Comments on Max Dama on Automated Trading: Ralph Vince 2009 Leverage Space ...

Thank you

2010-02-24T18:52:47.828-08:00

Thank you

Max, Your criticisms I certainly don't find naive ...

2010-02-24T06:26:41.729-08:00

Max, Your criticisms I certainly don't find naive -- they warrant response on my part. The nomenclature part I mention because I know you have an interest in the academic lineage of all these kinds of things, and perhaps your instructors -- for whatever good reasons of their own -- don't hold Latane's contributions to this as I do.
Your blog keeps getting better and better, thank you for sharing the things you are learning as you go along here. I'm sure I'm not the only one enjoying (and learnign from) this ride. This is one of my favorite sites.

Ralph, It's good to hear from you - I'm looking f...

2010-02-23T14:43:58.599-08:00

Ralph,

It's good to hear from you - I'm looking forward to testing Josh's implementation of the LSPM.

I've since come across other uses of the notation I naively criticized.

I personally love the empirical distribution approach to probabilistic modeling. It's unifying and I find it intuitive. It's a very natural generalization of 'numbers' to 'uncertain numbers'. Monte Carlo provides an efficient implementation, although it brings along many of the problems of optimization- getting stuck, running forever, and generally being harder to interpret and feel confident about. There is intuition behind it, which I'm sure you've developed, but I can see why you wouldn't want it in your book- it's hard to understand if a reader doesn't have the luxury of a good university professor.

Regards,
Max

Max, A couple of quick comments -- 1. I like your...

2010-02-23T14:30:08.659-08:00

Max,

A couple of quick comments -- 1. I like your blog very much, obviously others do as well -- please keep it up! (I mentioned your blog on a gambling blog and the readers there enjoy what you write very much) 2. The nomenclature I use is not my own, but has long been accepted nomenclature in the industry -- e.g. TWR/HPR come from the earlier works of Latane & Tuttle in the early 1960s. 3. I'm quite intimately familiar with Monte Carlo techniques; my problem with them is that although they converge to the solution, we don't see the Mathematical "Why's" of it -- hence the formulation, say, for determining drawdown.

American, Sorry, you're right. I didn't mean it w...

2009-11-20T15:45:57.812-08:00

American,

Sorry, you're right. I didn't mean it was that strongly equivalent. Here's a more complete explanation- http://www.maxdama.com/2009/07/kelly-criterion-equivalent-to-markowitz.html

The claim above now has that link embedded too for elaboration.

Regards,
Max

Max, It is not true that "MVAR optimization is e...

2009-11-17T08:03:19.854-08:00

Max,

It is not true that "MVAR optimization is equivalent to Kelly criterion betting. "

That is absolutely false. Kelly Criterion is equivalent to optimizing the log of utility.

MVAR just requires a utility function.

So MVAR is not equivalent to deploying the Kelly Criterion.

Cordura, I'm sure you can think of as many ideas ...

2009-08-19T18:18:31.347-07:00

Cordura,

I'm sure you can think of as many ideas as I could but I don't know of many published results on the topic.

One article I read said a trading firm basically put bollinger bands on each of their system's equity curves and when the system hit the bottom band it was shut off.

Most things I've heard of are heuristic like this.

Regards,
Max

yes, basically yo answer the questions: what diffe...

2009-08-15T02:42:56.856-07:00

yes, basically yo answer the questions: what different systems should I trade at the same time? How much capital to allocate to each of them? How do you rotate different systems? This is on the premise that more decorrelated systems will allow you to achieve better consistency than just one.

Cordura, I don't know of any resources specifical...

2009-08-14T13:52:30.964-07:00

Cordura,

I don't know of any resources specifically on mixing trading systems. I'm not sure exactly how you plan to mix them either- is that the question?

Regards,
Max

Hello Max. Can you recommend a good resource on th...

2009-08-14T12:40:37.420-07:00

Hello Max. Can you recommend a good resource on the web/book about mixing different trading systems? This book looked like a good resource, maybe there are others. I used to read Bill Rempel's excellent site, but it's not there anymore. Thank you.

You're welcome Josh. Many results show a so-calle...

2009-07-05T19:24:38.815-07:00

You're welcome Josh.

Many results show a so-called "fixed" fraction of assets is best. The fixed fraction results are based on the assumption that the distribution of returns is stable and stationary though. It could be better to determine the allocation adaptively based on a sliding window that gives you a shorter sample of the return distribution. Watch out for overfitting if you add this variable.

Regards,
Max

Max, That's a perfect example; thank you. It sho...

2009-07-05T18:56:15.006-07:00

Max,

That's a perfect example; thank you. It shows Vince's example is not "apples-to-apples".

Do you have any thoughts on his comments about the "schedule of positions over time"?

Thanks again,
Josh

Josh, (Sorry I didn't do this in R, I'm familiar ...

