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This discussion is very interesting.
Surely, for a martingale-type (or reverse-martingale) betting strategy to be
an improvement over a regular "1-lot", there must be some degree of
auto-correlation between consecutive trades within a system; otherwise, I
don't see (statistically) what is gained by changing bet size.
For instance, to take an extreme example, let's assume that we know that for
a certain hypothetical system, the trade AFTER a really profitable trade is
always a loser. Well, then we'd skip betting anything on the trade at all -
we'd only bet AFTER a loser, and we'd never bet after a winner. Not much
point in betting anything at all on a trade, if you're certain it'll be a
loser! Obviously, the less certain we are of whether the next trade will win
or lose, the less confident we can be that reducing/increasing the bet is a
sensible move.
So, if the relationship between Trade(N) and Trade(N+1) is completely
random, it seems to me that any bet modification strategy cannot hope to
have any meaningful effect on equity, compared with randomly changing bet
size.
As for Mark Johnson's "scary & intimidating" maths, I think the weak link is
the assumption that profit is proportional to risk. Obviously, we'd like it
to be (if profit can't be constant, of course!) but I don't think that
neccessarily makes it so. We have seen plenty of markets in the past where
less-risky has turned out to be more-profitable. Obviously, any profitable
system where you re-invest profits will have an exponential equity curve -
including putting the money in the bank (compound interest is effectively
just a power function Equity=Initial*(1+r)^n. Is guess Mark Brown's point
is really, "are you increasing your risk of ruin as you increase your
stake?" - there may be a drawdown out there waiting to blow you away. That's
why I always test systems on futures markets (where there is little
discernible long-term trend) rather than stocks (where buy-and-hold is often
a good strategy), and always on a constant bet-size.
Rus Newton
Tel: +44 181 360 8392 (old)
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+44 20 7681 1115 (new)
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