A stock bond model based on the average investor allocation to equities

This post makes use of a ratio presented in a post by the Philosophical Economics blog.  I highly recommend spending some time at that site if you haven’t already.  The author lays out the best critique of the Shiller CAPE ratio I’ve ever come across.

In one post titled, The Single Greatest Predictor of Future Stock Market Returns, the author presents a predictor of future stock market returns in the U.S. based on the average investor portfolio allocation to equities.  This ratio is calculated from the Federal Reserve’s flow of funds data and a convenient link is provided on the post for retrieving this ratio in FRED.  The two graphics below are from the post.  It’s obvious this ratio has been a very strong predictor of future nominal returns of U.S. stocks.




The ratio looks good for predicting long term performance but how might one use this to make allocation decisions in the here and now.  I’ve thought of a number of different methods to implement an allocation model based on this including:

  • based on where the ratio is in its historical range – lower the value, higher the stock allocation
  • based on how predicted 10 year returns compare to the 10 year treasury rate
  • based on whether recent years are under/outperforming the predicted annualized returns of the past ratio

This post will look at a variation of the first method.  Here’s how it will be constructed:

  • Calculate the rolling 4 quarter average of the equity share ratio
  • Calculate a relative position metric based on where the average ratio is in the 25-45 % range.  The average equity share ratio spends almost all its time between these two values.  The relative position will be equal to (average ratio – 25%)/20%.  Set the calculation to 0 if the average ratio is below 25 and to 1 if value is above 45.
  • The relative position metric indicates the bond percentage.  The stock allocation percentage is equal to 1 minus this value.
  • The stock/bond allocation values are lagged by three quarters in the model.  This allows plenty of time between when the data is available and when it is used.  Right now for instance, data through 4/2014 is available.  The model would incorporate data through this time period in 1/2015.
  • The equity share ratio is available for January, April, July, and October of each year. The model adjusts allocations at the end of each of these months using the lagged stock/bond allocation calculation.

Here’s a look at how the stock allocation would have varied over time.  The chart is slightly off due to the lag in the model but close enough for seeing how the values change.  The average stock allocation is a bit over 50% but this can stay quite high or low for long periods at a time.




Below is a look at the stock allocation returns over the entire period using the SP 500.  I’ve also included an inverse allocation model that invests in stocks at the same percentage that the model invests in bonds.  Bond returns are set to 0% here. You can see that the model has a low equity allocation during the two secular bear markets of the late 1960’s/early 1970’s and 2000’s.  It under-performs during parts of these periods but avoids a lot of downside volatility.


I tested out the model using VFINX and VUSTX as stock and bond proxies.  Both of these funds go back quite a ways. The model performs pretty well over this period.




Closing remarks:

I like the relative simplicity and historical strength of the equity share metric.  I’ve shown one implementation of a a strategy here and there are many other approaches one could take.  I should note that the use of different lags or a different average of the ratios (or don’t average it) will get very similar results.  The ratio doesn’t change that fast from quarter to quarter.  A real life implementation could easily re-balance annually and expect similar results to re-balancing quarterly.

Barbell investing with XIV / SVXY

Almost done reading Taleb’s book Antifragile.  It’s been a fun read.  (Note: I haven’t read his other books yet)

One of the concepts he presents is the idea of barbell investing. A barbell investment portfolio is constructed by combining a high percentage (say 80-90%) of very low risk investments with a small percentage (10-20%)  of very risky investments.  The idea is that the high proportion of the lowest risk investments ensures limited damage to one’s portfolio should all hell break loose while exposure to the riskiest investments allows decent upside.

While this sounds nice he leaves it to the reader to come up with practical implementations.

It seems to me that XIV/SVXY are near perfect choices for the very risky portion of a barbell portfolio.  One could even use dumb cash for the low risk portion (hard to get lower risk than that).  A portfolio of 80% cash/20% XIV re-balanced annually would have done quite well based on a backtest to 2004.  XIV is ideal in that you are limited in what you can lose but upside greater than 100% in a year is not uncommon.  Worst case scenario in the portfolio for any given year is a 20% loss, much less than the potential loss of a portfolio of mostly stocks.  And that is the barbell’s greatest potential strength – decent returns with a known, limited downside in this case.

Below is a look at monthly performance of the barbell portfolio vs SPY since 2004 (XIV simulated before inception per usual).

