Ways to Make Money Online

Investing In Equestrian

Investing In Equestrian?

The majority of us regular Joes wish we had more money, but it seems the only way to make more money, is to actually have money in the first place, i.e. to invest.

This is not strictly true. There are many ways of investing small amounts of money, some of them you would not necessarily class as “investing” but investing by definition means - laying out money or capital in an enterprise with the expectation of profit.

Now take betting on a horse for example, I’m sure your significant other isn’t going to buy into it when you tell them that you are investing, but by definition, you are. Every investment has an element of risk to it, betting on a horse of course, has a little more!

The other kinds of investing “Alternative Investments” are usually the area of collectors and hobbyists, but these can also generate a decent return on your money. This includes everything from art, antique furniture and wine to vintage cars, stamps and toys.

When it comes to wine, there is a convincing argument that as an investment, it produces returns comparable to equities and the cost of fine wines will keep on rising.

There are many other avenues to pursue when you are not wealthy enough already to invest your money into property and real estate. Taking a look in your attic to see what delights you may find could be a start.

The internet holds lots of information in regards to ideas for investing, there are bonds to consider, stocks and shares, gold or silver, even currency! Investing need not be for the privileged people, even us, the average Joes can start investing somewhere along the spectrum. Remember you have to start somewhere, and take your first little steps, but always think BIG.

Kelly Criterion And The Stock Market

Kelly Criterion And The Stock Market

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:

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.