TD,
Thanks for recommending The Mathematics of Money Management. It is already entertaining. I’m not far enough to know if it will make me a better investor. As I understand it the book it promises to make some of this discussion more practical. Hope so.
Jim, yes, I absolutely agree. It is essential people understand Kelly and probably more importantly Vince’s Optimal f, even if you would never entertain them in a real portfolio. Just as if one didn’t believe that markets are totally efficient, they’d sure as heck better understand efficient markets theory. Understanding how events might play out in a perfect world certainly helps you even in those circumstances where they are less than perfect.
Tom C
Chipper,
I’ve been trying to help. Sorry if I haven’t. I think, perhaps, you are trying to reinvent the wheel around ‘multi asset’ portfolio optimization with simulation based inputs in which there is a high degree of parameter uncertainty. This is a fairly well studied field going back to, at least, Markowitz in the 1950’s or so.
See:
I don’t think the correct comparison is insurance companies. I think it’s better for you to look at professional ‘multi strategy’ asset allocators. They face this problem every day. You are free to disagree with me.
The basic approaches taken are:
I have tried all of these. When there is a high degree of uncertainty around parameters (i.e. mean returns and/or correlations)…these models either a) recommend very low weights (most of the more modern methods) or b) have huge weight swings.
The above links and papers will show you how the professionals in this field use math and programming to do what you are trying to. And have links to many more papers.
However, looking at multi-asset managers, most have very small to zero allocations to options selling. They have answered this question (selling Vol. as an asset class) and said their optimal weights are zero (or typically well under 5%). When they allocate they tend to choose a basket of top managers with 5-10 years of out-of-sample results (often wanting to see risk management through 2 big down markets).
If you are interested, there is also a Barclay’s ETN (VQT)…that you could look at - they dynamically adjust exposure to VIX between 2.5% or so and 40 something %. You can look at their holdings at any point in time to see what they think is the optimal weight…but, from what I know, this is a very extreme approach.
Good luck.
Best,
Tom
Chaim,
Thanks for the information on auto-correlation. Can you give any more information an your techniques? I.e., did you run a regression of the VIX on the Y-axis and the previous month on the X-axis?
Chipper,
Here’s some interesting links to free reading on the ‘money management’ work Tom C. was mentioning above:
It’s interesting reading.
However…all of these ‘money management’ systems above remain very sensitive to the accuracy of the model ‘inputs’. In this case, these are all coming from our simulations. The inputs from the simulations have huge built in ranges of potential outcomes and inherent biases / mistatements around things like a) win rate and b) avg. gain per win. Many of these key inputs have been optimized. And (if using them, correlations…and distributions of underlying data for moving forward outcomes).
These guys write on this (and sell a software package to do…I think):
http://www.stator-afm.com/optimising-the-position-size/
One of the things they do…and that’s recommended is ‘randomization’ through monte carlo analysis of the historical backtest returns…so can see what would happen if the historically observed trades happened in different sequential orders. That would be a great feature on P123.
Best,
Tom
Jim, I tested auto-correlation of my strategy; not of the VIX itself. I simply used the Excel function Correl() to compare period x to period x-1 of my realized trades for my volatility model backtest. The VIX itself certainly has some auto-correlation tendencies which my model takes advantage of.
Tom, thanks. Most of the work in the portfolio optimization space was done on asset classes where the word “risk” is used interchangeable with volatility. Anyone who owned mortgage backed securities in 2008 found out that risk and volatility are two different creatures. You can often measure volatility historically but the risk of being wiped out is something that can often never be seen in backtests. I assume that most if not all of the portfolio optimization strategies that you mentioned aim to minimize volatility or to minimize the Sharpe or equivalent. That’s fine as far as it goes. But buying the XIV ETN has the additional ‘risk’ of going to zero that almost no other asset class has because if the VIX spikes by 80% or more within one day then XIV will terminate. The VIX has spiked by far more on Black Monday and I have to assume that it will happen again at some point in the future. Therefore it seems prudent to add additional measures of safety such as position sizing to limit the maximum loss, and only buying XIV when the ‘insurance premium’ is good enough to compensate for the risk (as Tom C pointed out). My question is if the maximum position size for the wipeout risk can be mathematically estimated or should I use a rule of thumb such as 5%. Rules of thumb are generally convenient and often approximately right but sometimes they can be totally off.
Chaim, thanks.
Thanks Tom. I was getting tired of Kelly yesterday when you posted. This is better at least: copied and pasted from investopedia. The first minus sign got deleted in my original post, I think.
Kelly % = W - [(1 – W) / R]
Where:
W = Winning probability
R = Win/loss ratio
I do think there are other correct formulas depending on whether you assume there is a difference in the amount traded and the amount risked. For example, one might assume they can’t lose 100% in US treasuries. An investor will trade more than than their potential loss. So, someone may have a different formula.
Agreed. That would be a nice feature.
Tom C
All the math formulas, optimization aside, if you all would like to have a book this summer to read while you have a drink by the pool, this is it:
Fortune’s Formula, by William Poundstone
http://www.amazon.com/Fortunes-Formula-Scientific-Betting-Casinos/dp/0809045990
Enjoy.