XIV Barbell1


XIV Barbell2

XIV saw wild fluctuations during this test period.  This included huge declines of 50%, 72%, and 46% in three of the years but also huge gains in the other years (including 5 years with > 100% gains). One could reduce or increase the XIV component of the barbell to reduce or increase expected return and volatility (a conservative investor could have 10-15% allocation and a very aggressive investor could have a 25% allocation).

I’ve also tested out re-balancing at the end of each month vs just the end of the year. Results are very similar.

XIV and the Whipsaw Regime

As I gain experience I realize more and more how fluid the markets can be. Always evolving and changing. Keeping short term traders on their toes. Finding strategies and relationships that endure for a significant amount of time is quite difficult.  You don’t appreciate that at the beginning of the journey.

I’ve been fascinated by the VIX futures market for a few years now, trading the futures through various ETPs.  Quite a number of trading strategies have appeared on the internet over the past couple years as these products gained popularity.

One thing I started noticing last year, and to a degree back in 2012 was that XIV (the popular short volatility product) was experiencing a change in character.  The first thing I noticed was that high realized volatility of the VIX was no longer reliably leading to significant declines in XIV. What used to be a good signal to go long volatility started acting more as a good entry point to short volatility.

I later noticed that mean reversion type strategies began outperforming those of a follow through flavor. I’ve documented this on the site in the case of daily and monthly mean reversion strategies doing relatively well. Just looking at a long term chart of XIV shows it has been far less “trendy” and far more choppy lately. I think this is ultimately the reason why many popular strategies (many of which benefit when XIV/VXX have long trends) have performed poorly of late. It has been whipsaw city for many trying to trade volatility using traditional methods. The topic of many popular strategies struggling was brought up recently on the Volatility Made Simple site in this post.  Check out that site if you haven’t already.

I am calling this choppy period the Whipsaw Regime. It too will pass and the VIX futures will behave differently yet again. Until that happens, I find it interesting to look at what’s done well the past couple years. Below are three strategies that would have thrived in this choppy period.

Strategy 1: Hold XIV when the volatility risk premium (VRP) is narrow or negative. There are many ways to calculate the VRP. I’ll use the same calculation used in the “Easy Volatility Investing” paper written by Tony Cooper. Strategy 1 will hold XIV when the VRP is below 3.

Strategy 2: Hold XIV when it closes at a three day low. Sell when it closes above a three day low.

Strategy 3: Hold XIV when VVIX (implied vol of VIX) is above 90.

The chart below shows how each strat performed since 2012. Impressive performance is mainly due to the choppiness experienced by the VIX futures.

MR Strats 2012

Why would few have predicted the success of these type of mean reversion strategies at the beginning of 2012? That’s easy. Such strats would have sucked big time in most earlier periods – often coinciding with the absolute worst times to short volatility.

Below is a more complete chart with performance back to 2007. You can see that the recent performance has been very different from the past.

MR Strats 2007

From a long term perspective, I believe playing mean reversion in VIX futures (at least on the short side) is a recipe for huge losses during the next big vol move or bear market.  I’m definitely not advocating anyone to do so.  Then again, perhaps it is this conviction by myself and others that will keep the mean reversion trade going for a while.

Trading strategy persistence and reversion

Deeper into the rabbit hole we go…

I’ve been playing around with automating trading system generation and evaluation.  It’s been crude and slow so far but has been a good learning experience.  One of the things that’s come out of this is my thinking about whether short term strategies exhibit a sort of persistence (good results followed by good results) or mean reversion (poor results followed by good results).

There’s no good reason I can think of that either has to be the case.  Still, it’s something that can be looked at when evaluating a strategy.

Let’s think about a simple mean reversion system – holding SPY when it’s below its 10 day moving average.  The inverse of this, a follow through system, will hold SPY when it is above the 10 day moving average.  Ok, how does the mean reversion strategy perform when it has recently outperformed or underperformed the follow through strategy? Below is a chart with results based on a 20 day look back period.

In this case recent underperformance has been a good predictor of strong future performance (especially since 2008). Recent outperformance has been followed by so-so to poor performance.


This makes me wonder what other simple systems show similar trends if we apply the same type of analysis.

XIV monthly follow-through – Part 4

Back in September of 2012, I ran a series of posts on profiting from XIV monthly follow through.  I showed how such a strategy did very well historically.

