Investing money using average returns and past history is not rational or productive. Retirement and college savings should not be invested in stocks, commodities, or any other vehicle other than guaranteed return or fixed income vehicles. Stocks and commodities are wonderful investments for speculation and if you have extra capital to risk AFTER you have saved for retirement and college savings. Using retirement and college savings as risk capital is not a rational act, even though the popular media and the financial industry encourage you to do so. Nonetheless many people believe they are smarter than the rest of, capable of picking the winner, and decide do move forward anyhow. In light of this I write this article in an attempt to assist you in making a better investment decisions before risking your capital, and to use Expectancy and Position Sizing to mitigate your risks.

**Beware the "Fat Tail"**

Most financial economists and investment advisors base their math on the assumption that investment returns fit neatly in to a Gaussian model, also known more commonly as the "Bell Curve". Because stock returns are not neatly distributed, mathematicians build Log Normal curves in order to see the skew of returns. But even log normal curves assume that there are limits to how far returns stray from the average return. They express these with obscure formulas and call them standard deviations. According to the Gaussian model 99.9% of all data is within five standard deviations of the average, and the further out we go, the closer the probability of occurrence is zero.

This type of thinking is what got the same investment and financial gurus in trouble during the Long Term Capital Management mess (they assumed Russia would never default on its bonds), the October 19^{th} 1987 stock market crash, the 2008-2009 market meltdown, and the one day April 26^{th} 2010 "anomaly".

The truth is that any system made of human beings yield irrational returns. Historically, we have "fat tails" in which the extreme ends of the bell curve point upwards, and these extreme returns occur more than just once in one hundred years.

In plain English â€“ very high negative and positive returns occur frequently. It is possible to get 10,000% returns, as well as to lose all your money (or more if you borrowed money to make the investment). Only in closed systems, such as casinos, can one use the perfect mathematical models for investing money. In the "real" world, where people panic and liquidity evaporates, returns vary frequently enough far away from the "average" return to hurt you. Make sure you invest only the amount of money you can afford to lose completely and not be affected by these events, and ensure that positive returns don't make you take on more risk than appropriate.

**Beware the "Average Return"**

Beware stock return averages as they lull you into a false sense of security! Salespeople often mentioned how their investment (stock, bond, whatever) returned 12% on AVERAGE but they rarely, if ever, gave you the actual information you needed to determine if this is truly the right investment for you. To ascertain an investment return look at the numbers that supports the claims.

Quickly: what is the average of six and eighteen? It is twelve (6+18=24. 24 divided by 2 is 12).

Quickly: what is the average of twenty eight and negative four? It is twelve (28 -4 = 24. 24 divided by 2 is 12).

Based on the two examples above, you can see that the average is exactly the same, but one of the two investments returned MINUS four percent one year. My bet is that most of you would bet money on the first investment to get the same return without having a risk of a loss.

Here is another example: if you had to cross a stream of water while holding your infant you would probably want to know how deep that stream of water is. Would you cross the stream if I answered you "the average depth of this stream is five feet"? Of course not! You would want to know where the stream is shallow and safe enough to pass. The average depth of the stream means nothing if you know that at one point the stream is only three inches, and at other parts the stream is thirty feet deep.

The next time you are told "the average return isâ€¦" interrupt the seller and ask for the supporting data. If the number of negative returns are too high and/or occur too frequently please walk away. We human beings are wired to avoid pain. Psychologically, we cannot withstand a long string of small losses or even one colossal loss.

**What You Should Invest In is the" Expectancy"**

Let us assume you have interrupted the investment salesman/advisor and made her provide you with enough raw data. What do you do with it? You should calculate the investment's expectancy, and only invest if the expectancy is positive and the expected return is frequent enough.

Expectancy is calculated by the following formula: (Probability of Positive Return * Average Positive Return) â€“ (Probability of Zero Return or Loss * Average Loss)

If the average positive return of an investment is 12%, and you have a positive return half the time, and the average negative return is 10%, which also occurs half the time, your expectancy would be one percent (12 times 0.5 minus 10 times 0.5 = 1%). For every dollar you are risking, you expect to make one dollar in return. Unless this investment yields 1% per day, I would not venture into the investment. If the investment yields 1% a day, I would jump all over it (do the math and you see that compounded returns of 1% a day are nothing to laugh at).

Assume an investment that yields 10% returns 90% of the time, with 20% of the time the loss being 10%. The expectancy would be 7% (10 times .9 = 9. 20 times .1 = 2. 9 minus 2 is 7). Seven percent return is pretty good for some people on an annual basis, but is it worth the stressful negative return? What if you got that negative 20% on your first day after you cut the check? Would you go back?

The expectancy ratio cuts through a lot of baloney, especially the "Average Rate of Return" nonsense. It doesn't protect you from the fat tails that have not yet happened, though no one can predict "unknown unknowns" and no one has enough time to gather information on the "known unknowns." Put simply, you must always make decisions without all the facts. But one must not only take into consideration their psychological strength to endure a string a off losses even though the investment's expectancy is positive, and also determine if the pain is worth the expected gain. In the end, most people will live a better life just investing in bonds or guaranteed return investments and let the financial economists and Wall Street traders take the bets.