# Growing Your Stock Portfolio to the Max

In 1956, John Larry Kelly, Jr. was a scientist working at Bell Labs. He became famous for his work on optimizing the signal level across communication lines, which resulted in the development of a mathematical relationship known as the Kelly Criterion.

The Kelly Criterion is very important to anyone studying electrical engineering and learning about signal communications, but the Kelly Criterion was also found to have very practical applications in the world of investing and even gambling. Instead of optimizing signals, the Kelly Criterion can be used to optimize the growth of investment portfolios and the returns of one’s gambling jigs.

The beautiful thing about the Kelly Criterion isn’t just about how practical it is, but rather how elegantly simple it is to use and apply.

The Kelly Criterion is defined as:

$f = \frac{p(b+1)-1}{b}$

where (from a stock investment point of view)
f = the fraction of your total stock portfolio to bet on a stock
p = probability of winning the bet
b = your average return from any stock (ratio of the average gain of the winning trades relative to the average loss of the losing trades)

## Applying the Kelly Criterion

As an example, let’s say that you have a stock portfolio of $10,000. You found that based on your past investing experience, you’re able to pick a winning stock about 60% of the time (this is actually quite good). This is p. Now you look at all the stock trades that you’ve made and find that on average, your return from any stock is 80% ($1.8 for every $1 invested). This is b. So if we plug p and b into the above formula, we find that f, the fraction of your stock portfolio that you should bet on a stock, is 10% (or$1,000 of your total stock portfolio). By extension, what this means is that your stock portfolio is optimized for growth when it is comprised of just 10 equally-weighted stocks.

## Important Considerations

It’s important to remember that the Kelly Criterion is a theoretically derived equation. In practice, especially in the world of investing, you should be a little more conservative in your application of the criterion. Why is this? The Kelly Criterion explains well the behaviour of an infinite number of stock bets and trades, however, most of us don’t have the luxury of dealing with infinite amounts of wealth. When exercising the Kelly Criterion as is, you will be exposing yourself to a high degree of volatility near the beginning of your portfolio lifecycle. So what can you do to reduce this volatility? In practice, many investors use the half-Kelly to determine the fraction of the portfolio that they are willing to bet. The half-Kelly is simply half of f, which means investing half as much of the stock bet recommended by the original Kelly Criterion.

On the flip-side, a recommended maximum for any single stock exposure is 25% of your total portfolio. This is a rule of thumb that is outlined by many proponents of the Kelly Criterion. The reasoning behind this is that if you expose yourself to owning more than 25% of one stock, your portfolio could be hit pretty hard if things went wrong for that stock in particular.

And, as always, discipline in your approach is very important. If you decide to use the Kelly Criterion for balancing your portfolio, be consistent about it. Using the criterion requires a long-term commitment.

## Try It For Yourself

If you combine the power of the Kelly Criterion with a fast wealth building philosophy, you are well on your way to substantially building your wealth.

 Probability of winning a stock bet (p) % Average return from any stock bet (b) %

### Johnny Q

Trying to succeed without studying is like trying to build a house without a hammer.
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