Wednesday, January 08, 2014

Variance Risk Premium for Return Forecasting

Folklore has it that VIX is a reasonable leading indicator of risk. Presumably that means if VIX is high, then there is a good chance that the future return of the SP500 will be negative. While I have found some evidence that this is true when VIX is particularly elevated, say above 30, I don't know if anyone has established a negative correlation between VIX and future returns. (Contemporaneous VIX and SP500 levels do have a very nice linear relationship with negative slope.)

Interestingly, the situation is much clearer if we examine the Variance Risk Premium (VRP), which is defined as the difference between a model-free implied volatility (of which VIX is the most famous example) and the historical volatility over a recent period. The relationship between VRP and future returns is examined in a paper by Chevallier and Sevi in the context of OVX, which is the CBOE Crude Oil Volatility Index. They have found that there is a statistically significant negative linear relationship between VRP and future 1-month crude oil futures (CL) returns. The historical volatility is computed over 5-minute returns of the most recent trading day. (Why 5 minutes? Apparently this is long enough to avoid the artifactual volatility induced by bid-ask bounce, and short enough to truly sample intraday volatility.)  If you believe in the prescience of options traders, it should not surprise you that the regression coefficient is negative (i.e. a high VRP predicts a lower future return).

I have tested a simple trading strategy based on this linear relationship. Instead of using monthly returns, I use VRP to predict daily returns of CL. It is very similar to a mean-reverting Bollinger band strategy, except that here the "Bollinger bands" are constructed out of moving first and third quartiles of VRP with a 90-day lookback. Given that VRP is far from normally distributed, I thought it is more sensible to use quartiles rather than standard deviations to define the Bollinger bands. So we buy a front contract of CL and hold for just 1 day if VRP is below its moving first quartile, and short if VRP is above its moving third quartile. It gives a decent average annual return of 17%, but performance was poor in 2013.

Naturally, one can try this simple trading strategy on the E-mini SP500 future ES also. This time, VRP is VIX minus the historical volatility of ES.  Contrary to folklore, I find that if we regress the future 1 day ES return against VRP, the regression coefficient is positive. This means that an increase of VIX relative to historical volatility actually predicts an increase in ES! (Does this mean investors are overpaying for put options on SPX for portfolio protection?) Indeed, the opposite trading rules from the above give positive returns: we should buy ES if VRP is above its moving third quartile, and short ES if VRP is below its moving first quartile. The annualized return is 6%, but performance in 2013 was also poor.

As the authors of the paper noted, whether or not VRP is a strong enough stand-alone predictor of returns, it is probably useful as an additional factor in a multi-factor model for CL and ES. If any reader know of other volatility index like VIX and OVX, please do share with us in the comments section!

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My online Backtesting Workshop will be offered on February 18-19. Please visit epchan.com/my-workshops for registration details. Furthermore, I will be teaching my Mean Reversion, Momentum, and Millisecond Frequency Trading workshops in London on March 17-21, and in Hong Kong on June 17-20.

55 comments:

Anonymous said...

There also are a gold ETF (GLD) volatility index (GVZ) and a gold Comex futures volatility index (GVX).

http://www.cboe.com/micro/gvz/introduction.aspx

http://www.barchart.com/charts/stocks/$GVX

Ernie Chan said...

Thanks, Anon.
I find that GVZ is like OVX: the lower the VRP, the higher the future return of gold future.
Ernie

Anonymous said...

Hi Ernie,

Here are some more:
"VIX","V2X","V1X","VSMI","VNKY","VHSI","VKOSPI","AS51VIX","INVIXN","VXEEM","VXEWZ","VXFXI","VXN","RVX","GVZ","VXSLV","OVX","CIV","WIV","SIV"

Cheers!

Anonymous said...

Hi Ernie,

thanks for sharing: I read this paper few months ago but I didn't pay attention on it. Now you publish this post on your blog and I'm finding it more relevant!

One question: which kind of R^2 level did you find with your analysis? Because the authors, on the multivariate analysis on monthly excess returns, found R^2 equal to 15-20%

Ernie Chan said...

Hi Anon,
Thanks for your extensive list!
Ernie

Ernie Chan said...

