Time Decomposition of FX prices

In this method, I investigate the behaviour of prices in off-market hours - if they have a consistent drift, and whether it could be used as a trading strategy.

The currency pair I've chosen to start with is the USDCAD as both countries share the same broad timezone. This makes for easy identification of 'busy' hours (normal trading hours) and 'quiet' hours (major markets are closed).

From there, we can construct two new price series consisting only of movements within those hours - one for busy, one for quiet.

The preliminary results (for the sample period 2018) indicate that the movements in the pair were driven mainly by activity in the Busy period - seeing how the Busy moves almost alongside the Actual. This is an expected outcome - we expect  that real money (coming in during the market hours) are what drives prices and create permanent impact.

However, the Quiet period, over the course of days/weeks, can move in the opposite direction of the Busy trend. As examples, the major down move from Jul to Oct driven by Busy period was partially offset by the Quiet period upward move. The following rally by Busy was also partially dampened by Quiet in Oct to Dec.

Do note though that this mean reversion in quiet hours is not strong enough on a daily basis to warrant a fade-the-move style of trading. The daily change correlation is near 0, and the cumulative prices correlations are near 0 too.

We need to dig deeper into how this effect plays out on an aggregate level to produce the offsetting effects we see in the 2 example periods highlighted above.

Beta of VIX Futures to VIX Spot

VIX Futures are the most direct way to trade the VIX. However, the price of the front month future will hardly track the VIX one-to-one. Thus it is important to estimate the sensitivity (beta) of the futures versus the index so that we can have some gauge of how our futures position might change in relation to the index.

The chart below shows that the front month futures (VF1) can be quite different from the VIX spot index.

Note that as VIX spot index gets higher, it is more likely that the VF is in backwardation. This is intuitive as at higher levels, it's much more likely that the VIX recedes back to some normalized lower level by settlement date.

Contango vs Days to Expiry

First thing to note is that VF is most of the time in contango, and up to 30% premium. The contango ratio here is simply VF/VIX such that a reading of 1.3 means the VF is 1.3 times the value of VIX.

Second thing to note is the decay of contango - looking at how the cluster of 5-10 DTE decays the fastest as it goes to the 1-2 cluster, compared to the decays of the other clusters. This means that the decay rate is fastest when the DTE is less than 10 days - something to note if you're selling volatility.

Estimating beta

Beta can be measured in many ways. Here we use daily changes in the front month future (VF1) over the VIX index, expressed as a ratio.

We should expect that as the days to expiry decreases, the VF will track the VIX more closely. This is because VF is essentially a bet on what the VIX will settle at the VF expiry date. As expiry gets closer, market participants have narrower ranges for their predictions.

We are able to see from the chart below that the median beta gets closer to 1 as the days to expiry goes down. The betas are however very noisy and it might be useful to use other ways to measure beta, perhaps using intraday data.







VIX Selling Strategies

This series of posts will look into ways to systematically short the VIX via VIX Futures.

Strategy 1 - Sell and hold to expiry

Strategy 1a is simply to sell on the open of a new front month future, and close just before expiry.

Strategy is not good, as we can see there are years of choppy growth, and a drawdown can take several months to recover. The strategy owes it profits to the stellar years in 2016-2017.

A look at the opening price vs ending profit shows us that opening trades at higher prices are more likely to end up profitable. We can thus attempt to use a simple filter - sell only if price is >15. The results are shown below as Strategy 1b.

The equity curve is much smoother, but it has years of missing out (when open price is lower than 15 e.g. during the calm of 2017 which were the best years of selling VIX). Realistically, you wouldn't want a strategy that hardly trades.

Strategy 1c is a play on the autocorrelation structure of the returns. If losing months are usually followed by winning months, then we can enter after observing a loss on the hypothetical portfolio.

While it is overall positive, it fails to capitalize on the winning streaks of the strategy, and it does not filter out the losing months well enough, and so overall it's not good.

Conclusion of strategy series 1

The simple buy and hold (or rather, sell and hold) is not robust enough for a strategy, and we will have to investigate further.


2013-05 is the first expiry date obtained from CBOE and data before that to 2007 obtained from macroption.com

FX Hedging

Main factors in deciding between whether to hedge or not: returns, volatility, and correlation. Very briefly:

  1. Cost of hedge: interest rate differential + any FX basis
  2. Volatility or underlying vs currency: check if a hedged position can give a better Sharpe; sometimes the currency is more volatile than the underlying
  3. Correlation between underlying and currency: some assets are better left unhedged i.e. JPY-denominated equities; denomination has a tendency to rise in times of equity stress

Typically, bonds are hedged while equities are left unhedged, but this 'typical' does not apply to everyone at every time - you have to see if it applies to your case.

Also, always do the analysis with your home currency in mind.

Predicting Limit Order Book Behaviour

I recently did an exercise on analyzing the limit order book for predictors of the first event that will occur in the next 1 second. There are 3 events: bid level retreating, ask level retreating, and no change in the top of the book price.

The result was that the log of (Bid/Ask) gave the strongest prediction. 

Below is a scatter plot for a small sample that shows the relationship between the bid and ask quantities, and the corresponding colours indicate the outcome (grey = no change, blue = bid retreated, red = ask retreated). Contours indicate the probability estimated by multinomial logistic regression.

Here's the full version using tick data of the entire day (about 127,000 data points). White = no change, for better visibility and truncated at size=300.

Below is the full version, without the ax truncation.