Optimal position sizing for a VIX ETN strategy?

Research
1

There are trading systems which switch between owning XIV (which is “short” “volatility”) and VXX (which is long volatility). Some of these trading systems have backtested results going back to 2004 of ~100%/year! VXX has lost money over every twelve month period. Lots of money. What it has going for it is that on rare occasions it spikes up and that spike is negatively correlated with the market. XIV on the other hand is roughly the inverse of VXX. It makes lots of money almost all the time except for rare occasions. If the VIX spikes suddenly by 80% or more then XIV can go to zero. As far as I know this has only happened once in the 25 or so years since volatility has started to be measured in the mid 1980’s. There is also a risk that Barclays can go under but I consider that relatively less likely as the ETN is a senior debt security (meaning that the ETN holders will be first in line for any assets remaining after bankruptcy) and Barclays may get bailed out in any case.

What is the optimal position size? Position sizing is a very important part of investing that doesn’t get enough attention. Having a position that’s too large will cause higher volatility than necessary, lower returns and eventually may even lead to gamblers ruin. Having a position that’s too small means leaving money on the table. (Most sane people would probably rather the risk of making too little over the risk of losing it all.) I am not confident enough in these systems that they can predict with absolute certainty when a spike in the VIX will happen that would wipe out XIV.

One strategy to estimate optimal position sizing is to optimize the ratio of stocks/bonds/volatility/cash for the optimal Sharpe ratio using historical backtesting data. Some calculations have pegged the optimal allocation to such a volatility strategy using this system in a bond portfolio to be 10% and in a stock portfolio up to 50%. I am not sure sure if this strategy is sound because the backtests only go back until 2004 and the tail risk (surprising enough) has not come up in the backtest period.

Another strategy to estimate optimal position sizing is with the Kelly criterion. See [url=http://www.quantwolf.com/calculators/stockbondcalc.html]http://www.quantwolf.com/calculators/stockbondcalc.html[/url].
Of course, the accuracy of these results depends on estimating the odds correctly and the payoffs correctly. But since we know that if you invest half the Kelly amount, you get about three-quarters of the return with half the volatility, and since it is better to take the risk of leaving some money on the table rather than the risk of gamblers ruin, we use conservative estimates.

What numbers should we plug into the Kelly calculator?
Because this calculator assumes that there are only two possible returns for the stock (or in our case ETN) in a given time period I chose to divide the periods into the average backtested year (2004-2013 with 100% upside) and 100% downside for the possibility of a VIX spike. (It is possible that the with proper position sizing the downside would actually be less despite the spike because of the fact that if you would have the guts to stick with the strategy it would probably recover some of it’s losses assuming that you don’t get wiped out)
I also punched in 0.96 as the success rate because 24/25 years = 0.96. I also chose 0.025 as the risk free return as that is basically what you can get these days risk free. The result: 92% allocation to the volatility strategy recommended; so a 1/2 Kelly = 46%.

This implementation of the Kelly criterion is limited because in practice you would have some money in stocks and stocks is not risk free, and may in fact be correlated with XIV. (Besides for the other problems of accurately estimating the future).

Is there a better way to go about this?

2

Chipper,

The question that you should be asking yourself is how much of a loss can you mentally handle if the VIX spikes? So if you can handle a loss of 5% of your portfolio then your allocation should be no greater than 5%. Whenever I invest a dollar into anything I always consider how I will feel and react prior to investing the dollar if things go against me and then make allocation decisions.

Scott

3

That’s right Scott, that’s also part of the equation. But if I carefully model a system and am virtually certain that it will continue to work then drawdowns matter less, as long as I don’t need to take out the money right away.

That’s one of the major reasons that value investors have a edge over most others. They have no need to bail out at every drawdown and can continue investing because they have reason to be confident that prices will recover to match values. I know firsthand because my carefully researched portfolio of 10 stocks or so had a 50% drawdown in 2008 but I didn’t lose a wink of sleep–because I was confident that they would recover. They did recover before March of 2010. Had I been investing blindly in a system then I don’t know if I would have been able to stick it out.

