Sure but its no reason not to trade strategies that easily beat the market.

Its a vitally important issue but its not an example of the arbitrage not working anymore. I'll deal with it in a second.

Very few brokers merely collect rake. The guaranteed +ev strategy I have will get you banned if you try to trade it with one broker (that has actually happened btw) even though you could easily trade it if you split it between two different brokers

Absolutely but its no objection to an arbitrage that easily beats the market.

I used to agree with you but this is in fact not a serious problem at all. Initially introduced to this subject the problem seems to be to try to trade in such a way that the catastrophe cannot happen but the correct approach is to assume it will happen andmanage your bankroll. Worship at the feet of Mr Kelly not Mr Martingale.

I'm tempted to go as far as to say its a good thing.


No way, the data is most definitely in my favour. The risk is the future not rhyming.

I agree with Rikers (next post)

That's my view too. He is attacking the weak end of the spectrum but we get to choose what we bet on and its the stronger part of the spectrum that matters.

We really shouldn't care if pairs trading doesn't work unless we can generalise the reasons why it doesn't work to all arbitrage and the example I gave shows it cannot be so generalise.

I have a set of limit orders well below the current market levels that never have hit. I cancel and replace these orders monthly based on new calculations.

These currently (and usually) are around 90-95% of my outstanding orders.

Haven't had any complaints from the brokers.

Well, we both attempts to do such things, so I am not arguing against the value (or perhaps motivation) to attempting such, but I have doubts as to whether + calculated ev is the same thing as +v.

Either you forgot to do this or Wittgenstein has a point.

This has me almost entrigued enough to ask you for specifics again. The funny thing is that I'd not likely change my strategy in favor of yours since mine meets my goals.

If you beat the market by 10% (not 11% if the market gives 10%, but 20% if the market gives 10%), you will be very rich in short order.

I am either a little bit humbler (or just a bumbler), and expect 1-2% greater (i.e. 11 or 12 % vs 10%) than what the market hands out and I am pinning my hopes on people continuing to act like people do in order to get that. I have significant downside possible if people either stop acting like people or if my model is significantly wrong.

Neither one of us is going to live long enough (or are rich enough) to take advantage of either Mr Kelly or Mr Martingdale.

They work only when one has infinite of number of bets and amounts of money.

At anything less than infinite, the math falls apart. But, yes, I use something approaching a combination of the two approaches. The difference is that I use only the difference between my expected results and my real results to make my bets. When I am below expectation, I put more in, when I am above my expectation I pull some out.

That is pretty much what I said. The data has been singing a pretty little tune, but it does not imply that it will not change its tastes significantly.

If spot and comex gold can differ by up to $0.50 for no particularly good reason, there is no reason why they can't differ by $5.00 other than that people bet things back into line.

This will have to wait. Lots of thoughts on this, but need some time. I'm pretty sure you are both wrong, but I am completely sure I am also wrong.

I said i'd get back to the vitally important issue of unexpectedly large price mismatches. I did, maybe it wsn''t clear but I ll get back to it and this time I'll tell you when i'm back

If it could be traded with a single broker then you could add it to your stratgey and mak a very handsome return on your non-invested cash. Sadly, as explaine din te BFI thread, you cannot (even if you knew what it was)

You still need a lot of time or to invest a lot to get rich at 20%. I dont have a huge pile of investable cash so working on very low 5 figure sums at the moment. Planning to sell a house to jump to low 6 figure sums and make some serious dough but that plan is to sell in spring of 2014.

I'm extremely humble, I recognise my luck at stumbling in to this but that's no reason not to take advantage, I'm going to slaughter 20%. It is however market independent so I'm just assuming the market wont shift to produce systematically astronomical returns. Very high inflation would be an issue as its also inflation independent but that's easy to spot.

This is a key point, I cannot eliminate risk in my approach but I can make it of the same sort of order as yours.

No they dont. We are now back (**BACK**)to the unexpected large price differences. The usual stat arb approach is to work out how large differences have got in the past, double it, add something for luck and then assume that's the largest you will encounter. Then you design a martingal approach of initial small bets, increasing your bets as the divergence grows and scaling it so you have enough money to cope with your assumed largest divergence. I started off with this approach but viciously argued it was flawed.

There are two problems with this a) the assumed largest divergence will be exceded and you will go bust b) it forces you to bet very small most of the time.

The alternative Kelly approach to limit how much you bet on a divergence based on your bankroll size. Now if a divergence grows significantly you have to reduce the bet size as your bankroll has been diminished. This deals with the two problems as a) you survive the larges divergences with a large part of bankroll intact and b) it encourages larger bet sizes most of the time which as each bet is hugely +ev make a mega difference.

