Daily Commentary -
Posted on **Saturday, November 15, 2014, 7:35 PM GMT +1**

## DDN’s Volatility Risk Premium Strategy Revisited (3)

A couple of weeks ago I started a series of postings, all dealing with trading volatility ETNs / ETFs like XIV^{®} (VelocityShares Daily Inverse VIX Short-Term ETN) and VXX (iPath® S&P 500 VIX Short-Term Futures™ ETN) and respective trading strategies. One of those strategies was DDN’s VRP Strategy (Double-Digit Numerics , Volatility Risk Premium) due to its exceptional performance – at least until December 2012 – and its compelling approach (from the paper Easy Volatility Investing from Double-Digit Numerics).

In my last posting DDN’s Volatility Risk Premium Strategy Revisited (2) I introduced the CBOE Mid-Term Volatility Index (Ticker: VXMT^{®}) as a proxy for implied volatility (expected volatility of the S&P 500 Index over a 6-month time horizon), which shows much better results than using the CBOE Volatility Index (Ticker: VIX^{®}). But there is a catch: the VXMT^{® }‘s outperformance ended in June 2013 (more on that below).

But first of all the original Volatility Risk Premium (VRP) Strategy rules (always market on close):

- Long
**XIV**: 5-day average of [VIX^{®}*or*VXMT^{®}– (2-day historical volatility of S&P 500 * 100)]**>**0

(*Please note: Before 2008, VIX*)^{®}instead of VXMT^{®}is used - Long
**VXX**: 5-day average of [VIX^{®}*or*VXMT^{®}– (2-day historical volatility of S&P 500 * 100)]**<**0 - Hold until a change in position.

Image I shows the respective equity curves, DDN’s VRP (original strategy) (**red line**, using a 10-day historical volatility), the VIX^{®} index version (**blue line**) and the VXMT^{®} index version (**black line**). The yellow area shows the VXMT^{®} ‘s index version percentage-wise outperformance compared to the VIX^{®} index version.

Please note: The CBOE provides VXMT^{®} historical data back to 1/8/2008. Before 2008, VIX^{®} has been used instead (therefore both strategies do not differ before 1/7/2008). The VXMT^{®} index version outperformed it’s counterpart by a wide margin (topping out in June 2013), but has given back half of its percentage-wise outperformance since then. The question is: What is the reason behing the VXMT^{®} ‘s index version decline in performance relative (not in absolute terms) to the VIX^{®} index version ?

**Image I – Total Equity and Drawdown Curve(s)****(03/25/2004 – present)**(slippage, fees and transaction costs are assumed to total 0.1% per trade)

The reason for the breakdown in performance ( DDN’s VRP Strategy ) and the out-/underperformance of the VXMT^{®} ‘s index version relative to the VIX^{®} index version imay be many-faceted, e.g. changes in the relationship between VIX^{®} and VXMT^{®} (ratio and/or premium, backwardation and contango, …), the relationship between implied and realized volatility, premium of VIX front and second month futures (as a basis for VXX^{®} and XIV^{®} ), among others.

Image II may present some insights and a first indication and shows:

**relationship/delta****of**VIX^{®}and VXMT^{®}**strategy****triggers**(for going long or short volatility):

5-day moving average of [VIX^{®}– 2-day historical volatility of S&P 500 * 100]**–**

5-day moving average of [VXMT^{®}– 2-day historical volatility of S&P 500 * 100]**Volatility Risk Premium**(potential gain):

1-month moving average of [VX_{1}|VX_{2}(30-day const. maturity) – 2-day historical volatility of S&P 500 * 100]- the S&P 500
^{®}Index

**Image II – Volatility Risk Premium and VIX ^{®} vs. VXMT^{®}**

(01/07/2008 – present)

(01/07/2008 – present)

Right at the start of the bull market in 2009 (at the end of the financial crisis), VIX^{®} front and second month futures (Ticker: VX_{1}|VX_{2}) (merged into a continual time series as a 30-day constant-maturity futures prices, as they are the basis for VXX^{®} and XIV^{®}) were trading at a huge premium to the then current realized (2-day historical) volatility, but as investor complacency grew into the ongoing bull market, the delta between realized and implied volatility faded and is now merely at half the levels of 2009.

