The VIX:VXV Ratio

The VXV is the VIX’s longer-term brother; it measures implied volatility 3 months out instead of 30 days out. The ratio between the VIX and the VXV captures the differential between short-term and medium-term implied volatility. Naturally, the ratio spends most of its time below 1, typically only spiking up during highly volatile times.

VIX VXV Ratio Chart

It is immediately obvious by visual inspection that, just like the VIX itself, the VIX:VXV ratio exhibits strong mean reverting tendencies on multiple timescales. It turns out that it can be quite useful in forecasting SPY, VIX, and VIX futures changes.

Short-term extremes

A simplistic method of evaluating short-term extremes is the distance of the VIX:VXV ratio from its 10-day simple moving average. When the ratio is at least 5% above the 10SMA, next-day SPY returns are, on average, 0.303% (front month VIX futures drop by -0.101%). Days when the ratio is more than 5% below the 10SMA are followed by -0.162% returns for SPY. The equity curve shows the returns on the long side:

short term EC

Long-term extremes

When the ratio hits a 200-day high, next-day SPY returns have been 0.736% on average. Implied volatility does not fall as one might expect, however.

More interestingly, the picture is reversed if we look at slightly longer time frames. 200-day VIX:VXV ratio extremes can predict pullbacks in SPY quite well. The average daily SPY return for the 10 days following a 200-day high is -0.330%. This is naturally accompanied by increases in the VIX of 1.478% per day (the front month futures show returns of 1.814% per day in the same period). It’s not a fail-proof indicator (it picked the bottom in March 2011), but I like it as a sign that things could get ugly in the near future. We recently saw a new 200-day high on the 19th of December: since then SPY is down approximately 1%.

200d high cumulative

 

This is my last post for the year, so I leave you with wishes for a happy new year! May your trading be fun and profitable in 2013.

Holiday Effects in the Chinese Stock Market

Various holiday effects are well documented for developed countries’ stock markets, typically showing abnormal returns around thanksgiving, Christmas, New Year, and Easter. Do similar effects exist in the Chinese stock market? In this post I’ll take a look at returns to the Shanghai Composite Index (SSECI) during the days surrounding the following holidays: New Year, Chinese New Year, Ching Ming Festival, Labor Day, Tuen Ng Festival, Mid-Autumn Festival. The index only has 22 years of history, so statistical significance is difficult to establish. Despite this, I believe the results are quite interesting1.

The charts require a bit of explanation: the error bars are 1.65 standard errors wide on each side. As such, if an error bar does not cross the x-axis, the returns on that day are statistically significantly different from zero at the 5% level (by way of a one-tailed t-test). The most interesting holidays are the New Year, Chinese New Year, and Ching Ming Festival, all of which have several days of quite high returns around them.

New Year

new year

Chinese New Year

chinese new year

Ching Ming Festival

The Ching Ming Festival occurs 15 days after the vernal equinox, which is either April 4th or April 5th.

ching ming festival

Labor Day

labor day

Tuen Ng Festival

The Tuen Ng Festival (A.K.A. Dragon Boat Festival) occurs on the 5th day of the 5th lunar month in the Chinese calendar.

tuen ng festival

Mid-Autumn Festival

The Mid-Autumn Festival falls on the 15th day of the 8th lunar month.

mid autumn festival

Bonus: Day of the Month Effects

Since we’re looking at seasonality effects, why not the day of the month effect as well? Using the walk-forward methodology as in my previous day of the month effect posts (U.S., Europe, Asia), here are the results for the Shanghai Composite Index:

dotm china EC

dotm china stats

Finally, the average returns for each day of the month over the last 5000 days:

dotm china days

The standard turn of the month effect seems to be present, but only for the first days of the month instead of the last and first days.

And with that, I’d like to you wish you all happy holidays! In eggnog veritas.

Footnotes
  1. I want to take this opportunity to thank the C# language designers; without the ChineseLunisolarCalendar class this study would’ve been a major chore.[]

IBS and Relative Value Mean Reversion

I’m writing a paper on the IBS effect, but it’s taking a bit longer than expected so I thought I’d share some of the results in a blog post. The starting point is a paper by Levy & Lieberman: Overreaction of Country ETFs to US Market Returns, in which the authors find that country ETFs over-react to US returns during non-overlapping trading hours, which gives rise to abnormal returns as the country ETFs revert back the next day. In terms of the IBS effect, this suggests that a high SPY IBS would lead to over-reaction in the country ETFs and thus lower returns the next day, and vice versa.