Tom C
Well you can mathematically estimate a maximum position size but the estimate will be no better than whatever assumptions you make in your mathematical model. I have played around with a simple approach that uses (annualized return / risk) * (1 - correlation). For risk I use standard deviation or the average of the standard deviation and max drawdown and correlation is the average correlation of the strategy to all other strategies in the portfolio. In the case of a strategy based on XIV, annual return would push for a higher position size but the high risk would significantly reduce that and then the high correlation to long stock strategies could reduce it further. I have found that calculating these values for each strategy and then normalizing these into percent allocations gives very good weightings based on the past. Like all other data based on the past their value in the future is likely to be much less. In determining allocations I think it is worthwhile to consider AR, risk, and correlation to the rest of the portfolio, but the future has so many unknowns you can’t account for that I don’t think it is worth the effort to try to be too precise.
Don
[quote]
Personally, I would estimate it in the context of my other systems. Add the position size I am considering allocating to the drawdown to the rest of the portfolio. So if I wanted to add an allocation of 5% XIV/VXX switch to my existing systems, I estimate the new MaxDrawDown to be .05 + 0.95 * MaxDD of the rest of the portfolio of systems. That is, estimating the drawdown assuming that XIV goes to zero, and see if I am comfortable with that drawdown possibility.
Also, I would put it in a Book and take a look at the equity curve I get when combining it with other systems. These systems that switch from XIV to VXX or XIV to cash can give you a good low correlation when combining with other tactical or market timed switching (incl. long/short) with stocks and bonds and help to smooth the curve.
Like Don said, given the future has so many unknowns, it may not be worth the effort trying to be too precise.
Tom C
What have people been doing with the XIV VXX etc. since this last post? The XIV is down almost 50% since its peak in Jully and the VIX is about 29 now.
I am posting now because the VIX term structure is in backwardation. Is anyone going to buy the XIV when the VIX goes back into contango (I will probably do this)? Any other strategies that people are following? If you haven’t found it already www.vixcentral.com nicely displays the VIX futures term structure that is also available at CBOE.com
Jim,
I just allocated 5% of my portfolio to options sellers (sent the stuff in today). I think should be able to make 40% over the next year or so…selling VIX. But could be a huge DD in there, so can’t bet too much.
Best,
Tom
Tom,
Thanks. I will invest 5% or less also. BTW, in looking at this again recently I found the KKM Armor Funds (tickers UMRAX, UMRIX ) which uses the VIX to hedge long SPY positions. They say they can do this with minimal losses due to roll yield. Here is a quote from their web site: “The ARMOR Index is a proprietary long volatility methodology that seeks a high correlation to the VIX index, and is designed to match and potentially exceed the total return of the VIX index over the medium and long term time frames.”
KKM financials: [url=http://kkmarmorfunds.com/us-armor-equity-fund/]http://kkmarmorfunds.com/us-armor-equity-fund/[/url] developed the Armor Index but it is now used by CBOE so this is probably a legitimate hedging technique. I do not really know enough to recommend the fund but it might be worth looking into.
It’s been a really long time since the VIX last crossed 30…
Tom and Jim,
I also considered opening a short VIX position on the same day but passed as I already have enough risk in my portfolio. However your timing looks promising. The armor funds are on my watch list but I will not consider allocating any funds to them until they perform out of sample. I have seen way too many alternative type funds break down out of sample.
Scott
Have a look at LTCM in the 90s. They played with vola too!
Pretty smart People had been blown away by assumptions that underestimate vola e.g. the Distribution of stock Returns (and other assets).
If you do it, Keep your bet size steady and do not leverage (wrong assumptions about Price distribution and leverage = 100% probability of 100% capital loss sooner or later.)
Optimal F, and all those models will not help because they base on assumptions that are in most cases absolutely wrong (at least in the Long term) for example normal Distribution or a Distribution based on a selection of stocks and a too short history backtest.
As Buffet said “Somebody talking to you about Beta? Zip your pocket book an go away”.
If you short vola, you have to look at the whole history of stock trading (1870?), because if your allocation is off only slightly when
(not if) you lose 100% of your capital allocated there.
In General:
If you calculate a drawdown of 25% because your backtest tells you it had a historical mdd of 15% that will never get in to my head.
The Modell I trade has a historical mdd of 20%, but there will be a time when the stock market tanks more 50-65% (small caps or tech, maybe even the dow) in the next 50 Years (hope to live that Long!) and my market Timing will miss one of those drawdowns (pretty sure about this!) and then my modell might have a mdd of maybe 70%. In this case I am also glad not to be invested in any structured or derived financial product but only in (Long!) stocks!
How to protect? Expect a Monster drawdown, e.g. never leverage, invest regulary (cost average effect) and never invest Money you need within the next 10 years. And base distributions assumptions on Monster black swan Events!
Sorry to be opinionated, might come from a very Long term perspective I plan my finances and the finance situation of the next generation (two sons that will hopefully be the next Buffets ;-).
Andreas
Andreas,
Could not agree more on leverage and even letting your winnings ride… My plan would be to use percentage betting in the following way: I will reset my allocation to 5% each year. This is almost certainly below any Optimal F. I may make 40% many years but plan on losing 100% in one of the years.
With a little luck, with time and with no change in the behavior of the markets the winnings should outweigh the losses. If the allocation is reset to 5% each year most or all of the winnings from the previous years would not be at risk.