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[M598]Money And Stock Market

by Zheng Fang, Zhe

Since the book "Fortune's Formula" is published, many investors are turning to the Kelly Criterion for determining the size of the investment. Unfortunately, most of these investors have not walked through the underlying mathematical derivation or read Ed Thorp's paper on how to apply the Kelly Criterion in the stock market.

There are many fallacies when using the Kelly Criterion directly in stock trading. Unlike most gambling games, the stock market is too complex and the underlying assumptions of the criterion do not hold.

For example, consider the following problem:

Company A is currently researching 3 different new products. In an upcoming convention, we know that A might announce the launch of one of the new products. We can also estimate the impact of different outcomes on the stock price:

30% increase in A's stock price if Product 1 is launched. There are 20% chance for this to happen.
10% increase in A's stock price if Product 2 is launched. There are 15% chance for this to happen.
12% increase in A's stock price if Product 1 is launched. There are 25% chance for this to happen.
15% decrease in A's stock price if no product is launched. There are 40% chance for this to happen.

Now you have $100 dollars in your bankroll, how much would you invest in A's stock so that your bankroll can have maximum growth in the long term?

The Kelly Criterion cannot help you solve this problem because it assumes only two possible outcome: FAVORABLE or UNFAVORABLE. It also assumes that if the outcome is unfavorable, you will lose 100% of what you invested (the wager).

In the stock market, you often have multiple outcome scenarios, and you almost never lose 100% of your investment in a single trade. Therefore, the Kelly Criterion alone is not directly applicable to the stock market.

I have looked through the mathematical derivation of the Kelly Formula, and it can be used to derive the solution for the above problem.

Let's define some variables:

F = % of your bankroll that you invest in A
W1 = ROI of Launching Product 1 = 30%
W2 = ROI of Launching Product 2 = 10%
W3 = ROI of Launching Product 3 = 12%
W4 = ROI of No Products Launching = -15%
P1 = Probability of Product 1 Launching = 20%
P2 = Probability of Product 2 Launching = 15%
P3 = Probability of Product 3 Launching = 25%
P4 = Probability of No Product Launching = 40%
B = Initial Bankroll
B' = Future Bankroll after N such investments
M = The Geometric Mean of N such investments

Using the above information, we can formulate:

B' = B * (1+W1*F)^(P1*N) * (1+W2*F)^(P2*N) * (1+W3*F)^(P3*N) * (1+W4*F)^(P4*N)

M^N = B'/B = (1+W1*F)^(P1*N) * (1+W2*F)^(P2*N) * (1+W3*F)^(P3*N) * (1+W4*F)^(P4*N)

M = [(1+W1*F)^(P1*N) * (1+W2*F)^(P2*N) * (1+W3*F)^(P3*N) * (1+W4*F)^(P4*N)]^(1/N)

M = (1+W1*F)^(P1) * (1+W2*F)^(P2) * (1+W3*F)^(P3) * (1+W4*F)^(P4)

We can find the maximum M by finding the maximum Ln(M):

Ln(M) = Ln[(1+W1*F)^(P1) * (1+W2*F)^(P2) * (1+W3*F)^(P3) * (1+W4*F)^(P4)]

Ln(M) = P1*Ln(1+W1*F) + P2*Ln(1+W2*F) + P3*Ln(1+W3*F) + P3*Ln(1+W3*F)

The above equation is what Ed Thorp stated in chapter 7 of his paper "THE KELLY CRITERION IN BLACKJACK, SPORTS BETTING, AND THE STOCK MARKET", in which he discusses how to apply the Kelly Criterion in the stock market.

There is no clean solution to this optimization problem. However, with the aid of modern technology, a web application that finds the Kelly Percentage can be developed through simulation. For example, you can find such web application at:

http://www.cisiova.com/betsizing.asp

The web application takes possible outcomes (ROI and probability) as inputs and calculates the Kelly Percentage and the maximized mean growth rate for you. Since the Kelly Criterion is just a special case of this maximization problem, the web application works perfectly well with simple Kelly problems such as sports betting or gambling.

It may not seem obvious to many people, but the strategies involved in real estate investing and stock market investing are different from each other. Many people, disenchanted with the lackluster performance of their stock portfolio, first become interested in real estate investing after someone they know makes a large sum of money in real estate in a relatively short time.

If that sounds like YOU, be warned: investing in real estate in the hopes that the market will increase rapidly and steadily is, and always has been, a risky strategy, and can cause severe difficulty if you guess wrong about a piece of property--or if the entire real estate market begins to collapse, as has happened many times in the past.

If you can afford to buy real estate and hold on to it for five to fifteen years, you will nearly always realize a substantial profit. If you are savvy enough to buy a significantly discounted piece of property and then sell it within a year, you'll make money, too. But buying an investment property at its fair market value that only gives you a break-even cash flow (or worse yet, loses money every month) can sink you in a relatively short time if you don't have the wherewithal to feed it until you CAN make money on it.

It's like riding a horse. If you don't know how to ride, you'd better take some lessons before you sign up for a rodeo! The results could be disastrous if you make a mistake. And if you haven't done your homework, you WILL make a mistake. The wrong real estate investment could cause not just financial hardship, but also financial ruin.

So know your real estate market, inside and out. Know where it is in its overall cycle, because all markets, no matter how hot, have ups and downs within the overall trend. There are always bargains available, regardless of the market. Watch your local housing market so you know how much rental income to expect and if there is a vacancy glut on the market. Two years ago you could buy an apartment building in Las Vegas for zero down because investors couldn't rent the apartments. Some investors who could afford to make up the negative cash flow each month made a killing in appreciation. Investors with financing or cash who transformed the apartments into condominiums made even more money.

Finding the lowest-priced financing also helps make the most return on your investment. Unlike stock investing, you need strong credit to use other people's money to finance investment property.

Even if you're frustrated by a lackluster stock market, don't expect to make a short-term killing in real estate to make up for it. In both cases, one of the best strategies is to buy excellent examples--and then hang on for awhile. It's also a good strategy to maintain a cash reserve, especially when it comes to real estate. That way, even if the market heads south, you won't find yourself being overwhelmed while you wait for the inevitable rebound in prices.

Real estate investing can carry more significant consequences than stock market investing if you guess wrong, since there's generally a great deal more money involved. So take it easy, do your homework, and don't rush into anything until you've learned as much as you can about how to become a prudent real estate investor.

Copyright (c) Jeanette J. Fisher

Article Source : Pg. 272

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Both Zheng Fang & Jeanette Joy Fisher are contributors for EditorialToday. The above articles have been edited for relevancy and timeliness. All write-ups, reviews, tips and guides published by EditorialToday.com and its partners or affiliates are for informational purposes only. They should not be used for any legal or any other type of advice. We do not endorse any author, contributor, writer or article posted by our team.

Zheng Fang has sinced written about articles on various topics from Finances, Entertainment Guide and Finances. Here Is The Free Web Application That Calculates The Kelly Criterion For The Stock Market.. Zheng Fang's top article generates over 1000 views. to your Favourites.

Jeanette Joy Fisher has sinced written about articles on various topics from Real Estate, Network Marketing and Real Estate. teaches beginning real estate investors how to find bargains, finance multiple properties, fix with designer touches for less money, and sell houses fo. Jeanette Joy Fisher's top article generates over 135000 views. to your Favourites.