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Gary:
Back testing over a long period of time over all kinds of market conditions
will tend to give you a more representative largest loss. Probably not the
career-ender loss that's in store for a person if they do this long enough,
but I suppose that's the risk ya' take :)
In my opinion, the key is to stay to the left of the optimal f peak (for
those not familiar with optimal f, picture the peak of a normal distribution
curve) and accept a lower return for the reduced risk. Not too far to the
left, mind you, because the reduction in return is not proportional to the
reduction in risk. Trading at less than optimal and how much less is up to
the individual and their own risk threshhold.
I would be interested in hearing more about your friend's Conservative f
technique. Also, be careful with substituting average loss for largest
loss. The effect of this is to reduce your equity-per-contract figure (f$)
which, in turn, might make your position sizes too big when you hit a string
of large or largest losses.
Regards.
----- Original Message -----
From: "Gary Fritz" <fritz@xxxxxxxx>
To: <realtraders@xxxxxxxxxxxxxxx>
Sent: Wednesday, March 01, 2000 2:45 PM
Subject: [RT] Re: Fixed Ratio or Fixed Fractional?? Pros and Cons of Each
> Before implementing a fixed ratio money management system, I would
> suggest you read Ralph Vince's Portfolio Management Formulas and
> his Mathematics of Money Management for a balanced viewpoint, not
> to mention a wake-up call regarding risk.
After reading Vince's book, I did a bit of experimentation with a
spreadsheet. The thing I didn't like about opt-f was that it
requires knowing the largest loss during the period -- which, of
course, you don't know ahead of time. It works great to decide what
you SHOULD have traded, after the fact, but it doesn't seem to me to
work so well for deciding what you should put on for your NEXT trade.
In reality, I think you'd have to use the "worst loss SO FAR," and
see what worked out best. Naturally, if at some point you take a
huge loss that wipes you out, that value of f will turn out to be
"too large" and won't come out as the optimal f value if you do an
opt-f analysis afterward. Which is nice in hindsight but wouldn't be
too comforting if you'd been trading near the previous opt f value
and got wiped out.
A friend of mine uses what he calls a "conservative f" which he
computes as AverageTrade / AverageWin. I forget his derivation of
this but he feels it's a safer approach than optimal f.
I decided to modify Vince's approach to use the AVERAGE loss SO FAR,
and use that to compute the f$ and betsize using that approach. The
formulas I used were:
AvgLoss = (average loss so far in the system's history)
f$ = -AvgLoss / f
BetSize = AccountValue / f$
Same as Vince, except I use average loss instead of largest loss.
Since the average loss is a bit more stable than the max loss, this
seemed to stabilize the results some. I usually ended up with an
"Average Loss f" value that was about 1/3 as large as the optimal f,
but the f$ value is only slightly smaller.
Interestingly enough, the TWR (Terminal Wealth Relative, the account
value at the end of the test) with my "Average Loss" f was MUCH
larger than the TWR for Vince's optimal f, which he claims is the
"largest possible TWR." (Although I used max loss SO FAR, and he may
be referring to the max loss during the whole test -- but that's not
too helpful for realtime trading.) E.g. in the test case I ran, my
"AvgLoss f" TWR was **25 times** larger than Vince's TWR.
Is this "AvgLoss f" any safer than optimal f? I think so. Certainly
trading *at* optimal f is lunacy, and you wouldn't want to do that.
I wouldn't want to trade at my "AvgLoss f" either. But you could
trade at 80% of the "AvgLoss f" (.142 instead of .178) and make as
much as you'd make trading at Vince's opt f, and I'd bet the non-
optimal "AvgLoss f" value is a LOT safer than trading at Vince's opt
f. So for less risk you get equivalent return. It seems to be a bit
more resistant to large losses, but I haven't studied that very much.
Is this really better than Vince's opt f? I have no idea. :-) I
don't have the math background nor the inclination to pursue it to
prove if it's a safer approach. But it sure *seems* to provide
better return for equivalent risk.
If anybody would like to pursue it, I can send you my spreadsheet.
It's about 420kb compressed, so it's too big to post to RT. It's not
really documented, but if you would like to take the above writeup
and a few additional pointers and figure out the spreadsheet on your
own, let me know and you're welcome to a copy.
Gary
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