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Walter and all:
Just a caution for those who have not read Ralph Vince's books, the Kelly
formula is only applicable where there are only two possible outcomes -- a
win of $X or a loss of $Y -- as with a roulette gambler using a fixed bet
amount. Do not apply this formula where the amount of wins and losses vary.
(A little useless trivia for the math nutcases here -- apparently the
Kelly formula was developed by some Bell Labs engineers to solve the problem
of random, unavoidable "noise" that would interfere with data transmission
over long distance telephone lines. Apparantly there are similarities
between this problem and gambling money management.)
Where you get an optimal f that suggests you buy, as you mentioned, 8.6 corn
contracts, Ralph Vince suggests you round down to the nearest integer (since
it's safer to be less than optimal than it is to be greater than optimal) or
buy a combination of full-size contracts and mini contracts.
I, too, would really enjoy Rick Mortellra's thoughts on this stuff as he has
been putting it to regular use for several years. What do we have to do to
bait you, Rick?
You also mentioned 3, 4 and 5 Sigma losses (the once-in-a-blue-moon ones 3,
4 and 5 standard deviations from the norm). Unless a person's historical
results include one of these monster losses, their optimal f calculations
will be too aggressive. The Mathematics of Money Management describes a way
to adjust optimal f for fat-tailed, leptokurtic distributions to take this
likelihood into account. Unfortunately, I can't see a practical way to
apply this. Again, maybe Rick has worked through it.
The GARCH information would be really interesting if it is written for
regular people. I recall trying to read one paper, and got stuck on the
pronunciation of "heteroskedasticity", let alone its definition :)
Regards.
----- Original Message -----
From: Walter Lake <wlake@xxxxxxxxx>
To: Metastock bulletin board <metastock@xxxxxxxxxxxxx>
Sent: July 2, 1999 18:26
Subject: Optimal f
> Hi Glen and Lionel
>
> In "Portfolio Management Formulas" Vince provides the following "Kelly
> formula" for determining Optimal f for a sequence of "bets".
>
> f=((B+1)*P-1)/B
>
> B = ratio fo amount won on winners to amount lost on losers
>
> P = Probability of inning bet
>
> F = optimal betting fraction
>
> This probably works using stocks because you can buy odd lots, i.e., 863
> shares. Not so easy in spreads or buying 8.6 contracts of corn.
>
> Rick has a stock and gambling background maybe he can help explain how it
> works in real life.
>
> With contracts, where this breaks down is when the price gaps through your
> stop and is off to the races. Sigma 3, 4 and 5 events are the real equity
> killers.
>
> Hence the use of non-Gaussian probability tools (e.g.,
> fat-tail estimators, rare event analysis) to quantify their risks. ..."
>
> Will dig out Mills' work on the GARCH (Generalized Autoregressive
> Conditionally Heteroskedastic) models for stochastic processes to generate
> fat-tail distributions and volatility clustering if you're interested
Glen.
>
> Best regards
>
> Walter
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