While that sounds appealing, I don't see the point of it when you can use Kelly to achieve maximum growth per a tolerable risk of ruin.
I'm pretty sure it can. I guess Thorp / the literature I've seen don't give a formula but we can just take Thorp's calculation for Example 6.1 (simultaneous wagers) and replace some probabilities with conditional probabilities if the coins in that example were correlated.

False. Kelly doesn't account for correlation of returns if you're bad at math and cribbed the formula from a website without understanding what you're doing.

Big difference.

Do you have link(s) to resources or books on using Kelly in the equity market?

http://www.amazon.com/Beat-Market-Sc...eat+the+Market

Only useful if you can do the other quant/arbitrage things that he did.

Thx for the link, will look into it

Since many of us have some advanced math under our belts, we'd love to see your analysis of how you are using Kelly to size your equity bets.

Here is the origin of your 200-day SMA (10-month instead, so actually +/- 210 trading days):

http://3.bp.blogspot.com/_kUcjE0BhmC...1600-h/EC2.jpg

Works great only during the time period you mentioned. It is crap otherwise. TANSTAAFL.

note: the period tested is a fluke

1980 - 2000 over-represents the amount of upmarket on average (and it's a credit/debt bubble). The only problem is you're active life is shorter then market variance....

see below:

Layer on top of that lesson that you cherry picked one of the best behaving stock markets in the world over even the longer period.

ok guys, king of newb questions here. I just saw a pomotion for sharebuilder. Rollover or fund an ira for 125k+ and earn $600 bonus, not bad, would get taxed though. I want to get out of prudential anyway. Well to the point, are these promotional bonuses common? i am going to call them tomorrow to see if I have to fund the account for "x amount of days?" could i rollover my retirement fund each year to scoop these type of bonuses? im bonus whoring in the US and A

9 months, i have to let it in there, thats cake. 9 months for a $600 bonus while i get to invest it however i please. what's the catch? what kind of fees would i pay if i did not perform a single transaction after i roll it over, just let it sit for 9 months?

That is going to be a gain of less than .5%. I would think you can probably increase your expected return by .5%/yr investing w/ an advisor who knows what he is doing.

an advisor eh? my current advisor at prudential, meh. its mostly buy and hold and i think his fees(not exactly sure of them but i have looked sparingly) will outweigh his expertise in the long run. may move to vanguard but that $600 offer seemed enticing from sharebuilder. i wish there was more time on this earth and then maybe id be a little more savy with this ****. lir

Lately, I was skimming through a book The New Money Management by Ralph Vince (1995). He says that the optimal f depends on the number of trials (and asymptotically approaches the kelly f).

He's maximizing something he calls "expected average compound growth" (EACG). He uses an example of a 50/50 coin with 2:1 payout.
If we're going to quit after:
1 flip, the f is 1.
2 flips, the f is 0.5
3 flips, the f is .37868
4 flips, f = .33626
...
8 flips, f=.2871
...
infinity flips, f = .25 (kelly bet)

That table is on page 80. I don't understand how he got those numbers or how they're justified. Anyone know?

I can see why f would vary with #flips. If you're only playing 1 flip, it's meaningless to talk about exponential growth. With a few flips, you want to make the most of your finite-time opportunity, hence be a little more aggressive than kelly.

In practice, the f approaches kelly pretty quickly, so knowing the finite-time f might not be useful. Still interesting though.

Edit: then on p. 81 he says: would you guys agree?

For all of you that think "buy and hold" is the way to go, this is the ONLY chart you need to see to show you that theory is the worst thing you can do.

http://charts.stocktwits.net/product...png?1395879992

good luck

It is simple math. What you would want to do to get an explanation is to not just skim the book, but actually read it. He gives a thorough explanation.

Doesn't matter if you aren't making coin-flip-like bets though.

Yes. A simple demonstration is the example from above where you are only offered 2 flips on your entire net worth the year before you retire. If you are a wealth maximizer, you would put 50% on the first flip. Most people would say that such a thing would be a bit foolhardy, indicating that most people are not wealth maximizers.

The ones who thought they were (and bet the correct 50% as a result) who lost on the first flip would decide quite quickly that they just want to avoid having to work as a Wal-Mart greeter in their old age rather than being an actual wealth maximizer.