2009-07-05T18:16:14.004-07:00

Josh,

(Sorry I didn't do this in R, I'm familiar with these Matlab functions already - it should be clear enough)

Here's the code for calculating the MPT's recommended leverage i.e. allocation to the portfolio vs cash:
ExpReturn = [1 1.0001]
ExpCovariance = [std([-1,2]) 0; 0 std([-1,2])*1.0001]
NumPorts = 50
[PortRisk, PortReturn, PortWts] = frontcon(ExpReturn, ExpCovariance, NumPorts)
RisklessRate = .0001
BorrowRate = .0001
[RiskyRisk, RiskyReturn, RiskyWts, RiskyFraction, OverallRisk, OverallReturn] = portalloc(PortRisk, PortReturn, PortWts, RisklessRate, BorrowRate)

outputs => RiskyFraction = 0.3142

(Due to Matlab stupidness the two assets have to be slightly different, hence the .0001, and the interest rates can't be 0, hence .0001 there.)

The result is that MPT says ~.3142 should be in the portfolio and ~.6858 should be in the risk free asset. Obviously this is less than than Kelly/LSM because MPT assumes gaussian returns while the example is highly skewed. The "downside" part (-1) of the standard deviation/risk is lower than the "upside" part (+2) but MPT's gaussian assumption ignores this information and assumes symmetry. In this case less is at risk than MPT thinks, based on its inadequate summary statistics.

Regards,
Max

That's exactly the example I had an issue with. In...

2009-07-05T17:29:55.478-07:00

That's exactly the example I had an issue with. In MPT when you provide a risk-free rate and borrow rate it allocates a portion of the money to the risk free asset - which can be positive or negative.
Agreed. Though, in that example, the LSM suggests a 54% allocation to a risk-free asset paying no interest. What would MPT suggest as the optimal allocation to that same asset, given the example?

Josh, That's exactly the example I had an issue w...

2009-07-05T03:02:41.121-07:00

Josh,

That's exactly the example I had an issue with. In MPT when you provide a risk-free rate and borrow rate it allocates a portion of the money to the risk free asset - which can be positive or negative. (In finance class you might remember this as the part where you draw a line from the risk free asset to the efficient frontier such that it's a tangent.) This is the same thing as leverage. Vince seems to have rejected the things he criticizes without understanding them.

"I haven't yet worked through the math to convince myself why the latter is preferable to the former, but they are different and Vince argues that leverage causes the difference."
1/4 of the time both assets will be down. With the 50/50 allocation that means you're broke and can't recover. Therefore less than 50/50 is preferable for a long-term investor.

Regards,
Max

Max, I'll admit I'm not intimately familiar with ...

2009-07-04T15:34:13.275-07:00

Max,

I'll admit I'm not intimately familiar with either MPT or LSM. I'm educated in economics and I taught myself most of what I know about finance.

With that caveat, Vince provides some explanation in The Handbook of Portfolio Mathematics, pp. 297-303 (with an example on p. 302). To paraphrase the example: for two uncorrelated and identical coin-toss games with 50/50 odds and 2/1 payout, MPT suggests allocating 50% to each game. The LSM suggests allocating 23% to each game.

I haven't yet worked through the math to convince myself why the latter is preferable to the former, but they are different and Vince argues that leverage causes the difference.

Best,
Josh

Josh, Doesn't MPT consider both "the snapshot of ...

2009-07-04T09:22:13.912-07:00

Josh,

Doesn't MPT consider both "the snapshot of cash vs. the position and the schedule of adding/subtracting from that position"? I'm not sure what I'm missing.

Regards,
Max

Your critisism of his claim that MPT doesn't consi...

2009-07-04T08:08:03.627-07:00

Your critisism of his claim that MPT doesn't consider leverage is misplaced. You need to remember that he assigns two meanings to the word "leverage". His definition of "leverage" is both a stock and flow variable (the snapshot of cash vs. the position and the schedule of adding/subtracting from that position).

I haven't read this book, but I just finished The Handbook of Portfolio Mathematics. I don't imagine they're terribly different. That said, I have a hard time believing he suggests agents should maximize unconstrained geometric growth when he suggests maximizing geometric growth subject to a probability of a specific drawdown, since that is more in-line with agent's objectives.

Thanks for the review!

Max, Wow, after all the comments about Kelly by y...

2009-06-27T09:46:25.533-07:00

Max,

Wow, after all the comments about Kelly by your readership, I would have expected a little more heat from them about what Ralph has to say.

He does make one think out of the box ;-)

Cordially,

-Digital Dude-

"A standpoint is an intellectual horizon of radius zero." -Albert Einstein-

An article on interactive brokers and R. http://c...

2009-06-12T08:34:59.499-07:00

An article on interactive brokers and R.
http://cran.r-project.org/web/packages/IBrokers/vignettes/IBrokers.pdf