Hi Anon,
I analyzed only daily returns, and regress only against VRP. The R^2 is very small (0.002).

Ernie

Anonymous said...

Hi Ernie,

What is a typical IP (intellectual property right) clause in a hedge fund contract? Is is standard that all models you develop may not be used when you move to a new firm? And how do you define a "model", is it exactly the same code or more loosely the concept? These seem to be tricky issues.

Ernie Chan said...

Hi Anon,
Each contract is different of course.
But most probably you can't take the software code from one fund to another. Whether you can take the trading idea or not is more murky and hard to define.
Ernie

Paul said...

Hi Ernie
Happy new year and thanks for the sharing.
I am curious that given the R square being zero, how would you interpret the regression coefficient? I think whether it is positive or negative it doesnt have much indicative power?

Cheers

Ernie Chan said...

Hi Paul,
Happy New Year to you too.

Your question is a very good one.

I have found that whenever we are using linear regression for predicting future returns (as opposed to, say, finding the hedge ratio between two cointegrated ETFs), the R^2 is always close to 0.

This is not surprising because if the R^2 is significant, every trader in the world would be trading it already, erasing the predictability!

However, a R^2 close to zero does not mean that our trading strategy won't be profitable. That is the great irony of quantitative trading in contrast to most economic or commercial predictions. (I bet Walmart can predict next month's customer demand for a brand of toaster much better than I can predict tomorrow's SPX level!)

Ernie

Anonymous said...

Following up on your discussion about R2. If you have a statistically significant coefficient and an R2 an epsilon above 0, you have slightly better odds than 50/50. Hence you should take that bet as often as possible, while of course managing your risk correctly.

/Hank

Ernie Chan said...

Agreed, Hank.

Anonymous said...

Hi Ernie,

Have you ever come across a deal whereby an employee that leaves the firm, the former employer continues to run his strategies and pays him a royalty on the strategies P&L he developed?

I guess the former employer could always say they have improved/altered the strategy to such an extent that the original model/code does not warrant any royalty anymore, right?

What are your thoughts on this?

Thanks

Ernie Chan said...

Hi Anon,
One can certainly sign a contract with one's employer with such favorable terms to you, though unless you are a well-known high-powered trader, I doubt many employers would opt for such a contract.

More typically, and by default, the employer owns all rights to your work there. Not only are you not entitled to royalties after termination, you are not permitted even to trade those models you developed during your employment.

Ernie

Anonymous said...

Ernie, thanks for your reply.

Would you say prop trading firms compared to hedge funds are lighter in terms of IP rights and non-compete clauses meaning they allow one to go on and trade ones models elsewhere?

Ernie Chan said...

Hi Anon,
There are 2 kinds of prop trading firms.

First kind: you are not an employee, and often you have to risk your own capital to trade your model, though the firm will provide sky-high buying power (leverage). You typically own all IP in this situation.

Second kind: you are an employee and are paid a salary no matter your model is profitable or not. In this situation, it is no different from a hedge fund: the firm typically owns all IP.

Ernie

Anonymous said...

Hi Ernie,

What's the typical way of starting ones own fund? Say I trade with around $300k of my own money and have a Sharpe above 2 over a 1 year period.

Would it be possible to start attracting funds on this performance? I guess first family offices would be the place to go, right?

Do investors value the track record higher if you have actually traded for a fund rather than with your own (limited) money?

Ernie Chan said...

Hi Anon,
To start a fund, you would need to get a 3rd party administrator to assure people you won't take their money and run, and to prepare monthly statements. And you need to get a lawyer to write the Disclosure Document. Finally, you need to get accountant and auditor separately to prepare tax filings and annual audits. It is going to be expensive.

Typically, you would convince wealthy individuals to invest before you can convince institutional investors. Obviously you can do it in whichever order you think works for you.

I think it is much easier to start a managed account business than to start a fund.

Ernie


Anonymous said...

Ernie,

A low cost option seems to be to start an off-shore incubator fund and trade on IB with managed accounts. What's your view on that?

Ernie Chan said...

Anon,
I don't know why you need to start an incubator fund if you are going to manage separate accounts anyway.

Offshore funds are even more expensive to start than US-domiciled funds, if your investors are US entities. Unless you have pension plans investing with you, I see no benefit in doing so.

