The naïve, long vol premium buy-and-hold strategy suffers large losses occasionally. For example, at the height of the financial crises in 2008, the naïve strategy would have suffered a loss of more than 14% in September. The key is to introduce simple indicators to alert yourself when turbulence threatens and avoid taking bad risk.
There are endless ways of improving the naïve strategy, but two simple filters will be applied: The first filter is statistical and backward-looking, which uses its own history to draw an intelligent inference about its future. The second is forward-looking and derived from the most recent, traded market prices that contain vital information about financial market sentiment.
A perfect forecast of upcoming actual volatility does not exist. A good statistical model can, however, help you build a sound forecast. By default many would use a rolling window standard deviation of daily returns as the forecast. Also popular is an exponential moving average of squared daily returns. These two proxies are easy to implement and are widely used by traders, analysts, and the like to get the first proxy of actual volatility. With the availability of intra-day data however, it is possible to just sum up high frequency return squares, which is itself a valid proxy for actual volatility. Figure 1-6 shows one-month historical volatility of USDJPY from July 29 to August 13, 2013, computed using tick-by-tick data compared with using only one data point a day. The difference can often be substantial.
If high frequency data is not easy to obtain though, the next best thing you can do is use GARCH to measure and forecast actual volatility. GARCH stands for Generalized Autoregressive Conditional Heteroskedasticity. Simply speaking, it says: Volatility is time varying, meaning it changes over time from times of calm to times of anxiety, and periods of different volatility tend to cluster together, which any good forecasting model should incorporate. GARCH is a simple, elegant statistical model that incorporates all these observed properties.
Financial markets tend to behave anxiously in response to disruptive events such as wars, natural disasters, or market crises. During these crisis periods, volatility tends to be much higher than it typically is as prices sharply fluctuate. This means that the volatility of the financial markets is not constant over time. A more sophisticated model would reflect that behavior.
Also, dependencies in the data would have to be taken into account. Times of calm are generally followed by calm, and volatile days are followed by volatile days in a cluster. So if today’s stock price is extreme, it is likely tomorrow’s price will be extreme as well. Also, these events display mean reversion, meaning that in weeks or months, an anxious market will eventually calm back down and return to its typical long-term behavior.
Hence, GARCH in the end can be thought of as a simple yet sophisticated way to describe the volatility process. It is seen as sophisticated because, rather than weigh events from yesterday and events from last month equally, recent events are given greater weight through an exponentially weighted moving average. And the model also recognizes that financial markets display mean reversion. There are countless varieties of GARCH models, and for our purposes the simplest case of GARCH (1,1) will suffice. In GARCH (1,1), today’s variance depends on yesterday’s variance, the first “1”, and yesterday’s shock (in squares), the second “1”.
Figure 1-7 shows GARCH (1,1) predicted volatility against observed realized (measured using close-to-close returns), both with one-month tenor. GARCH(1,1) is the simplest model among the GARCH families. It uses only four parameters to describe the dynamics of return and its volatility. As you can see, GARCH mimics the up and downs of realized vol well, with some lags due to its backward-looking characteristic. The model relies on historical data only, so necessarily market events must occur (and be read as data) before the model can respond.
Armed with a decent measure of actual volatility, the “sophisticated average” GARCH provides, you can now apply the first filter to the naïve vol premium strategy. Every month, you enter a volatility swap contract with one-month tenor in fixed amount of capital. The contract obligates you to receive a pre-determined strike level closely associated to the one-month at-the-money implied USDJPY volatility and pay upcoming realized volatility. If GARCH predicts upcoming high volatility, it indicates that recent market has experienced an unexpected large move. Something is happening behind the scenes that’s raising anxiety. If GARCH predicts a higher move, you don’t take the risk of paying upcoming actual vol in the coming month. You stay on the sideline. More specifically, if the difference between implied volatility and GARCH predicted actual volatility does not exceed a threshold, you will not take the risk of shorting volatility.
Table 1-1 compares the result of vol investing with and without the GARCH filter. From January 2001 to June 2013, imposing the GARCH filter would achieve a similar level of return as the naïve strategy, which is annualized 4.74%. Standard deviation, however, is reduced from 10.1% to 8%, hence the Sharpe ratio increases from 0.47 to 0.59. In particular, the largest one-month loss of 14.7%, which occurred in September 2008, is avoided by the GARCH filter. Out of 150 months from January 2001 to June 2013, the GARCH filter switched off a total of 40 months to avoid taking risk in USDJPY vol premium. All these results assume a 0.4% transaction cost (that is, you pay 0.4% per month), which is a conservative assumption.