No-one can avoid this, capitalism could end, neither strategy will work, not worth worrying about. The most likely way my golden egg gets cooked is if some huge money starts exploiting the same arb but then all that happens is the arb ceases to exist.

Mr Kelly is there for me. Thinking about trading this example you can imagine how seductive it would be to martingale yourself to death and how hard it is to dance with kelly but its what has to be done. You also have to grasp how stunning unlikely and rare it is which is the other reason to embrace kelly and explouit more fully the commonplace.

You are wrong

you obviously don't spam with limit orders....

try recalculation on a tick based time-frame and post the results (prediction: broker will call you within that day)

You will find that average Joe (let's give him a $100k account to play with) will lose his shirt to transaction costs quite quickly using anything approaching a high-frequency approach.

The only reasons why the big boys can do it is because their transaction costs are lower, they are highly leveraged and they can skip line and split the difference between bid and ask prices and take the resulting profit (or use micro-stat arb practices that are questionable). Even with those advantages, they still don't make a lot.

If they were doing quite well at it, they'd not be having trouble making a profit and they'd not be reducing their reliance on such techniques. They are pretty smart and, if I understand them correctly, like money.

You did (and did again below) but it lacks a certain sense of correctness. See below.

I keep that non-invested cash around for a reason. I need it for other things.

Plus, I have 4 brokerage accounts.

If you can make 20% returns, you should be massively leveraged.

Somewhat less importantly, an 20% returns (with no addition of capital) gets you 100 times your initial investment somewhere around 25 years. $100k times 100 isn't exactly chump change.

Just a point, but that is where we differ significantly. I have significant cash and sold my house before I moved to my current location. No plans on buying out here (unless I suddenly find $10m or so between the couch cushions and concurrently develop some sort of mental illness that involves me forgetting about how nice Costa Rica is). I have invested in real estate before (owned a couple of duplexes) and don't envy you. It is way too much like a job even if you farm out all of the real work.

Inflation doesn't matter too much to returns on most investments unless it gets seriously high (or if there is deflation at all). Most things keep up with inflation nearly by definition.

When you are doing any sort of long-short technique, inflation is a huge deal. High inflation indicates a long only approach.

[/quote]No they dont. We are now back (**BACK**)to the unexpected large price differences. The usual stat arb approach is to work out how large differences have got in the past, double it, add something for luck and then assume that's the largest you will encounter.[/quote]

It isn't quite that. There are techniques to approximate confidence intervals for non-parametric data. But, in a nutshell, you are close enough in describing the "usual" approach.

A smarter approach is to make loads of concurrent bets that are independent.

A really smart approach is to realize that you still have the problem of determining whether independence of bets actually exists. Still, it is better than the usual approach.

A better approach is to make multiple ongoing and overlapping bets of a similar nature amongst non-correlated things. Of course, you have to find loads of them, which might be a problem.

This can be fixed by making numerous independent bets of the same size. You eliminate the problems inherent with having money on the sidelines. Money on the sidelines is only useful if you expect deflation. Even then, there are things that do much better if deflation hits.

I use a somewhat different approach. I change the size of my bankroll instead.

Or, rather, I have multiple bankrolls. When my stock portion gets "too big," I make a brand new bankroll (buying fine cured meats with it, perhaps) instead of making larger stock bets.

I then pray to the god of fine cured meats that it is as undervalued as I think it is, and that I will have a bit of time to get my ill-gotten gains into it before it takes off.

Or things behave the opposite of how you expect them to 10 or so times in a row... That might not be a bigger probability, but it is the biggest risk probability times utility loss for you.

See above. Neither Kelly nor Martingale approaches work outside of imaginary scenarios.

Granted, you've got to do something, so I generally approve of your approach.

I forget what I wanted to talk about at some later date already, which makes you correct in a fashion.

probably my fault for not being clear

The 'risk-free' arbitrage could be closed at any time, its always in profit and highly liquid. It would be as good as cash but earn a very high rate of return. Sadly as I said you would get banned by your broker

That wont help. Put it all with one of them and they will ban you, put it with two of them and your counter-party type risk is too high.

I hope its been clear that this 'risk-free' arb although real is not the one I trade (for obv' reasons) and makes up the rest of the discussion

True and if i was young it would be lovely. Now it wont make me rich until i'm dead.

I do very little for my returns. I agree very little is still too much like a job and if I wasn't benefiting from criminally low mortgage rates (lucked into base rate trackers) I would sell them now.

It was a simplistic discription. all the more advanced techniques are good ways to convince yourself of something that will bust you.