That’s why I think that is important to estimate what optimal allocation is–so that I will have the confidence during drawdowns to stick to my chosen allocation (which will be a fraction of “optimal” allocation).

4

Chipper,

The difference between value stock and VIX investing is that unless you buy really crappy stocks ( perhaps fraudulent chinese companies ) your stock portfolio will not go to zero but your VIX investment can. We also have less historical data on the VIX relative to stock indexes which makes modeling less reliable. I also am never certain any system will continue to work (markets change) despite my attempts to break them down prior to investing capital. Therefore I like to invest in many systems with negative to moderate correlation and if one or two prove to be suboptimal then it does not damage my portfolio.

Scott

5

Chaim, thanks for the link to the calculator. I had been using a formula:
Kelly % = W [(1 – W) / R]
W = Winning probability
R = Win/loss ratio

I believe your analysis is sound on the Kelly criteria. I like how you addressed the concern that the average loss may not be the best number to use. You addressed it by plugging in 100% loss. Why this is important can be shown with an example from one of my ports. It has an average gain of 14% an average loss of 8% with a win percent of 57%.

If you plug those average numbers into the calculator it says I should leverage up at least 400% on the port. Problem is that during times that are not average (e.g., 2008) I go broke.

Anyway, my useful points are these. First, I like your analysis. Second, you have to consider your opportunity cost with stocks, possibly even using some leverage with the stocks. Third, I don’t really know how to use the Kelly criteria for stocks but if you are not using leverage you are likely to be below the optimal Kelly criteria.

BTW, a bigger problem with using Kelly criteria with stocks is that each “bet” on stocks is not independent. I saw that yesterday. The chance of almost every one of my 40 stocks going down if they were independent and were a random sample would be very small.

6

Chipper,

I’m definitely not a VIX trading pro. I do play around with VIX. I’ve read many papers on vix trading (since 2009 or so), built a lot of systems with Vix and invested in both vix systems and professionally run ‘option selling’ industries. In fact, I’ve followed and invested in the options space going back to 2000. Including reading some monthly newsletters and commentary fairly regularly from several top firms since about 2010. So, that’s about 14 years now of looking at the space.

Yes. There is money to be made for aggressive investors. But, by and large, most of the money is made by the fund managers. So…Having said that…what would I suggest (and/or what do I see other top asset allocators doing / suggesting)?

First…I don’t believe much in mean-variance optimization based asset allocation. There are huge problems with it.

For a conservative investor, I’d allocate 0% to such strategies. Cash and bonds can achieve very similar DD minimizing affects. And shorting broad market indexes can get you negatively correlated strategies with more reliable behavior.

I wouldn’t put more than 5% of a portfolio in them for a moderately conservative investor. I wouldn’t put more than 10% into them for a very aggressive investor. That’s me. I know some people with 100% in aggressive options selling systems…who’ve made 20% plus for over 20 years. So…it can be done. But, I wouldn’t do it. And, I would want at least a basket of 3-5 strat’s to get to that.

Why do I say that? First, I look at best practices among many, many professionals multi-asset allocators and institutions. Many avoid the asset class entirely. (Option sellers are largely selling a) volatility and b) time decay). Those pro’s that do allocate to it, tend to do so in very small amounts with a lot of due diligence, and select at least 5 underlying managers (often 10) with low historical correlation and low day-to-day position overlap.

These are among the best multi-asset class asset allocators in the world and they are treading very lightly in this space. Why do I think I am better then them with 10 years of VIX data in excel and some simple models? I don’t have the confidence to feel I am.

I also look at ‘data points’ like the fact that Merrill Lynch and most of the ‘big firms’ will sell almost anything they can make money on. High fee overlay managers. High cost hedge funds. Futures. Yet, they don’t even put option sellers on their platforms to sell to retail investors because of a) the very high risk of 100% loss, b) the huge challenges in assessing real manager talent and risk control and c) fear of litigation.