To quickly recap, Internal Bar Strength (or IBS) is an indicator with impressive (mean reversion) predictive ability for equity indices. It is calculated as follows:

IBS

Using a selection of 32 equity index ETFs, let’s take a look at next-day returns after IBS extremes (top and bottom 20%), split up by SPY’s IBS (top and bottom half):

 returns by SPY IBS

The results were the exact opposite of what I was expecting. Instead of over-reacting to a high SPY IBS, the ETFs instead under-react to it. A high SPY IBS is followed by higher returns for the ETFs, while a low SPY IBS is followed by lower returns. These results suggest a pair approach using SPY as the first leg of the pair, and ETFs at IBS extremes as the other. For a dollar-neutral strategy, the rules are the following:

  • If SPY IBS <= 50% and ETF IBS > 80%, go long SPY and short the other ETF, in equal dollar amounts.
  • If SPY IBS > 50% and ETF IBS < 20%, go short SPY and long the other ETF, in equal dollar amounts.

The results1:

pair strat returns

The numbers are excellent: high returns and relatively few trades with a high win rate. Let’s take a look at the alphas and betas from a regression of the excess returns to the pair strategy, using the Carhart 4 factor model:

four factor regression

Values in bold are statistically significantly different from zero at the 1% level.

On average, this strategy generates a daily alpha of 0.037%, or 9.28% annually, with essentially zero exposure to any of the factors. Transaction costs would certainly eat into this, but given the reasonable amount of trades (about 23 trades per year per pair on average) there should be a lot left over. The fact that over 90% of days consist of zero excess returns obscures the features of the actual returns to the strategy. Repeating the regression using only the days in which the strategy is in the market yields the following results:

four factor regression trade days only

Values in bold are statistically significantly different from zero at the 1% level.

Unfortunately, these results are pretty much a historical curiosity at this point. Most of the opportunity has been arbitraged away: during the last 4 years the average return per trade has fallen to 0.150%, less than half the average over the entire sample. The parameters haven’t been optimized, so there may be more profitable opportunities still left by filtering only for more extreme values, but it’s clear that there is relatively little juice left in the approach.

In fact if we take a closer look at the differences between the returns before and after 2008, the over-reaction hypothesis seems to be borne out by the data (another factor that may be at play here are the heightened correlations we’ve seen in the last years): low SPY IBS leads to higher next-day returns for the ETFs, and vice versa.

pre and post 2008 results

The lesson to take away from these numbers is that cross-market effects can be very significant, especially when global markets are in a state of high correlation. Accounting for the state of US markets in your models can add significant information (and returns) to your IBS approach.

Footnotes
  1. As with any dollar-neutral approach, calculating returns is a tricky matter; in this case I have calculated the returns as a % of the capital allocated to one of the legs[]

A Quick Look at IB’s Equity Index CFDs

I recently got a mail from IB touting their new lineup of equity index CFDs. As I trade a lot of equity index ETFs I thought I’d take a look at them, in case I could get away with lower margins and/or commissions. Here’s a quick summary of what they offer:

Pros:

  • Granularity compared to futures, minimum size $1 x index value (for U.S. indices).
  • Reasonable commissions.
  • Low margin requirements compared to ETFs.

Cons:

  • No MOC/LOC orders, or any way to not pay the spread.
  • Local regular trading hours only, sometimes not even that. Can’t trade foreign index CFDs at the end of the US session.
  • Trade in local currency, conversion costs if trading foreign indices.
  • Pretty low size limits for any one order.
  • Interest amounts to an additional cost of ~0.004% per day held.
  • Found fills to be somewhat haphazard, even for small order sizes.

Assuming $0.005 per share in commissions and $0.01 in slippage for ETFs, and $1.64 in commission and 1 tick in slippage for futures, here’s how they stack up against each other:

  S&P 500
  CFD ETF (SPY) Futures (ES)
Market (1 tick slippage) 0.023% 0.011% 0.020%
Limit/On Close (no slippage) N/A 0.004% 0.002%

 

  NASDAQ 100
  CFD ETF (QQQ) Futures (NQ)
Market (1 tick slippage) 0.019% 0.023% 0.012%
Limit/On Close (no slippage) N/A 0.008% 0.003%

The costs are similar for all three instruments if you’re doing market orders, though CFDs can of course get costlier if held for longer periods of time. The main advantage of CFDs is the ability to control size compared to futures which are not particularly granular. For that privilege you give up the flexibility of trading outside RTH, which can be a significant disadvantage if you want to place protective stops, or want to trade foreign indices at the end of the day.