What as a way of reducing risk using a statistical approach?

Thank you. The interdependence of divergences (and even what constitutes a complete convergence-divergence cycle) is something I think about but mostly because I'd like to exploit it. A lack of independence however doesn't change the Kelly or Martingale issue significantly. As I point out again later were talking about handling a few times in a generation type events.

Yes well when you find a way of slaughtering my returns that slaughter yours then let me know.

Fixed is basically a martingale and will bust you. Independence as smart people realise is a dnagerous game.

That's just finacnial masturbation. you have one bankroll.

Anotehr advantage of Kelly. Martingale (inc fix bet size) will bust you unless you bet stupidly small.

They work precisely above. The 10 in a row example is a reason to kelly and not Martingale - set them for the same return and Kelly does it as a significantly lower risk (or set them for the same risk and kelly produces amuch higher return). There is nothing imaginary about this scenario at all.

but in practice the 10 in a row is simply not an issue, its so unlikely compared to one crushing huge divergence. 1 in a row is a few times a generation type event, the only reason to worry about it is it will bust you.

Too polite. I read it too quickly.

Intrigued, but...

I seldomly make bets that I can't make...

So, if I understand, you make a trade that is close to, but not quite exactly, the one that doesn't actually exist in real life.

It is scalable. One does need to expect some amount of life left in oneself in order to make returns something to be desired.

Being leveraged does help. I'd not be in a hurry to sell in the current environment if I were you. I think we are in agreement on this.

MAY bust you. The more advanced techniques make one less sure, not more sure.

I think that I have mentioned how wide my band is on what is the population real return on stocks as a whole at a 95% confidence level. I'm feeling lazy and won't re-do the math, but it is a very large band.

Only as a way of getting closer to Kelly's assumptions of infinite numbers of bets.

Of course.

This is wrong. Kelly and Martingdale assume stable (and known) probabilities. Regime changes are not taken into account.

I would. Anything important that I find will go completely against human nature and you (as a silly human) will not have the stomach for it.

Fixed is assumed by Kelly as well.

No, I have one net worth.

I can change my bankroll through leverage.

You can't Martingale with fixed bet sizes.

Both require infinite numbers of bets as a possibility for the math to work. (Large numbers of independent bets get you pretty close though, as long as the odds are known, which they aren't)

Kelly gets you to nearly nothing, and Martingale gets you to precisely nothing. No real difference in utilitarian value other than working 10 hours per week or 11 hours per week at minimum wage as an old person trying to make ends meet.

The math gets messy because future returns are correlated negatively with your past returns. There is every indication that the assumptions that Kelly and Martingale REQUIRE are not only not met, but that something approaching the opposite of their assumptions is true.

All it takes is an unexpected regime change.

No two diferent beasts. The one I trade is conventional type stuff, the one i I dont trade is the one we discussed in BFI where apart from trivial transaction costs its always in profit - there is a simple maths proof that shows whatever way the market moves it makes money. I still hope to have a go at exploiting it but the counter party type risk of the necessary multiple brokers is daunting.

Generally I might agree. In London we have a boom and if the government wasn't shovelling money at me with the low base rate I think selling would be correct. Some tax and partner issues make this very complicated.

The real danger of the advanced maths is it encourages believing the result when in fact its a garbage in garbage out process.

The maths proofs assume them. Anyone who uses the approach of reacting to losses by betting larger (in proportion to bankroll) is following a martingale type approach to bet sizing and you can do maths on it. similarly with kelly.

Strictly speaking kelly is a martingale but how literal do you want to get?

No you cant, you can chose to leverage your bankroll to different extents. Not sure we need to continue what is a semantic point.


You most definitely can.

Maths always works.


This is a good point, whenj doing the kellying you have to count a workable minimal bankroll as the nothing, below that you are bust. Remember I'm not claiming kelly is riisk free just much lower risk for the profit made.

Why so?

I disgaree, it would be true for very large positions but while I remain insignificant which even with a fair wind I easily will its not an issue is it?



As for you and everybody else.

I believe there were also leverage and whether it could beat some sort of risk-free rate of return that were also problems.

Of course, if you can find such a beast with minimal counter party risks (or protect yourself through dividing yourself into several corporate entities), I'd say try to get 100x leverage and have a go at it.

The problem with the government supporting housing prices through low rates is that your long-term prospects suffer. They are, in effect, propping up prices. Quite nice of them for average Joe who is struggling to get by, but it doesn't matter if prices drop in the future that your returns are great now...

The partners thing is an issue. You should have been too smart to get yourself into that pickle.