Historically, the most reliable money in volatility is to be made on the short side. However, VIX is currently around 13. I haven’t run numbers in a long time, but when I did the historical average of VIX since the 1980’s was right around 20…somewhere in there. I want to say the St. dev of this was around 8. So, right now VIX is still about 1 St. Dev below it’s average over the trailing two and a half decades. So…the market’s not nervous at all. Not really. Should it be?

That’s for each investor (and history to decide).

But…in making the allocation question…each investor has to answer…is now a time I really want to start making a large portfolio allocation to selling volatility? Is the current market environment really mispricing volatility in some major way? If so, in which direction?

Going long vix is historically much harder bet…I think it’s very hard to call correctly no matter what backtests show. Usually, it has to be done on a daily or intraday level…if you want to trade VIX long. That’s what I have seen anyway. So…that’s my opinion after watching professional option firms for over a decade, talking to some founders and reading a lot of papers. Spikes are generally uncertain in terms of the timing and size. And require intraday or day trading systems. Yes, you can use trend filters and market direction models - and they help…but nearly all money in options is made selling volatility and time decay…not buying it. And these guys are the best at vol. modeling there is. That’s what there business models depend on.

My opinion…this current period is likely the ‘end’ of another great run for 3-5 year period for option sellers. I expect vol. sellers to have 50-90% DD’s sometime in the next 2 years. That’s me. How much further will VIX really fall?

More comfortable ranges…when VIX gets up in the 28 or above range…maybe you’d want a somewhat larger allocation to selling it. If It gets down around 8 or 10…maybe want to be more on the long side.

Again. I’m no pro. These are just my thoughts. I would say…if you do trade VIX through ETF’s, likely better shorting the opposite leveraged ETF to your ‘bet direction’ to get your directional exposure. This takes advantage of some inherent construction issues in these vehicles.

I’d also suggest a ‘constant’ bet sizing in this arena. So…take 60% of your allocated capital and invest it in constant bets. Collect your winnings without upping the bet size. Adjust your bet sizes some based on where VIX is relative to it’s historical band ranges. Then, when you get your 100% losses (and you will), you still have money here to play with.

Last story. In terms of the very first option seller I invested in (I was 29 at the time)…who I mentioned earlier…he had a great education, over a decade on an options desk at a top firm, a great reputation and references from people I knew, and 4 years of 600% total return on his money with minimal DD. I gained 50% in the first 6 months. Then, in the first 3 months of the tech bubble, he (I) lost 100%. It was a 2-3% piece of my portfolio. I learned my lesson.

But…I think that most retail investors aggressively trading VIX with a large % of their portfolio will, in my opinion, likely have it end badly.

Good luck.
Best,
Tom

7

I think the historical average VIX value is irrelevant. Here’s why:

  • SPX options volume are growing steadily. 400% in the last decade alone. More volume = a more efficient and less volatile options market = lower VIX.

  • A great deal has changed since the internet revolution in 2000. More and faster information = a more efficient market = less market volatility = lower VIX.

The long-term downtrend in the VIX reflects the growing market and the ever faster ways the informations spread.

8

Aurelian,

Fair enough. But…that’s not what I see looking at the numbers.

What long term downtend in VIX? Since 2000, the average VIX level is 21 and St. dev of weekly closing prices is 9 or so. That’s slightly higher, but still right in line with the longer term (albeit still very short) two decade plus historical averages back to the late 1980’s or early 1990’s. (The decade of the 1990’s showed an average VIX around 18 or so, with Stdev of weekly closes of 8 or so…so the 1990’s was less volatile than the 2000 to 2014 period).

Can also look at how many times the VIX has topped 30 and how many days it’s been above 30. More since 2000, then prior to (that’s the eyeball test, not the 'math). But…take a look at it.

I see a sort-of downtrend since 2009 or whatever (with a huge spike in 2011). But…I take that as the same reason I see a large growth in margin dollar borrowing. People and ‘smart money’ went big into the equity markets at this time…with the feeling the US gov’t was behind them. Now…many of those same people are saying ‘tread lightly.’