It shows that you shouldn't chase returns, and quite possibly that you should diversify outside of just owning stocks in a communist country. Nothing more than that.

And I'm not a buy and hold investor. After seeing the "ONLY chart you need to see" I am considering becoming one just because you are a silly person and I don't want to be associated with you.

It is a stupid waste of time. Plus there are often fees associated with transfers out of an account. Sharebuilder charges one.

If you want to roll it over into a place you'd rather have it, that is a good idea.

The advisor thing is stupid. Ignore that advice unless you will benefit from someone not letting you do stupid things with your account (actually quite common) or have in-depth knowledge on how to pick an advisor that will outperform (not so common).

I don't get that chart

It seems to imply that a stock markets return should align with its GDP which I reject

I reread those pages and now I see what he did. Yes it's simple and anyone can imitate it, but he doesn't explain why he does it. Specifically: why does he maximize EACG, why is EACG what matters for this problem?

Also, for what other things might EACG be used?

I am pretty sure the reason why he did so was so that people would buy his book.

You could also use it to help you get laid.

Maybe next time I'm single, I'll try that EACG thing out.

In the meantime, is my question too dumb for you to bother with, or do you not know the answer yourself?

He did it to show a math technique for bet sizing. I don't know if it was his intention, but it shows the difference between being wrong by just considering geometric means and being wrong by only considering arithmetic means.

Arithmetic mean is "correct" to maximize with one trial, geometric mean is "correct" to maximize over infinite trials. By "correct" I mean "gives you the best average overall win rate." As the number of trials increase, it becomes more (very quickly at first) "correct" to worry about geometric means.

Of course, this is only true on coin-flip games. I'm fairly sure that he only considered coin-flip games because they are easy to deal with mathematically. The problem is that there aren't a lot of coin-clip games in the marketplace other than actual coin-flip games.

An additional wee little problem is not knowing the actual odds or payoffs.

As far as other uses, I guess you could apply it to any sort of serially uncorrelated coin-flip-like game (known payoffs and probabilities with finite number of outcomes).

Still, overall, good math to know. Hope that helps.

Thanks. So EACG is like a middle ground between arithmetic and geometric mean that approaches geometric mean as n goes to infinity. I'll still need time for it to fully sink in (the way it makes perfect sense to use geometric mean for n=infinity), but this is a good starting point.

Do you just mean it's too simplified to apply to the market (which I wouldn't dispute), or are you saying we couldn't apply the same process to another simple discrete game with >2 outcomes?

It will sink in if you play with the numbers.

You can use the same techniques with 6-sided dice rather than coins and with different payoff amounts for each possible dice roll.

Beyond that you are going to need calculus. The funny thing is that it is exactly this sort of problem that led to the invention of calculus!

The big issue in real life is that you actually don't know the probabilities or the payoffs.

Something occurred to me. Having put Vince' algorithm into the form of an equation, to me it looks like what he's calling "eacg" is actually just an expected geometric mean. For finite n, it's a series instead of a closed form. I expect that for infinite n, the infinite eacg series will sum to the weighted geometric mean and I'll test that now.

Is my epiphany true? It's just expected geometric mean and there's no reason to call it eacg? (Btw from googling, the author seems to be the only one using that term.)

For n=infinity, I've been saying that we calculate "the" geometric mean, but no, I'm reminded that it's an expected geometric mean. The growth won't perfectly follow the expected curve just like linear growth doesn't perfectly hug the EV line. At the end of a finite number of trials, the actual and expected geometric means will differ. (I knew this, but were it in the front of my mind, I might have had the epiphany sooner.)

Sort of. It converges to the Kelly criterion (which maximizes the expected logarithmic growth rate) as the number of bets approaches infinity. At n=infinity, the only thing that matters in maximizing wealth is maximizing your geometric returns. If you are going to live forever (n=infinity) you can't improve the log of your geometric returns beyond Kelly betting. If you bet extra, you have worse results, and if you bet less, you have worse results.

At n=1, you can beat Kelly on average* by going all in. Going all in maximizes your average. This is because there is no effect from compounding (it doesn't make sense to even think about geometric returns with n=1).

At n=2, you can beat Kelly on average, but not by as much. There is a small effect from compounding (it makes a little bit of sense to think about geometric returns).


At n=infinity, expected = actual.

*In real life, you would be considered somewhat strange to go all in with your net worth on a single bet.