Part 1, Part 2, Part 3

Well, it turns out my timing for these posts could not have been worse.  Perhaps they marked the top of such a strategy?

Consider the chart below showing both monthly follow through and monthly mean reversion for XIV using both simulated values from the futures and actual values once brought into existence. (Note: defining monthly follow through as holding XIV through the current month if it rose the prior month and mean reversion as holding XIV through the month if it declined the prior month).  The chart runs from 2004 to September, 2012.  As you can see, the monthly follow through strat dominated.

XIV Monthly FT1

What happened after I published my series of posts? Check out the chart below which shows performance between September, 2012 and the end of 2013.  The tables turned and monthly follow through took a hit while monthly mean reversion prospered nicely.  XIV decided to be less trendy and more choppy.

XIV Monthly FT2

What’s also interesting is that September, 2012 marked the beginning of a period when not only monthly mean reversion did well but daily mean reversion did well, too.  I documented that in this post.

Monthly follow through hasn’t looked bad since last September.  Maybe the relative under-performance was just a phase.

Using VXO to time the SP 500, part 2

Happy New Year!

This is a follow-up to the popular post I did last January on using weekly closes in VXO to time the SP 500.  In that post I showed it has historically been much more profitable to own the SP 500 following weeks when VXO rose vs. weeks when VXO declined.  Beautifully simple.

In this post I’ll add another indicator to the timing model.  Just a bit more complexity.  This indicator will show that many weeks following a VXO decline are really not that bad. We can separate those that have tended to decline from those that tended to rise.

The indicator I’ll introduce is an acceleration measure based on SP 500 weekly highs and weekly closes.  First I calculate each week’s high divided by the previous week’s close.  The final indicator just looks at whether this number increases or decreases from week to week.

In other words, is HIGH t/CLOSE t-1 greater than or less than HIGH t-1/CLOSE t-2 ?  I’ll refer to the high divided by previous close as H/C in the rest of the post.

In the chart below, you’ll see three equity curves.  One invests in the SP 500 whenever VXO declines the prior week.  The other two will distinguish weeks with an accelerating H/C vs. weeks with a decelerating H/C.

HC 1

Nice.  As you can see, the index tends to fall when H/C accelerates and rise when H/C decelerates.  We are also closer to having a decent short setup based on times when VXO declines and H/C accelerates.  We can make the short trade more appealing by simply requiring the previous week’s VXO close be above 19.  A VXO close of 19 works well but other values around it work well too.

The below chart shows profit curves for investing in the index when VXO declines, H/C accelerates and either VXO closes above or below 19 the prior week.

HC 2

Finally, let’s combine all long and short trades together. Here is how the final model rules could work.

Long SP 500 when either VXO rose or when BOTH VXO declined and H/C decelerated.

Short SP 500 when VXO declined, H/C accelerated, and VXO closed greater than 19.

Cash when VXO declined, H/C accelerated, and VXO closed less than 19.

Below are equity curves for buy and hold, a long only model, and a long/short model. Not bad.

HC 3

Cheers and best of luck to you in 2014!


**Technical note: All data are from Yahoo finance and exclude dividends, commissions, fees, slippage, etc. etc.


Update: Here is an Excel file with data and calculations for the last chart.  Enjoy! SPY VXO Weekly Strat Part 2


Update2: Here are some stats that were requested.

VXO System Stats

A weekly QQQ strategy

I was browsing my twitter feed this week and saw a couple old Quantifiable Edges posts (here and here) linked to by @PsychTrader. The two posts were written in mid-2009 and detail a simple weekly strategy that uses the relative performance of the S&P 500 and Nasdaq indexes to time the market. They showed how investing in the SP 500 or Nasdaq  when Nasdaq has been outperforming (based on 10 week relative performance) has generally beat out buy and hold.

Since the posts were written a while ago, I took it on myself to test out the strat with recent data.  I used SPY and QQQ weekly data from Yahoo Finance for my test.  I compared price performance (adjusted for dividends) over 10 week periods. All performance calculations and trades take place at the end of the week.  One tweak I made was to add a lagging week between a signal change and when a trade takes place.  An example – if at the end of a week SPY goes from outperforming to underperforming over the past 10 weeks, I will not adjust holdings until the end of the following week. This seemed to enhance returns but results will be similar without it.

Below I will examine holding QQQ or cash depending on whether QQQ is outperforming or underperforming SPY. I’ll leave it to the reader to test holding SPY.