The same reason, but a different effect: While at first (2009) the VIX^{®} index came down from historical high levels back to historically normal levels (from backwardation into contango), 6-month looking forward implied volatility (VXMT^{®}) remained relatively flat, reverting a positive spread between VIX^{®} and VXMT^{®} into a widening negative one. But that trend was reversed in 2012. As investor complacency grew, 6-month looking forward implied volatility (VXMT^{®}) was (and still is) on the wane. (Looking forward) Volatility slumps as complacency regains the upper hand.

Between 2009 and the end of 2012, every up-move in the markets was accompanied by a widening spread (regularly up to -7 – -8 percentage points) between VIX^{®} and VXMT^{® }(investor scepticism remaind relatively high), but since January 2013 the (averaged) spread between VIX^{®} and VXMT^{® has }remained well below -5 (percentage points). For examplary purposes: With VIX^{®} at or around **13**, it is like VIX futures with a 6 month maturity would’ve been trading at or around **21** in 2009, while they’re trading below **18** today. Means investor fear looking 6 month ahead is currently at significantly lower levels than it had been in 2009.

Image III now shows the relationship between implied (VXMT^{®} index as expected volatility of the S&P 500 Index over a 6-month time horizon) and historical (annualized, 2-day realized) volatility. Since 2013, the gap has remained flat (constant) at historically low levels at or around -15%.

**Image III – VXMT ^{®} and Historical Volatility **

(01/07/2008 – present)

(01/07/2008 – present)

Due to the fact that the gap between implied volatility and historical (realized) volatility remained constant/flat over the course of the last year and a half, the Volatility Risk Premium Strategy utilizing the VXMT^{®} index was at a disadvantage compared to it’s VIX^{®} counterpart : With volatility of volatility dwindling away, the “*5-day average of [VXMT ^{®} – (2-day historical volatility of S&P 500 * 100)] > 0*” remained almost constant/flat in positive territory and closed below ‘0’ (trigger value for going long volatility) less often than before June 2013 (to be exact: now in 1 out of 30 sessions only instead of 1 out of 10 sessions before), means it mimics more or less a Buy&Hold XIV

^{®}strategy instead of taking benefit of both sides of the trade (assumed going long volatility after 6/30/2013 had been as profitable as it had been before 6/30/2013). By contrast the VIX

^{®}based strategy remained (almost) unaffected (because the VIX

^{®}is trading a couple of index points below the VXMT

^{®}index), still going long volatility in approximately 1 out of 10 sessions.

Image IV shows the distribution of the results of the formula “*5-day average of [VXMT ^{®} – (2-day historical volatility of S&P 500 * 100)] > 0*” , overall, before and after 6/30/2013.

**Image IV -Distribution of Trigger Values**

(01/07/2008 – present)

Possible solutions to fix that problem:

- using a different cutoff (other than ‘0’),
- using a different x-day historical volatility and/or y-day moving average,
- making the system adaptive (incorporating a learning curve, from my perspective the most interesting approach),
- …

* to be continued* … (means more on this to come, stay tuned)

__________________

Have a profitable week,

**Frank**

**Disclosure**: I’am long/short XIV, and long/short VIX, RVX and EURO STOXX 50 volatility futures.

*________________________________*

**Remarks**: Due to their conceptual scope – and if not explicitly stated otherwise – , all models/setups/strategies do not account for slippage, fees and transaction costs, do not account for return on cash and/or interest on margin, do not use position sizing (e.g. Kelly, optimal f) – they’re always ‘*all in*‘ – , do not use leverage (e.g. leveraged ETFs), do not utilize any kind of abnormal market filter (e.g. during market phases with extremely elevated volatility), do not use intraday buy/sell stops (end-of-day prices only), and models/setups/strategies are not ‘*adaptive*‘ (do not adjust to the ongoing changes in market conditions like bull and bear markets). Index data (e.g. S&P 500 cash index) does not account for dividend and cash payments.