Ernie

Anonymous said...

So how does it usually work with managed accounts? I only need a simple company with an IB account to start hooking up managed accounts? Or I can even by an individual person (not a company of any form) that hook up managed accounts?

Ernie Chan said...

If an investor hires you to manager his/her account, you don't need to do anything but to get him/her to give you power of attorney to enter trades.

If, on the other hand, you want to directly withdraw fees from those accounts, you need to be a Registered Investment Advisor, or Commodity Trading Advisor, before IB will let you do that.

Ernie

DR said...

If you want to trade equity indices using a similar strategy you have an additional indicator, not available in crude space.

Namely you can use the same logic on the implied and historical correlation. Implied correlation you can back out by subtracting VIX from the mean ATM Black-Scholes implied volatility for each individual name in S&P 500. Similarly you can construct a CRP (correlation risk premium).

Since correlation and volatility in equities tend to move together CRP and VRP will be somewhat correlated. But my guess is that CRP might be more predictive than VRP for several reasons.

1) It's not directly observable like VIX, so less people probably trade on it. 2) Correlation tends to be more indicative of systematic risk than even volatility (correlations almost always go to 1 in crises). 3) Premiums for correlations indicate how many people are stock-picking vs indexing, which affects market dynamics.

Ernie Chan said...

DR,
Thanks for your insight.

There is a slight disadvantage in computing implied volatility of stocks based on the BS model: it depends on the correctness of BS. On the other hand, VIX is model-free.

Ernie

Anonymous said...

Hi Ernie,

Sorry, the previous list contains only indices available in Bloomberg. There are many more volatility indices calculated by CBOE using the variance swap replication method.
http://www.cboe.com/micro/volatility/introduction.aspx.

Cheers,
lcs

Alexander Kurguzkin said...

Hi,

I've made some research, it seems VRP works ok at least for S&P 500:

http://volatility-fighter.blogspot.com/2014/01/using-variance-risk-premium-for-price.html

Anonymous said...

Have anyone used the new Trading toolbox in Matlab R2013b to connect to IB? Any views or comments are highly appreciated.

I am currently using IB-Matlab provided by undocumentedmatlab.com but find it a bit slow when requesting multiple quotes.

Ernie Chan said...

Hi Ics,
Thanks for the link!
Ernie

Ernie Chan said...

Hi Alexander,
Nice results! Thanks for posting!
Ernie

Anonymous said...

Hello Ernie
In the chapter 6 of your new book,where you use TU as an example to illustrate the time series momentum strategy, I am confused with the concept "lagged roll return". How you define lagged roll return? Lagged Total Return minus lagged spot return?
阮迅

Ernie Chan said...

Hi 阮迅,
Yes, lagged roll return is the roll return over a lagged lookback window. Roll return is total return minus spot return.
Ernie

experquisite said...

Hi Ernie,

I finally have enough confidence in my maths to work through your second book properly. I notice you make extensive use of the jplv7 econometrics toolbox. Is the textbook itself worth a purchase? I do have a ton of reading to do already, but if I don't buy books when I think of them, I just forget about them :)

Thanks.

Ernie Chan said...

Hi experquisite:
The jplv7 toolbox and manual are both free for download at spatial-econometrics.com.
Ernie

HK said...

Hi Ernie,

Happy Chinese New Year!

I find out one of the famous proprietary trading firms in US has one of their 3 offices in Hong Kong, and the firm mainly uses stats arbitrage. What could be the possible reason that they choose Hong Kong for stats arbitrage? I cannot see there is any good stats arbitrage opportunity in HK market except they do something like index arbitrage. Besides, why would they hire traders to manually do stats arbitrage? Seem like the firm mainly uses their own money to trade so I guess their traders shouldn't be focus on entertaining clients.

-HK

Ernie Chan said...

Hi HK,
Happy CNY!
Just because a firm has office located in HK doesn't mean it is trading the HK markets. It may be trading Singaporean or Japanese stocks or futures.
Algo trading shops still need "traders" because the software can break down from time to time.
Ernie

HK said...