Is the tax thing a penalty?

I generally think that it helps (and it is far from advanced). Understanding that the sample mean is not the population mean. People get into much more trouble thinking that the market returns 6.5% on average, than if they think the market returns somewhere between 1% and 11%. (I am not going back and doing the real math again for this thread, so the numbers are made up)

It is only a Martingale in the sense that they are both betting schemes.

I can also pull money out of my bankroll. Leaving aside the semantics that I cannot willy nilly just chose on some random Tuesday how much money I have, I can decide how much to have in the game.

I actually looked at a strategy of keeping the size of the bets the same and making more of them as they became more and more of the no brainer sort.

I didn't have to look at any data to double check the results of the idea. It was incredibly stupid.

Technically true, but I was using the common idiom.

You could do the same with a standard Martingale double down strategy.

It still fails massively. That the future is not independent of the past makes both of them (as standardly used) stupid.

The standard argument is that people assume that when things have been going downhill, people are excessively pessimistic about the future, and when things are going uphill, people are excessively optimistic about the future.

This creates supply-demand changes that are partly emotionally (optimism/pessimism) based. In other words, sometimes things get a bit more expensive than they should be if everyone were Mr. Spock, and sometimes a bit too cheap.

I think it is a bit more complex than that, but the standard argument doesn't lead to much different results than my take.

It isn't just your returns that are important. It is the market returns that are not independent.

This is not craps, where each throw of the dice is independent. If the (for instance) S&P doubled in real* value tomorrow morning because of some magical great news (probably something about Europe ceceding from the earth), then it is highly unlikely that it would be a good idea to buy tomorrow, right? To think not is to believe that it (today) is underpriced by 50%, which seems quite silly.

FWIW, my silly calculations have the S&P undervalued by 12% or so today. I am unimpressed, as it being half off or double is not a rare occurance (if I were stupid enough to trust my calculations too much**).

I assume that there will be regime change (of the statistical/probability sort, in case people think we are talking about politics).

I think that with such complex relationships between all of the players (who are playing using human brains), it is nearly certain that we will have regime change.

One can weigh making perfect bets under the current equations, or assume that the equations will change (suddenly and without warning) and take a safer route of making suboptimal bets today that are likely to save one's bacon tomorrow.

*bandying about real returns instead of nominal returns is fun when you are talking about tomorrow.

** I do have very very pretty graphs as well.

The only problem is counter-party type risks. The other issues come about from trying to avoid the counter-party risk.

Sure it matters. The low base rates are a transfer of wealth from savers to people like me. They wont ever get it back.

So true.



Its predicting divergence sizes and lengths that would be useful but advanced maths to calculate the worst case is just garbage - its not a maths problem.

no either they arfe both martingales or neither are. However I would hope its clear I'm using the words in to distinguish two different approaches. One increases bets to bankroll size and one keeps the bet to bankroll fixed or even reduces it.

The amount you stick on a table at poker is not your bankroll size, not is the amount you have in your pokerstars account (free world only). the markets are no different, if you have the money available to gamble/invest then its part of your bankroll, even the less liquid stuff.

Yes we're assuming fixed betting rates but of course frequency matters. i could add to my position in tiny ammounts but it if I do it very frequiently its much the same as adding one large amount.

I was making the point that if we follow some finite version of your idealised K or M then we can still do the maths. Infinities are not required.

You can yes but still have to bet relatively tiny most of the time. This is a bad ideas when the bets are +ev.

I have no idea why you say that.

None of that makes any difference to me.

As above.

They may not be but they're not biased against me.

pretty much indpendent. What you say may well aplly to the type of stuff you do but stat arb type stuff does'nt care whrether the S&P doubless in real value or not or is cheap or expensive. That's kinda the point of market neutral type strategies.

Mine have it as overvalued. I say mine but its just a feeling in my gut as I dont measure it. I appreciate your approach to this, makes a lot of sense but only compared to othr ways of investing in equities.

If I assume things stay the same then I slaughter you. The issue is our different risk profiles if things change in significant but not totally destructive ways. My approach is inherently more risky.

tbh, I didn't understand your point on this...

if I bet x amount on divergence and it goes against me...
"averaging down" but reducing your bet size still exposes you with a greater risk to a bankroll bust (but not so big as a martingale)

after you have a size that is bigger then the average best bid/offer calculating how much you bet on a divergence based on your bankroll size is irrelevant because it becomes a liquidity problem and not a bankroll (on average)

doubling every day ~ 1000x every 10 days, so we get to ~10m in 30 days. So I guess 27 days and the offers are about even.

that seems to simple?!