*________________________________*

**Disclaimer**

The information on this site is provided for statistical and informational purposes only. Nothing herein should be interpreted or regarded as personalized investment advice or to state or imply that past results are an indication of future performance. The author of this website is not a licensed financial advisor and will not accept liability for any loss or damage, including without limitation to, any loss of profit, which may arise directly or indirectly from use of or reliance on the content of this website(s). **Under no circumstances does this information represent an advice or recommendation to buy, sell or hold any security.**

I may or may not hold positions for myself, my family and/or clients in the securities mentioned here. Actions may have been taken before or after information is presented, and any opinions expressed in this site are subject to change without notice.

(Data courtesy of MetaStock and Pinnacle Data Corp., and for data import, testing, surveys and statistics I use **MATLAB** from MathWorks)

## Comments (18)

Frank,

Thanks for all the good work you’ve done on this. Some of my readers contend that there’s a bit of data mining/over-optimization you’ve done to arrive at your instrument choice/parameters, which I intend to test.

That stated, if the VIX variant catches up to the VXMT variant, is that necessarily a bad thing? So long as the original hypothesis of the volatility risk premium holds, the strategy should be solid, right?

Ilya,

thanks for your kind words.

Except for the 2-day historical volatility, DDN’s original version remained unaffected (I don’t think that using a 2-day instead of a 10-day historical volatility represents curve-fitting; its simply the better choice in all its facets). It doesn’t matter if you’d be using the VIX or the VXMT (both strategies are solid), but one of the findings is that the VIX will probably work better (outperform) during market phases with a low mid-term (6-month) implied volatility (investor complacency) and/or when implied and historical volatilty are trading flat (low volatility of volatility with a relatvely constant gap in between), and vice versa.

The next step would be to build in some kind of position sizing, and/or to make the system adaptive (learning curve) to the ongoing changes in market and volatility behaviour.

Best,

Frank

Frank,

I recommend you to try average realized SPX volatility from 2 to N days. This method gives significantly better results.

For example, 2-day average of [VXV – (average 2-5-day historical volatility of S&P 500 * 100)] > -2.3: 160% return, 43% max drawdown and 190 max days in drawdown. 1-day average of [VIX – (average 2-8-day historical volatility of S&P 500 * 100)] > 0.4: 130%, 38% drawdown and 270 days.

I got VXV data from 2004 to 2007 from sixfigureinvesting guy.

Alex,

thanks for sharing, but that is curve-fitting at its best (modifying every kind of strategy parameter in order to optimize returns). This might work for the past, but will probably deliver poor results in the future. The best strategy would be which worked (almost) equally well during all market phases (bull/bear markets), time frames (from lets say 3 month up to several years), even with minor modification to the respective set of parameters (e.g. using a 4 and a 6-day moving average instead of a 5-day moving average, a 3 or 4-day historical volatility instead of a 2-day, and so on; this is a test of robustness). If any of these changes has a significant effect on strategy statistics (performance, drawdown, win/loss ratio, …), you can be quite sure that your strategy of choice won’t work as expected in the future.

Best,

Frank

I agree with you about curve-fitting. My point is when using my method of calculating realized volatility, you can get better optimized results than with the traditional method. The problem with realized volatility calculations is that more recent returns must have bigger weights than results from the past, and averaging volatility gives this effect. I also tried all known methods like Parkinson, Yang-Zhang, etc.; they do not work well with VRP strategies.

Also note that trading SPY vs cash using VRP strategies also improves performance compared with holding SPY.