And…for what it’s worth, I don’t think there is any real reason to expect markets to be less volatile because volume and computer driven trading has grown so much. In fact, I actually expect the opposite (bigger flash crashes…and cascade effects - as a growing number of shorter-term holding period and higher-turn mechnical systems with similar/the same forms of ‘stop losses’ and ‘market timing rules’ all buy and sell at the same time). But…only time will tell. I am curious if you really think equity market volatility will be lower going forward? I haven’t seen any papers talking about this, but have seen a lot arguing for rising vol. and bigger peak DD’s.

So…Just curious…do you agree / disagree with any of my other main points around allocation ranges? If so, why?

Best,
Tom

9

Chipper, IMHO you should choose your position size assuming the drawdown that will occur if XIV goes to zero. Anything over 5-10% allocated to this is madness. Although that 5% has the potential to give a nice boost to diversified tactical portfolio. I trade VIX ETF strategies personally and have modelled and backtested several such systems.

Ralph Vince always said with Optimal f is that the problem is, you never know what your largest drawdown is because it may be in front of you. Anyone dealing with this would be smart to heed that advice.

10

A couple of books everyone should have in their library:

http://www.amazon.com/The-Mathematics-Money-Management-Techniques/dp/0471547387

http://www.amazon.com/Portfolio-Management-Formulas-Mathematical-Trading/dp/0471527564/ref=pd_sim_b_2?ie=UTF8&refRID=08HC7HS1TVJN6PPCARCA

11

@Tom, your asset allocations strategies makes sense to me and are definetely very American.

I have learned to do things differently than you, probably because of the culture.

I would allocate the major portion of one’s wealth to hard assets: real estate, farmland, wine, forests, livestock, precious metals… all of which have intrinsic value and can either be sold later for a profit or bring a steady stream of income. And then a big chunk to life insurances and annuities, invested in Treasury securities. And then the equity money.

So I would take considerably more risk in the stock market than you would, because it represents a way smaller chunk of the pie. I have made money last year with SVXY, with large positions. As someone else said, the moment when the term structure reverts back from backwardation to contango is a powerful time. And yes reinvesting these profits in SVXY or XIV is probably not a good idea. But if you have no more than 15% of your net worth in financial instruments and equities, you can do these types of things and not mess up your overall risk/return profile…and sleep well at night.

12

@Chipper6
Using Kelly criterion for position sizing in investing is a dangerous urban legend: the formula is an invariant by leveraging, think of it.
It is useful as an indicator of probabilistic robustness, not risk.

13

I have models on XIV and ZIV (weekly rebalancing), with less than 5% of my account on them. They go only long (short volatility).
They are profitable since I use them (8 months) and YTD, but below the historical CAGR. Backtests since ETN inception date (2011) show a CAGR about 60% and a maxDD of 15%. I had a look since 2009 reversing the models with VXX and VXZ: it’s OK. And since 2004 with simplified models and synthetic data: looks OK, but this is very approximate.

14

@Aurelian,

I don’t disagree with your ideas. Although…I would be pushing this type of portfolio towards real income generating assets (net income positive local small businesses and a diversified basket of rental properties in particular). Some of my friends have nearly all their wealth in diversified bundles of rental homes and small businesses. They’ve done great for decades and rolled right through 2008 without issue. I envy their portfolio’s. They are throwing off way more cash then they need to live and it’s all inherently inflation indexed.

But many other people I know have 50-100% of their assets in 1-2 rental properties. I don’t think these are smart investments…because the risk is so concentrated.

A person basically has to look at a) income they are generating vs. b) cash needed to live and c) potential future shocks that demand liquidity. If you are early in your career and plan to work for decades, I get wanting to acquire a portfolio of income generating properties as part of your investment plan. Maybe. But…it takes a lot of time to build out and manage. Most of my friends doing this either a) do it full time, b) have a spouse or partner who does it full time or c) hire a management company.