First let’s look at the period from 1999 (inception of QQQ) to the end of 2008.  The strategy to invest in QQQ when it underperformed SPY got crushed during the bear markets and just treaded water during the bull market.  The inverse strategy did much better and held its ground through bull and bear period alike.

QQQ weekly strat 1

What happened from 2009 forward? Take a look.

QQQ weekly strat 2

The strategy that sucked big time before has been steadily rocketing higher while the formerly better strategy has been treading water.

I guess this is just another example of strategies being turned on their head at the market’s whim.  This is one I’ll be keeping tabs on going forward.


On a personal note, I’m proud to announce that my wife recently gave birth to our first child, a beautiful baby girl.  We are greatly blessed if a bit sleep deprived.  Still trying to keep up on markets but can be challenging while juggling my new dad responsibilities.  :-)

Using volume in an EOD trading system

I sometimes wonder if there’s anything useful in the volume data accompanying daily OHLC values from sites like Yahoo, et all.  I haven’t had much success in the past.  I’ve mostly ignored it.

Well, I got inspired to give it a go again and think there’s potential to use volume to enhance a trading system. Enough data mining can solve any problem, right?  :-)

I’ll describe a system I tested on various index ETFs and then compare the results with and without a volume filter.  My goal isn’t to prove the system is great, just that using volume can potentially enhance a system’s profitability.

Ok, here are some rules for a base mean reversion system:

Buy at the close when 1) the close value is less than yesterday’s close AND 2) the close value is at least .5% below the 10 day SMA.  Sell position 4 days later at the close.

Now we’ll add a volume filter:

In addition to the previous criteria, only buy at the close if current day’s volume is less than the volume of EITHER of the previous 2 days. (Note: we could use 1 day or 3 days, the farther out you go the less restrictive this filter becomes).

I think my initial thought was that buying on a  bigger volume day would be better. Perhaps signaling capitulation.  But no, a lower volume day is better in this case. And I guess that makes sense too as a type of negative divergence or perhaps exhaustion of sellers.

Here are some summary results for the system with and without the volume filter. Each ETF is tested from inception to July 9, 2013 using Yahoo Finance data.


The volume filter cut down significantly the number of trades. While total profits of the backtests were lower, the average trade profit and winning percentages were generally improved.

I’ve attached an excel book containing the backtest, summary stats, and profit curves for each ETF.  Enjoy!

Excel Download – Trade System with Volume Filter

Getting defensive

This morning I placed an interfund transfer request in my TSP account.  This is a discretionary override of my systematic TSP strategy.  I changed allocations to 25% C 75% G funds for my existing balance. I will keep a 40% C 60% G fund allocation for new biweekly contributions.

I’m getting more and more bearish for the rest of the year.  What does this mean? Probably that the market is about to soar and you should load up on stocks. Well, maybe not…

We’re pretty far above the 200 day average and near all time highs and in a very mature bull market.  I could be wrong but am playing it safe(r) here.

The allocation displayed in the top right of the site will continue to reflect the 40/60 allocation until an official strategy change occurs.


On a side note,  XIV daily mean reversion (long only) has continued to crush daily follow through since my March post. I’ve been keeping an eye on it and playing it occasionally.  I’m sure it will stop working eventually but am enjoying it (in small sizes) while it lasts. 


On another side note, my life has been pretty hectic recently and I haven’t been able to do much of the market research I love.  I’m hoping things will calm down by the summer.

Change of character

Question: What’s one way you could have nearly doubled your money since last September with minimal drawdown?

Answer: XIV daily mean reversion! Well, a long only approach that is.

Daily mean reversion just means holding XIV if it declined in price the previous day.  Daily follow through would be holding XIV if it increased in price the previous day.

Daily mean reversion was hardly a good strategy in recent years.  In fact, since 2009 when VXX came into existence, this strategy performed relatively poorly while a daily follow through strategy did fantastic. That changed last September.  I have no clue why.

Check out the chart below illustrating the recent performance of the two series.


One note, if one looks at simulated XIV before 2009 you can see this isn’t the only time mean reversion would have dominated.  The same thing would have happened in 2007/2008.  Is there anything to be read into that? Possibly not.  Could just be random changes in the market.

There’s no telling how transitory this change will be.  Just thought it was worth sharing.

Technical note: I just used inverse changes in VXX to create the series for the chart above.  Good enough for illustrative purposes.


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