Frank – have you ran any of these tests using ZIV instead of XIV? Am going to work on today. Drawdowns are likely less but not sure if upside as good.

Dave,

not yet, but the guy behind http://volatilitymadesimple.com/blog/ run some test. Drawdowns are of course less, but unfortunately upside isn’t very promising. And due to the fact that I am always short of time, I focus on the most interesting assets/strategys (from a risk:reward perspective). And that is XIV and VXX …

Best,

Frank

Frank thanks so much for your great site and sharing it and

all your work and thinking.

I think I found one small mistake on your returns as I didn’t

initially see your chart and did my own.

When i saw it I compared out of compulsivity!! :)

For XIV Nov 3-10: 37.97-34.50=347/3450=10.0597

by my little handheld calculator…. yes?

Thanks again.

Mit freundlichen Grüßen

Larry K.

Leeds, Massachusetts USA (western massachusetts)

Larry,

thanks, this was a typo, you’re absolutely correct. Portfolio page has been updated.

Best,

Frank

Thanks for the explanation Frank. I think we should find the way to optimize the parameters adapting to a certain moving average of the gap between implied and historical volatility.

http://nightlypatterns.wordpress.com

Hi Frank,

Regarding the Volatility Risk Premium strategy system whose signals you publish on your site.

Could you share its longer term performance metrics: sharpe, maxdd, max time in dd, etc.

I ask as many/most volatility strategies that have outstanding returns also have bungee jump like drawdowns and as I’m sure you’ve developed a system or two in your day I was curious as to what you’ve found posssible performance-wise in a volatility system.

I.e. maybe high performance and less terrifying drawdowns are possible.

Hope I haven’t asked you anything proprietary — my apologies if I have.

Regards,

Robert

Robert,

this is a strategy of my own.

Everything you’re asking for is covered here:

http://www.tradingtheodds.com/2014/10/volatility-risk-premium-trading-volatility-part-ii/

Best,

Frank

Hi Frank,

Are the trades you post on your site under Portfolio and Track Record the signals defined by http://www.tradingtheodds.com/2014/10/volatility-risk-premium-trading-volatility-part-ii/ ? I’d guess not.

What I was asking was whether you’d share, not the algorithm and calculations of what you trade, but rather its longish term performance measures (sharpe, dd, etc). I’m trying to get an understanding of what’s possible trading volatility and thought your personal method would be a good point of comparison against the universe of volatility systems out there. I totally understand If the performance measures are something you’d rather not disclose. But as they say – if you don’t ask you don’t get.

Regards,

Robert

Robert,

trades posted on “Portfolio and Track Record” page represent a strategy mainly based on the optimized strategy presented on the respective page you mentioned.

I’ve no problem with making lonish term performance measures public, but it takes some effort and may take a day or two. But I’ll never share in detail (strategy rules) what I am trading for myself (e.g. the strategy posted on the “Portfolio and Track Record” page, among others).

Best,

Frank

Hi Frank,

If you have the time, no hurry, it would be interesting to see longer term performance numbers (sharpe,dd, etc). There are many volatility systems described on many blogs so it’s interesting to see the range of performances that could be achieved. Gives me something to shoot for.

Regards,

Robert

Hi Frank, a quick question- VXMT is based on implied 6 months’ volatility, so I presume that for the calculation of the HV you should be using a SQRT(125) multiplier instead of SQRT(251), correct? Thnx

Krystian,

no. 2-day HV is based on daily quotes (and has nothing to do with the calculation of IV), therefore annualized historical volatily is calculated by using a SQRT(252). If you’d be correct, consequentially you’d have to use a SQRT(52) or SQRT(12) due to the fact that VIX is/was based on implied volatility of weekly/monthly options and so on … (forget about that)

A SQRT(125) would’ve been used in order to calculate the historical volatility in the event only 1 quote for every 6 month would be available.

Best,

Frank

Best,

Frank

gotcha, thank you