Hi Ernie,

I am thinking why the ETF of china market 2822, 2823 in Hong Kong Exchange don't move much after China market closes at 3pm, while the "GXC" SPDR S&P China ETF in USA market would have continuously movement in US trading hours. Could that because there are active ADRs of china stocks in US market while there is no ADR of china stocks in European market? There are a lot of H-share stocks in Hong Kong market that are main shares of China market, but seem like these H-share stocks would not affect 2822, 2823 pricing after 3pm while HK stock market closes at 4pm.

-HK

Ernie Chan said...

Hi HK,
Yes, GXC does contain ADRs, so definitely it should move during US market hours.

I don't know what the compositions of 2822 or 2823 are, so I wouldn't know why they don't move in the last hour.
Ernie

HK said...

Hi Ernie,

ETF 2822 directly holds A-share stocks in China. 2823 holds derivatives to simulate direct holding A-share stocks.

-HK

Ernie Chan said...

Hi HK,
Good to know that.
In that case, these ETFs definitely should not move after Chinese markets are closed.
Ernie

HK said...

Hi Ernie,

Thanks. The concept is very interesting that 2823 and 2822 suppose to follow the A50 future in SGX which trades 16 hours day, but the components inside 2822 and 2823 are A-shares real stocks/derivatives then they just don't move much after 3pm. I just check the A50 future SGX daily chart, and it looks like it keeps moving in 16 hours including that 3pm to 4pm period.

-HK

HK said...

Hi Ernie,

Let's say if I have 100K US dollars to buy a very popular huge trading volume stock for day trade, which case would have better chance to execute faster? Here are the two cases:
1. 100K in one brokerage firm A
2. 50K in brokerage firm A and 50K in brokerage firm B, both have buy command at the same time.

-HK

Ernie Chan said...

Hi HK,
Execution speed is highly dependent on the smart router of your brokerage. Most times, your order will never even make it out to the open market: they are internally matched.

Ernie

HK said...

Hi Ernie,

You make a very good point, thanks.

-HK

HK said...

Hi Ernie,

I checked and the interest cost to short etf/stock per trade within a day should be between 0.5% to 0.75% per trade for normal size retail account. So seem like this is too expensive to arbitrage for day trade especially ms speed range. So is that arbitrage day trade only makes sense for millions or more US dollars account to decrease the cost to reasonable level?

-HK
-HK

Ernie Chan said...

Hi HK,
If you don't hold your positions overnight, there is no interest charged.
Ernie

The Wave said...

So, BTW, since no one else has asked, what were the returns for the two approaches in 2013 (or alternatively, what were the annual returns you came up with)? That would seem to be of great interest! Thank you!

Ernie Chan said...

Hi Wave,
Actually, I only have data up to 20130617, and for that half year, the annualized return for the CL model is 4.7%. For ES model, it is -17%.
Ernie

Anonymous said...

Hi Ernie,

May I ask how much annual return we can expect from pairs trading using proper leverage in a normal year?

Thanks.

Ernie Chan said...

Hi Anon,
Pairs returns have decreased in recent years due to reduced spreads and volatility. The returns will depend on your exact implementation, but I don't expect it to be more than 10% p.a.
Ernie

Anonymous said...

Hi Ernie,

Is 10% before leverage or after leverage?

Thanks.

Ernie Chan said...

Hi Anon,
10% is levered, assuming an appropriate leverage based on Kelly formula.
Ernie

Anonymous said...

Hi Ernie,

May I ask how many pairs you usually trade in your pairs portfolio?

Do you apply Kelly formula to each pairs?

Or you apply Kelly to the whole pairs portfolio?

It seems stock pairs is more volatile than ETFs pairs.
Would you try to trade some stock pairs?

Thanks

Ernie Chan said...

Hi Anon,
I only traded ETF, not stock, pairs. Typically we have 4-8 such pairs. We apply Kelly to the portfolio of pairs.
Ernie

seetheworld said...

Hi Ernie,

VRP looks like a good indicator for stock and oil futures. Do you think so? What other factors do you think of as good indicators?

I am a Phd finance candidate trying to come with meaningful research on return prediction. Could you suggest some topic in the regard?


Thanks,
Charlie

Ernie Chan said...

Hi Charlie,
Please see all my blog articles labeled "factor model" and you will find many other factors relevant to stocks.

Ernie