Tag: S&P500

Equity Returns Following Extreme VIX and WVF Movements, Part 1

Can extreme changes in implied volatility help predict future returns? And can we use a VIX surrogate as a substitute? First, let’s take a look at the WVF and its relationship to the VIX.

The Williams’ VIX Fix (WVF) is an indicator meant to roughly approximate the VIX. It can be useful in situations where there is no implied volatility index for the instrument we want to trade. The WVF is simply a measure of the distance between today’s close and the 22-day highest close; it is calculated as follows:

WVF Formula

A quick visual comparison between the VIX and WVF:

The WVF and VIX behave similarly during volatility spikes, but the WVF fails to emulate the VIX when it hovers at relatively low values. The correlation coefficient between VIX and WVF returns1 is 0.62, while regressing VIX returns on WVF returns using OLS results in an R2 statistic of 0.38.

We’re not going to be using the level of the VIX and WVF (hardcoding strategies to specific levels of the VIX is generally a terrible idea), so the above chart is somewhat useless for our purposes; we’re going to be looking at the 100-day percentile rank of the daily change. Here is a comparison over a couple of recent months:

Some times they move in lockstep, other times there seems to be almost no relation between them. Still, for such a simple indicator, I would say that the WVF does a fantastic job at keeping up with the VIX.

As you probably know, (implied) volatility is highly mean reverting. Extreme increases in the VIX tend to be followed by decreases. These implied volatility drops also tend to be associated with positive returns for equities. Let’s take a look at simple strategy to illustrate the point:

  • Buy SPY on close if the VIX percentage change today is the highest in 100 days.
  • Sell on the next close.

Here’s the equity curve and stats:

Nothing spectacular, but quite respectable. Somewhat inconsistent at times of low volatility, but over the long term it seems to be reliable. What about the same approach, but using the WVF instead?

The WVF outperforms the VIX! A somewhat surprising result…the equity curves look similar of course, with long periods of stagnation during low volatility times. Over the long term the stats are quite good, but we might be able to do better…

There is surprisingly little overlap between the VIX and WVF approaches. There are 96 signals from VIX movements, and 109 signals from WVF movements; in 48 instances both are triggered. These 48 instances however are particularly interesting. Here’s a quick breakdown of results depending on which signal has been triggered:

performance VIX WVF Both

Now this is remarkable. Despite performing better on its own, when isolated the VIX signal is completely useless. This is actually a very useful finding and extends to other similar situations: extreme volatility alone is not enough for an edge, but if used in combination with price-based signals, it can provide significant returns. I leave further combinations on this theme as an exercise for the reader.

A look at the equity curve of “both”:

both equity curve

Long SPY when VIX % change and WVF change are both the highest of the last 100 days, $100k per trade, 1993-2012, no commissions or dividends.

Now that’s just beautiful. You may say “but 37% over 20 years isn’t very impressive at all!”. And you’re right, it isn’t. But for a system that spends almost 99% of the time in cash, it’s fantastic. Want more trade opportunities? Let’s see what happens if we relax the limits on “extremeness”, from the 99th percentile through to the 75th:

extremeness tests

Net profit increases, but profitability per trade, and most importantly risk-adjusted returns suffer. The maximum drawdown increases at a much faster rate than net profits if we relax the limits. Still, there could be value in using even the 50th percentile not as a signal in itself, but (like the day of the month effects) as a slight long bias.

Finally, what if we vary the VIX and WVF limits independently of each other? Let’s have a cursory look at some charts:

As expected, the profit factor is highest at (0.99, 0.99), while net profits are highest at the opposite corner of (0.75, 0.75). It’s interesting to note however, that drawdown-adjusted returns are roughly the same both along the (0.99, 0.75-0.99) and (0.75-0.99, 0.99) areas; as long as one of the two is at the highest extremes, you can vary the other with little consequence in terms of risk-adjusted returns, while increasing net profits. This is definitely an area deserving of further analysis, but that’s for another post.

That’s it for now; I hope some of these ideas can be useful for you. In part 2 we’ll take a look at how the above concepts can be applied to international markets, where there is no direct relation to the VIX and there are no local implied volatility indices to use.

