative roll yield. The trading strategy aims to profit from this negative roll yield.

The strategy is defined as maintaining a long position at the two-month point on the VIX futures curve by continuously rolling between the second and third month futures contracts, and a short position at the one-month point on the VIX futures curve by continuously rolling between the first and second month futures contracts.

If the VIX futures curve stays upward sloping, the long position at the two-month point on the VIX futures curve keeps rolling the second-month futures to the third-month, thus suffers a negative roll yield. Meanwhile, the short position at the one-month point on the VIX futures curve keeps rolling the short position between the first-month futures to the second-month futures, thereby earning a positive roll yield.

The future curve is concave while it is upward sloping. Therefore, the positive roll yield earned from the short one-month VIX futures positions is bigger than the long two-month VIX futures position.

This strategy’s Sharpe ratio is around 0.60: The reason why it can make money is because it takes advantage of the time series volatility term structure premium.

### Cross sectional VIX

This strategy aims to capture the cross- sectional stocks’ risk premium on VIX term structure. One can calculate each stock’s sensitivity to the changes in VIX term structure, as similar procedure to calculating the stock’s beta to the market return. The stocks with higher sensitivity (beta) on the VIX term structure will load higher VIX term structure risk, thus they “require” higher return to compensate the extra risk. By going long on the stocks with high beta on VIX term structure and going short on stocks with low beta on VIX term structure, we capture the cross sectional stocks’ risk premium on VIX term structure.

The strategy looks like this: At the end of each month you run regressions for the past month’s stocks’ daily returns on the VIX term structure slope. Long the stocks with the highest betas on the slope and short the stocks that have the lowest betas on the slope. The strategy achieves an alpha of around 5% per year.

The volatility term structure is a measure that can be more useful than looking at volatility itself. Based on the Regime Switching Rare Disaster Model, volatility term structure can be used as a new measure to reflect the investor’s expectations on a potential disaster’s (or lack of one) length.

The model offers advisors greater information on which to base profitable strategies regarding harvesting the volatility term structure risk premium.