ince the book "Fortune's estimate the impact of different
Formula" is published, many outcomes on the stock price:
investors are turning to
the Kelly Criterion for 30% increase in A's stock price
determining the size of the if Product 1 is launched. There
investment. Unfortunately, most are 20% chance for this to
of these investors have not happen.
walked through the underlying 10% increase in A's stock price
mathematical derivation or read if Product 2 is launched. There
Ed Thorp's paper on how to apply are 15% chance for this to
the Kelly Criterion in the stock happen.
market. 12% increase in A's stock price
if Product 1 is launched. There
There are many fallacies when are 25% chance for this to
using the Kelly Criterion happen.
directly in stock trading. Unlike 15% decrease in A's stock price
most gambling games, the stock if no product is launched. There
market is too complex and the are 40% chance for this to
underlying assumptions of the happen.
criterion do not hold.
Now you have $100 dollars in your
For example, consider the bankroll, how much would you
following problem: invest in A's stock so that your
bankroll can have maximum growth
Company A is currently in the long term?
researching 3 different new
products. In an upcoming The Kelly Criterion cannot help
convention, we know that A might you solve this problem because it
announce the launch of one of the assumes only two possible
new products. We can also outcome: FAVORABLE or
UNFAVORABLE. It also assumes that = -15%
if the outcome is unfavorable, P1 = Probability of Product 1
you will lose 100% of what you Launching = 20%
invested (the wager). P2 = Probability of Product 2
Launching = 15%
In the stock market, you often P3 = Probability of Product 3
have multiple outcome scenarios, Launching = 25%
and you almost never lose 100% of P4 = Probability of No Product
your investment in a single Launching = 40%
trade. Therefore, the Kelly B = Initial Bankroll
Criterion alone is not directly B' = Future Bankroll after N such
applicable to the stock market. investments
M = The Geometric Mean of N such
I have looked through the investments
mathematical derivation of the
Kelly Formula, and it can be used Using the above information, we
to derive the solution for the can formulate:
above problem.
B' = B * (1+W1*F)^(P1*N) *
Let's define some variables: (1+W2*F)^(P2*N) * (1+W3*F)^(P3*N)
* (1+W4*F)^(P4*N)
F = % of your bankroll that you
invest in A M^N = B'/B = (1+W1*F)^(P1*N) *
W1 = ROI of Launching Product 1 = (1+W2*F)^(P2*N) * (1+W3*F)^(P3*N)
30% * (1+W4*F)^(P4*N)
W2 = ROI of Launching Product 2 =
10% M = [(1+W1*F)^(P1*N) *
W3 = ROI of Launching Product 3 = (1+W2*F)^(P2*N) * (1+W3*F)^(P3*N)
12% * (1+W4*F)^(P4*N)]^(1/N)
W4 = ROI of No Products Launching
M = (1+W1*F)^(P1) * (1+W2*F)^(P2) However, with the aid of modern
* (1+W3*F)^(P3) * (1+W4*F)^(P4) technology, a web application
that finds the Kelly Percentage
We can find the maximum M by can be developed through
finding the maximum Ln(M): simulation. For example, you can
find such web application at:
Ln(M) = Ln[(1+W1*F)^(P1) *
(1+W2*F)^(P2) * (1+W3*F)^(P3) * (1+W4*F)^(P4)] size="-2">http://www.cisiova.com/
betsizing.asp
Ln(M) = P1*Ln(1+W1*F) +
P2*Ln(1+W2*F) + P3*Ln(1+W3*F) + The web application takes
P3*Ln(1+W3*F) possible outcomes (ROI and
probability) as inputs and
The above equation is what Ed calculates the Kelly Percentage
Thorp stated in chapter 7 of his and the maximized mean growth
paper "THE KELLY CRITERION IN rate for you. Since the Kelly
BLACKJACK, SPORTS BETTING, AND Criterion is just a special case
THE STOCK MARKET", in which he of this maximization problem, the
discusses how to apply the Kelly web application works perfectly
Criterion in the stock market. well with simple Kelly problems
such as sports betting or
There is no clean solution to gambling.
this optimization problem.
About the Author:
Here Is The Free Web Application That Calculates The Kelly Criterion For The Stock Market. Kelly Criterion Calculator
Read more articles by:
Zheng Fang
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