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As an alternative, you might look at the Kelly Ratio. Vince discusses
this, and McMillan discusses it in "McMIllan on Options" (as I recall).
[the following is excerpted from McMillan's Option Strategist
newsletter, circa 1994.]
How Much to Invest?
One should not put all of his speculative funds into one position: if there
is only a 40% to 50% chance of any one recommendation making money, then
he should alot his money over several different positions. In fact one
of the things that is hardest for any speculator to decide is "how much
of my speculative funds should I put into this one position?
It is actually possible to derive a mathematical answer to this question,
if one adheres to the "Kelly System". Kelly was a programmer at Bell
Telephone Laboratories, who derived a formula to answer the above question.
His formula is actually used by most gamblers who have a fixed result
(100% or -100% less "commission", on any one outcome). Therefore, we
have to adapt a little to use the Kelly formula. Here is the original
formula in its simplest form:
Amount of bet = (W + L) * p - 1
where W = amount you win, L = amount you could lose, and p = probability
of winning. For example, in a situation where you risk one "unit" and
pay a 10% commission, the Kelly formula would read: 2.1*p - 1.1*p.
Thus, if you can predict winners under the criteria at a 60% rate,
the Kelly system would tell you to bet 2.1*0.60 - 1.1*0.6 = 0.16 or
16% of your total bankroll on one trade. In this case, if p is less
than about 52%, the Kelly system would tell you not to bet all
(2.1*0.52 - 1.1*0.52 = -0.01).
Since the stock market is more complicated, we not only have to guage
the probability of having a winning trade, but also have to take into
account how big the wins and losses are. In this case, the Kelly formula
becomes:
Amount to risk = ((r+1)*p - 1) / r
where p = probability of winning and r = average win/average loss
(assuming equal investment in each trade).
In the data on page 2, we had 12 wins and the average winning trade
made $1444; we had 11 losses, and the average losing trade lost $501.
Therefore p = 0.52 (12 winning trades divided by 23 total trades), and
r = 2.88 (1444 divided by 501). This yields 35% as the amount to risk.
That is one should put about one third of his speculative funds into
each of our speculative recommendations, if he believes that our
recommendations will continue to profit at the same rate shown in
the table on page 2.
As we stated earlier, these returns are higher than normal, if you wre
to go back over all 83 speculative recommendations we have made since
our inception in December of 1990, you would find 35 winners and
48 losers (42%) with the average win netting $1113 and the average
loss costing $620. Using these figures, the Kelly System will tell
you to risk 9.7% (about 1/10) of your speculative bankroll on each
recommendation. That is much more conservative, and seems to make
more logical sense in the long run.
The Kelly criteria is a dynamic formula as the percentage of winners
and losers changes over time, but overall it is a reliable way to
be sure that you are risking enough, but not too much on your trades.
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