Another alternative, of course, are leveraged ETFs, which tend to offer a lower commission per unit of exposure, but have other costs associated with them: spreads for ETFs such as QLD (2x) and TQQQ (3x) are generally at 2-3 cents, management fees of around 1% p.a. (or about 0.0027% per day), as well as potential rebalancing costs. They also do not offer any advantage in terms of margin.

Hedging VIX ETP Strategies Using SPY

Introduction

A quick intro to VIX ETPs (some are ETFs, others are ETNs)1 before we get to the meat: the VIX itself is not tradable, only futures on the VIX are. These futures do not behave like equity index futures which move in lockstep with the underlying, for a variety of reasons. A way to get exposure to these futures without holding them directly, is by using one or more VIX futures-based ETPs. These come in many varieties (long/short, various target average times to expiration, various levels of leverage).

The problem with them, and the reason they fail so badly at mirroring movements in the VIX, is that they have to constantly roll over their futures holdings to maintain their target average time to expiration. A 1-month long ETP will be selling front month futures and buying 2nd month futures every day, for example. Front month futures are usually priced lower than 2nd month futures, which means that the ETP will be losing value as it makes these trades (it’s selling the cheap futures and buying the expensive ones), and vice versa for short ETPs. This amounts to a transfer of wealth from hedgers to speculators willing to take opposite positions; this transfer can be predicted and exploited.

I’ll be looking at two such VIX futures-based instruments in this post: VIXY (which is long the futures), and XIV (which is short the futures). As you can see in the chart below, while the VIX is nearly unchanged over the period, VIXY has lost over 80% of its value. At the same time, XIV is up 50% (though it did suffer a gigantic drawdown).

prices

There are many different approaches to trading these ETPs (for example Mike Brill uses realized VIX volatility to time his trades). The returns are driven by the complex relationships between the value of the index, the value of the index in relation to its moving average, the value of the futures in relation to the index, and the value of various future maturities in relation to each other. These relationships give rise to many strategies, and I’m going to present two of them below.

I’ll be using different approaches for the long and short sides of the trades. Short based on the ratio between the front and 2nd month contract, and long using the basis. Here are the rules:

Go long XIV at close (“short”) when:

  • 2nd month contract is between 5% and 20% higher than the front month contract.

Go long VIXY at close (“long”) when:

  • Front month future is at least 2.5% below the index.
Finally, if both of the above conditions are triggered, go to cash.

Results

First let’s have a look at how these strategies perform without the hedge. Using data from January 2011 to November 2012, here are the daily return stats for these two approaches individually and when combined:

stats unhedged

Equity curves & drawdowns:

EC-and-DD-unhedged

The biggest issues with VIX ETN strategies are large drawdowns, and large sudden losses when the VIX spikes up (and to a lesser extent when it spikes down; these tend to be less violent though). A spike in implied volatility is almost always caused by large movements in the underlying index, in this case the S&P 500. We can use this relationship in our favor by utilizing SPY as a hedge.

  • When long XIV, short SPY in an equal dollar amount.
  • When long VIXY, go long SPY in an equal dollar amount.

The stats:

stats hedged

And the equity curves & drawdowns:

EC-and-DD-hedged

The results are quite good. The bad news is that we have to give up about 40% of CAGR. On a risk-adjusted basis, however, returns are significantly improved.

  • CAGR / St. Dev. goes from 38.7 to 45.9.
  • CAGR / Max Drawdown goes from 4.5 to 4.9.

All risk measures show significant improvement:

  • The worst day goes from a painful -12% to a manageable -9%.
  • Maximum drawdown goes from -36.5% to -25.7%.
  • Daily standard deviation goes from 4.28% to 2.76%.

Of course, just because risk-adjusted returns are improved does not mean it’s necessarily a good idea. Holding SPY results in both direct costs (commissions, slippage, shorting costs) as well as the opportunity cost of the capital’s next-best use. The improvement may not be enough to justify taking away capital from another system, for example.

Another possibility would be to implement this idea using options, which have the benefit of requiring a small outlay. Especially when holding XIV, SPY puts could be a good idea as both implied volatility and price would move in our direction when the VIX spikes up. However, this must be weighted against theta burn. I don’t have access to a dataset for SPY options to test this out, unfortunately (anyone know where I can get EOD options data that is not absurdly expensive?).

If you want to play around with the data yourself, you can download the spreadsheet here.

Footnotes
  1. If you live in the U.S. there can be important differences in tax treatment depending on which one you trade, so do your research.[]