Optimalf 155
Return now to what was said at the outset of this discussion. Given
a stream of trade P&Ls, the optimal fwill make the greatest geometric
growth on that stream (provided it has a positive arithmetic mathematical
expectation). We use the stream of trade P&Ls as a proxy for the distribution
of possible outcomes on the next trade. Along this line of reasoning, it may be
advantageous for us to equalize the stream of past trade profits and losses
to be what they would be if they were performed at the current market
price. In so doing, we may obtain a more realistic proxy of the distribution
of potential trade profits and losses on the next trade. Therefore, we should
figure our optimal f from this adjusted distribution of trade profits and
losses.
This does not mean that we would have made more by using the optimal
foff of the equalized data. We wouldnothave, as the following demonstra-
tion shows:
Underlying Number of
P&L Percentage Price f$ Shares CumulativeAtf=.09, trading the equalized method: $10,000
- 2 .1 20 $33.33 300 $10,600
− 3 −.15 20 $33.33 318 $9,646 - 10 .2 50 $83.33 115.752 $10,803.52
− 5 −.1 50 $83.33 129.642 $10,155.31
Underlying Number of
P&L Percentage Price f$ Shares CumulativeAtf=.17, trading the nonequalized method: $10,000
- 2 .1 20 $29.41 340.02 $10,680.04
− 3 −.15 20 $29.41 363.14 $9,590.61 - 10 .2 50 $29.41 326.1 $12,851.61
− 5 −.1 50 $29.41 436.98 $10,666.71
However, if all of the trades were figured off of the current price (say
$100 per share), the equalized optimal fwould have made more than the
raw optimalf.
Which, then, is the better to use? Should we equalize our data and
determine our optimal f(and its by-products), or should we just run ev-
erything as it is? This is more a matter of your beliefs than it is mathe-
matical fact. It is a matter of what is more pertinent in the item you are
trading, percentage changes or absolute changes. Is a $2 move in a $20
stock the same as a $10 move in a $100 stock? What if we are discussing