  1. In order to calculate returns for WVF I re-scaled it so the minimum value is 1 instead of 0, thus eliminating the problem of infinite/undefined results.[]

Read more Equity Returns Following Extreme VIX and WVF Movements, Part 1

S&P 500 Returns Following New Lows (and Highs)

Today the S&P 500 closed at a 20-day low. Is there anything useful we can do with this piece of information? Let’s take a look at the performance of SPY after it closes at a 20-day low:

spy performance after 20 day low


Not particularly useful I’m afraid, just random variations around the average. What about other look-back lengths?

spy performance after x day low


Now this is more interesting. 60-day lows and up appear to have a bit of an edge, both for the day immediately after the low, as well as the medium term afterwards.

Let’s take a closer look at the returns after a 200-day low, with 95% confidence interval bands around them. Naturally, returns tend to be highly volatile around 200-day lows, which (combined with the small number of observations) means a very wide confidence interval.

spy performance after 200 day low


The 200-day low effect also seems to be prevalent in most equity indices, but without the regularity and strength that has been displayed by the S&P 500. Finally, what about new highs?

spy performance after x day high

Nothing to see here, move along! Slight underperformance compared to the average, but nowhere near enough to even consider shorting.

Read more S&P 500 Returns Following New Lows (and Highs)

Day of the Month Seasonality Part 1: S&P 500, NASDAQ Composite, Russell 2000

My first post is inspired by the recent day of the month seasonality posts over at MarketSci (one, two). In this post I will show how day of the month seasonality applies to the S&P 500 as well as two other popular indices: the NASDAQ Composite and the Russell 2000.


The methodology:

  1. Standardize every month to 21 trading days; round to the nearest integer when the number of days in a month is different.
  2. Use the last 5000 days of daily returns and estimate the average return on every (standardized) day of the month.
  3. Rank the days by their past returns. If the next day is in the top 6, buy on close and sell on the next close.
  4. Move forward by one trading day and repeat from step 2.

As such, the approach is 100% walk-forward; there is no look-ahead bias in these results.


The results:

 S&P 500:

The sample starts in 1950; the results thus start in 1970.

S&P 500 day of the month seasonality results


A quick comparison of the statistics:

S&P500 stats

While the returns from the “Top 6” days are very impressive, they exhibit somewhat higher volatility, and can actually under-perform for very long periods of time.


NASDAQ Composite:

The equity curves:

NASDAQ Composite day of the month seasonality results

And the statistics:

nasdaq stats


Russell 2000:

The equity curves:

russell 2000 graph

And the statistics:

russell 2000 stats

The Russell 2000 stands out as rather strange: the Top 6 days did great during the bear market, but have been ineffective ever since. Of course, we only have a few years of useful data in this case, so it could very well be the case that we have stumbled on a period of under-performance by the day of the month effect.


Here are the actual statistics for the last 5000 days for each of the indices (with the top 6 days highlighted in bold):

daily stats

It’s both unexpected and quite interesting that despite extremely high correlations the last few years among these indices, there is significant variation between the optimal days for each one.

One common feature across all three indices is that the Top 6 days tend to be more volatile. Could it be that the day of the month effect is not an anomaly, but compensation for taking on more risk? Given the very small magnitude of volatility differences but significant differences in returns, I doubt it.

Another possible explanation that seems intuitive is institutional money flows. Yet it is difficult to justify that explanation when there are such large differences between the three indices: why would big money pile in to the Russell 2000 stocks, and out of the S&P 500 stocks on the last day of the month? For now, a good explanation of the effect eludes me…


By itself, day of the month seasonality is not a trading strategy. While there is substantial protection on the downside compared to buy & hold, commissions would completely destroy the returns. On the other hand, there seems to be potential in using the day of the month as an additional factor in an existing trading model or as an input in a discretionary swing trading approach.

As an example I have constructed a very simplistic trading strategy based on the S&P 500: go long if RSI(3) is below 5. I then filter the trades based on whether they are in one of the top 6 days (once again, the top 6 days are determined using walk-forward optimization so there is no look-ahead bias here).

The “RSI(3) < 5” rule by itself has an average daily return of 0.046% (0.259% since 2002); after using the filter, the rule returns 0.143% on average (0.458% since 2002). Overall using the filter, the strategy achieves roughly the same returns with less than a third of the trades.

RSI(3) Rules S&P500 Equity Curves


In the next parts I will investigate how these effects hold up in European and Asian Markets, and perhaps even non-equity markets.

Read more Day of the Month Seasonality Part 1: S&P 500, NASDAQ Composite, Russell 2000