The January Effect – Part 2

Continuing from Part 1

Comparing between strategies

S2 strategy invests in months {1,3,4,7,10,11,12} and yields better Sharpe and higher total return than the benchmark. It also has less negative skew.

S1 invests in only 4 months of the year {3,4,11,12} and so the total profit is much lower. The Sharpe does not improve, but the skew is significantly improved – it is now positive.

S1b squeezes out a little more total return by shorting month 9, giving us less of a max DD, but does not improve on the Sharpe nor the skew, so it might not be worth the effort.

Because this is an active method, the number of trades needed is proportional to the number of months. S2: 7, S1: 4, and S1b: 5.

Active method equity curves

Using the active method, we can see that the curve is significantly smoother than the benchmark, especially for S1 strategies.

Passive method

The passive method is what we normally do in real life – a hypothetical growth of $1. We do not rebalance the amount, but simply let it grow. The percentage returns are compounded, not simply added as per previous method.

Conservative strategies (like S1) are penalized because they tend to miss out on some of the compounding gains accrued in bull runs. This makes a sizeable difference in the long run.

The passive strategy comparisons show that S2 allows us to beat the benchmark, with slightly lower SD and drawdown measures.

S1 strategies are far superior in terms of Sharpe, but don’t eke out as much of a profit. To solve that, use leverage.

Using leverage of 1.5x, we can get the S1 strategies to beat the the total return of S2 and the benchmark, with somewhat similar SD and drawdown.


However, implementation is not so simple – we will need to find a way to get the 1.5x monthly return of the index, and keep compounding it. It’s not as easy to implement as S2.



Following a simple strategy like S2 can give us better total and risk-adjusted returns than the benchmark.

Continue reading "The January Effect – Part 2"

The January Effect

Many have heard of January effect in stock markets - stocks generally go up in January. Here we take a look at this phenomenon and see if it still persists.

Below are the results for the S&P 500 for 1951 to 2018 using monthly simple percentage returns

It shows that while the mean return is indeed positive, there are many other months with higher mean returns. Might as well call it the January-and-March-and-April-and-July-and-November-and-December-effect.

What's more important is that the Sharpe of the other (Mar, Apr, Jul, Nov, Dec) months are higher.

The only advantage that January has is that it is the only month with a positive skew, albeit very slight.

Below are the return distributions for each month.

We are also interested in the smoothness of the equity curve, and whether the strategy is robust through time.

Below we can note the following observations:

  • The January effect lost its effect from 2000 onwards
  • Mar, Apr, Nov, Dec are remarkably good month
  • Sep is consistently bad
  • Oct (while having the reputation for worst declines) is still on a general up trend

In the next part, we will look at implementing a market timing strategy that invests only in certain months, and see how it fares against the benchmark.

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