ABC. And why shouldn’t you? If you can afford to buy 100 shares of a stock
priced at $80, for a total value of $8,000, then you also can afford to buy 200
shares of stock priced at $40, also for a total value of $8,000. If you say you can
only afford to buy 100 shares of a stock priced at $40, for a total value of $4,000,
then you can still equalize the results by buying only 50 shares of the stock priced
at $80, also for a total value of $4,000.
In the latter case, you won’t make as much money in the end, but the point is
that the dollars made are not a good indication of how good the system is or how
likely it is that it will hold up in the future. In real-life trading, obviously, other
considerations come into play when you decide how many shares to buy in each
trade, but we will get to that later in the book.
For now, we have to remember that we’re talking about how to build and eval-
uate a back-tested system, and during this process, we either need to adjust the
number of shares traded to the price of the stock in question (so that we always
buy and sell for the same amount), or buy and sell one share only (but measure the
results in percentage terms). Otherwise, we won’t place each trade in all markets
on the same ground, or equal weighting, as all the other trades in all the other mar-
kets. And if we don’t do that, we might come to a suboptimal conclusion, as this
second example shows.
If you can choose between buying two different stocks, one currently priced
at $12.50 and the other at $20, and you know for sure that the one priced at $12.50
will rise 1.75 points over the next couple of days, while the one priced at $20 will
increase 2.60 points (almost a full point more) over the same period, which one
would you buy? If you answer the one for $12.50, you probably have taken the
story about the cubicle buddies to heart and understand what I am hinting at.
If, however, you answered the one for $20, you probably are a little too anx-
ious to chase that elusive dollar. If you stop and think for a second, you will real-
ize that there is a greater return for you if you just do the math. In this case, the
price of the low-priced stock divided by the price of the higher-priced stock (12.5
/ 20) equals 0.625, or 5/8. Thus, if you plan to invest $10,000, you can buy either
500 $20 shares, or 800 $12.50 shares. If you buy 500 $20 shares, you will make a
profit of $1,300 (2.60 * 500), or 13 percent of the invested amount (1,300 / 10,000
0.13). If, on the other hand, you buy $10,000 worth of the $12.50 stock, your
profit will be $1,400 (1.75 * 800), or 14 percent of the amount invested (1,400 /
10,000 0.14).
If you think this difference isn’t that much to worry about, what if you could
chose between 20 trades like this for the rest of the year, being able to use the prof-
its from all trades going into the next one? Then your initial $10,000 would grow
to $115,231 if you only bought the $20 stock, but to $137,435 if you only bought
the $12.50 stock. And what if you could do this for three years straight? Then your
initial $10,000 would grow to $15,300,534 if you only bought the $20 stock, but
to $25,959,187 if you only bought the $12.50 stock. A difference of more thanCHAPTER 1 Percentages and Normalized Moves 9