So…I have looked into this basic approach in the US, but have been ‘lazy’ in that regard. The reason is…it takes a lot of work (and money and local and asset class knowledge) to successfully build a geographically diversified mix of rental assets and small businesses. You basically have to have a LOT of money (probably more than $10MM plus american) if you want to do this in the major cities and achieve even minimal diversification. So, that pushes you to smaller regional areas…I have flown to areas in North Carolina & Texas and talked with people in Nebraska, ‘suburban California’, and Ohio. But…it takes a lot of work and in these cases, and a local partner is often needed or a lot of time on the ground. It’s hard (i.e. time intensive) to build out a network of trusted advisors. And local management needs to be hired.

So…there are funds that do this for you, but they are frequently at 2/20 with long-term lock-ups and issues of ‘trust’ around fund management and asset custodianship. So…it’s not that easy to execute what you are describing in anything approaching a diversified way (say min. of 5-10 assets with some geographic distribution).

Owning small businesses (particularly in niche areas with minimal competition)…can make sense. I’ve talked with dozens of ‘business brokers’ around this. But you have to trust the management teams that run them, and they typically have to be local. My friends managing groups of franchises, work 60-80 hours a week making sure they aren’t getting ripped off, putting out fires, etc.

Other options to public markets? Angel and seed investing. I know many people who just do seed stage investing and claim to be earning 30-50% annual returns. But, again…they typically have over $10MM US. And can afford to invest in at least 50 companies. And they have a sector focus and do it full time.

So…For most people, home ownership, public equity and bond markets (and cash) are still the foundations of wealth.

In my case…I don’t think, if someone owns under $10MM that they really need to consider anything like farmland or gold or wine…or venture outside of the income producing hard assets like rental homes or small businesses. I don’t think most people can afford this level of illiquidity or have the time it takes to build out anything close to diversification.

I’ve always viewed precious metals as much more speculative than equities. I don’t think they have any intrinsic value apart from public psychology.

Best,
Tom

15

You definitely have to be passionate to do this, since it is so much work. On the other hand it’s incredibly fun and gratifying. Making money in the stock market is no easy task either. I mean losing is easy, winning not so much. I’m guessing you spent a LOT of time studying ?

In France we have structures to facilitate these types of investments. A pool of investors will buy several assets and retain direct ownership but hire a management company to do the work. You can get started with as little as $10,000, all the average Joe has to do is to fill a form and send a check. The company will split the profits 20/80. These are highly illiquid investments though, but you get the added benefit of diversification since you don’t own one building but 1% of a hundred building. And you can fire the management company and get another one. Real-estate, livestock and wine can be bought this way here.

Farmlands, forests demand work and knowledge but how amazing is it to pass land on to your kids, and them to theirs ?

16

Another difference between directly owning rental properties/real estate and stocks in the US is that so far you have been able to recover your principle investment in stocks if you wait long enough after a downturn ( those who live in Japan and have Japanese stocks will strongly disagree with this ) but if you have rental properties that can no longer cover their liabilities after a downturn it can cause you to foreclose and/ or become bankrupt.

Scott

17

Fred, I’m not sure what you mean.

As far as I know the Kelly formula properly applied would rarely recommend leverage. It was designed to be used for serial bets (one bet at a time; not making a second bet until the first one is over and so on) and not for multiple bets in parallel that correlate to each other. In investing it can be used to size the overall allocation to stocks for example; but not to size individual stock positions except perhaps relative to each other.

I’m not sure how you would use it to estimate probabilistic robustness.

18

[quote]
I believe your analysis is sound on the Kelly criteria. I like how you addressed the concern that the average loss may not be the best number to use. You addressed it by plugging in 100% loss. Why this is important can be shown with an example from one of my ports. It has an average gain of 14% an average loss of 8% with a win percent of 57%.

If you plug those average numbers into the calculator it says I should leverage up at least 400% on the port. Problem is that during times that are not average (e.g., 2008) I go broke.
[/quote]How not to use the Kelly formula in investing
Jim, as I wrote to Fred, I don’t see how the Kelly formula can be used for individual stocks in the way that you described. The Kelly formula is designed to prevent gamblers ruin. But leveraging 400% guarantees gamblers ruin!

Therefore either the Kelly formula is flawed (I reject this premise because the math works very well in the case for which it was designed for) or that this is a misapplication of the Kelly formula. I vote for the latter.

The reason why Kelly doesn’t work that way is because in a market crash all stocks tend to get very correlated, so even a basket of stocks is almost the equivalent of making one single bet.

When and how is the Kelly formula useful to investors?
It makes sense to me conceptually to use Kelly on the portfolio level to estimate the optimal allocation to an asset class such as stocks–as long as it’s entirely uncorrelated to any other asset class in your portfolio (such as cash or gold). You would limit the size of your equity allocation to the Kelly edge/odds for the entire portfolio (plus a margin of safety). You may also want to limit the amount of money in stocks to the Kelly maximum for the single best stock in your portfolio (the one with the best edge/odds). Here I would not worry about using a fractional Kelly because this number probably underestimates the true Kelly for the stocks overall.

Another way where it may make sense to use Kelly is to size positions relative to each other. This way if the Kelly formula recommends 50% in investment ‘a’ and 25% in investment ‘b’ then you would take the portion of your money allocated to stocks for example 60% and put 2/3 in ‘a’ and 1/3 in ‘b’.

This approach has some advantages. The Kelly formula is probably too much for most investors, both because it maximizes returns at the expense of volatility and because it assumes that you have the odds calculated correctly (which is rare in practice). Using a fraction of Kelly gives you most of the returns with a fraction of the drawdowns and gives you a margin of safety if your estimates are too optimistic.

19

@Chipper6
The Kelly criteria never propose to leverage, it is always below 1 (100%):
W is between 0 and 1, so (1-W)/R is positive, so W-((1-W)/R) is below W, which is below 1.

The point is, if you consider a strategy (or asset) A and a strategy B which is strategy A leveraged N times, Kelly criterion give the same recommended allocation for both: W (probability) is the same, and R (avg win/avg loss) is the same. example: if you take a daily bet on SPY and a daily bet on UPRO, you get the same allocation for both games, nevertheless the risks are very different. Maybe there’s a mistake in my reasoning, but where is it?

I use Kelly to compare P123 models, as an additional information to maxDD, Sharpe and Sortino ratios. The higher, the better. I have a spreadsheet for the calculation.

20

@Chaim,

I agree that it is difficult to use Kelly criteria for stocks. Indeed that is why I said: “I don’t know how to use Kelly criteria for stocks.”

Thank you for repeating my point on correlation and independence with regard to stocks.

BTW, you are not claiming that volatility is not auto-correlated are you? It seems bad news begets more bad news to me. Look at a chart of the VIX around 2008 if the is not obvious to you. Or just look at history.

My point about leverage in the context of this post was really an indirect proof (Reductio ad absurdum) showing how some simple assumptions about gains and losses cause problems. I have used other assumptions (including annual returns of the port) but none of them are perfect. Plus, each person still has to answer how much they are willing to invest in a single stock. Any “math” was done with the calculator in your link.

My main point was to applaud your assumptions. I’m sorry you missed this point.

That having been said, unless you assume that a 10 stock port can go to zero, all stock going bankrupt at once, there remains the possibility that some small amount of leverage would still keep you under the optimal Kelly %. The chance of 10 stocks going to zero at once is certainly far less than the chance of XIV going to zero (that would only require on company going bankrupt i,e., default risk, among other risks).

I am not the first to notice that a small amount of leverage can be used without going above the optimal Kelly %. This is in the literature and to state otherwise would be to claim leverage can never be beneficial. I did not say I know what that optimal leverage would be.

Additionally, I’m not recommending 1/2 Kelly to anyone. So, any strategy based on 1/2 Kelly will be extreme, IMHO. If you go that route, I would recommend that you convince yourself that your assumptions are perfect an not just good.