How easy is it to make money? If you immediately answered "not easy," you must be thinking of the current times. In other eras, when you were flush and heady making money (say, from 2005 to 2007), you may have spontaneously given the opposite answer. The question seems to take on different meanings at different times.

But if you stepped back and looked at the question hard enough, the answer ought to be the same at all times.

Consider the odds of making money in a coin toss game. If you played the game many times, you would almost certainly come away with nothing-you would have played a "fair game." But then again, entering the game to begin with meant you thought you knew something your opponent didn't, something that would bowl her over. You thought you had asymmetrical information. Of course, she entered the game with a similar idea. And without this conflict of expectations, the game would never have taken place.

Does such a long-term zero sum game sound too far-fetched? Too much like some academic theory developed in a void? Well, think again. Long-term currency market speculators face scenarios very close to these "fair games," or gambles, all the time. The proper term for such games in the ivory towers is "martingale" processes.

It is probable that a fair game may produce different results in the short run. For example, in coin toss games, you could encounter winning streaks in heads or tails. If you catch a wave, fortune certainly favors you. It's the scenario favored by the fantasy in movies about Las Vegas gamblers. But if you were playing such a game in Vegas yourself, i.e. playing against the house, then the fortune would certainly turn to disaster, as the difference in wealth of your opponent would almost certainly lead you to what is known in statistics as "gambler's ruin."

At every point in time, we investors face a very similar situation. Consider the first significant outcome of your next investment. You may win, lose or draw. Figure 1 shows these expected outcome possibilities. If these outcomes followed the chance structures of fair games, then we could expect that the chances of winning or losing from the next move would be equal. In other words, assume there is an

*approximately 50%*chance of either winning or losing from the next move in your portfolio. The expected return of 0% could then be translated to a rough rule where the chance of losing may be subtracted from the chance of winning to lead to an expected return. Thus, in a fair game, expected return equals zero as a sum of 50% - 50% = 0%. By the same token, if you could call the outcomes correctly 55% of the time, then you could expect to earn a 10% (55% to 45%) rate. Now, ask yourself this question: How easy (or difficult) is it to make 10%? Even being right just 55% of the time doesn't sound so easy anymore, does it?
To make money, therefore, the first step is to predict the directional change in your investment correctly. If you can do so, i.e. predict an up, down or a sideways move, and if you can be consistently correct in your predictions about 55% of the time, then you will end up earning 10% over the long term. (The only other way to consistently make 10% is to be Bernie Madoff.) Furthermore, note that being correct in your predictions does not mean finding winners only; it will be equally lucrative to find losers and no-changers. Instead of buying the winning stocks or their call options, you can also short sell the stock or buy put options on them. If you expect no change in the next price movement, you can make money by writing both a put and a call (a short straddle) and you will make money just as you would in the other two scenarios.

The main point to understand is that if you are right (or wrong) in your predictions, then you will make (or lose) money. Making it or losing it hinges solely on whether you are calling the price changes correctly.

So far, we have looked only at the direction of the first price change. Next you predict the magnitude of the coming price change. Figure 2 shows both the direction and magnitude of all possible price changes. In a sense, bringing up the magnitude refines the original prediction in a very precise way by magnifying our money-making possibilities. The better our prediction, the more often (more than 55% of the time) we are right and the higher our expected profits. Being correct implies that we understand which path (in Figure 2) our investment will follow. That is, we must understand the "path dependency." If we are consistently correct in identifying these paths, then we are one step away from the Midas touch of a Buffett or a Lynch. It does not matter if the predicted magnitude is small or large, but only that such precision in path identification is exploited for unlimited gain.

It is easy enough to see that when one is confident about the direction and magnitude of price changes, then it is much more lucrative to speculate with derivatives than to use the underlying security. In Figure 3 if the expected change is very small, not only could you buy calls (up paths) or puts (down paths), but also sell their opposites. For example, when we expect upward movement, we can also sell (write) puts and use the money earned from writing to buy the calls. In this way, we can speculate at zero cost to create profit schemes (arbitrage) as long as we are sure of our predictions. If we were to be wrong in our predictions, of course, the consequences would be dire-dire in that it magnifies the effect of buying losers. So if you are faint of heart about your predictions and expectations, these approaches are not for you. The operations described here are for stronger gutted women and men.

In Figure 3, we reasoned that positive and negative price changes would be close to 50%, but not exactly, since we wanted to leave open the possibility that the next price change has a zero value-in other words, a sideways price movement. If we are superb in our predictions, then writing a put and a call would lead us to profit from the sidewise movement. Figure 4 shows the payoff from such a positional move, the so-called short straddle.

The straddle and the exploitation of a sideways change temporarily closes the discussion about exploiting the first price change. Now consider the second significant price change for your portfolio. Note that from the current perspective, the second price change would imply a total of about five outcomes with nine possible price paths. Figure 5 shows these nine possibilities.

Note the directional changes portrayed in Figure 5. For us to consider volatility, we need at least two significant price changes that are not simply the result of a hit on the bid and offer. Observe that of the nine paths, there are two changes that represent the greatest volatility, four changes of medium volatility and three changes signifying the lowest volatility. This means that volatility is the least common outcome of our predictions, as it should be. At any time, the observations of heightened market volatility in security markets must then imply the dominance of uncommon or tail region outcomes. These conditions exist when we cannot reach the outcomes through more predictable paths, as shown in Figure 6, a tabular version of Figure 5.

Continuing in the same vein, if we introduce the magnitude of changes against these two periods, then we will also specify all possible price paths, illustrated by Figure 7.

Now we are in the realm of the adventurous. There are a few ways in which we can try to identify the most likely path to the most expected outcome. It's important to note that each price path is equally probable and the sum of all path probabilities must equal one, since one of those paths will be actualized with certainty (i.e., the probability is 1). A second methodology is the Monte Carlo simulation, which tries to ascertain from the nature of the path shapes (statistical distributions) the most likely path with the associated dispersion. If the paths are normally distributed, then there is an expected (mean) path and around that path there is dispersion (with a certain standard deviation) and volatility. If the distribution is non-normal (for example, it's a chi-square distribution or beta or another one) then the most likely associated outcomes may be in the form of ranges and scales. Now we would need a statistician to interpret their meanings before we could rattle off fancy terms such as "z-stats," etc. Finally, we can also use mathematics of normal distributions (integration) to arrive at the same calculations, such as Black-Scholes calculations in option pricing. Nonetheless, it is obvious that if we can determine the most likely price paths, we can also reap the maximum benefits.

To summarize, let us now tabulate all possible two-period price paths and look at their speculative trading counterparts for broad path regions. Figure 8 shows these possibilities and their trading solutions. (Note: To reduce option premiums, you may buy options that are out-of-the-money. They work just like deductibles in auto insurance.)

These ideas would likely never be palatable to readers without real life examples. As luck would have it, I came across two articles in the

*Financial Times*of December 12 as I was putting the finishing touches on this article. One, called "Fat-Tail Fears Catch Oil Traders Between $50 and $150 Bets," by Javier Blas, the commodities editor, offered a perfect illustration. The report starts with the salvo, "Investors and traders are buying large numbers of oil (option) contracts that would profit from a price super-spike-and a collapse." (I urge my readers to read the entire story.)
If you're thinking of investing in the ways I've described, you might look out for hypothetical events that offer opportunities:

1. A downturn in the U.S. markets with a correction of about 12% in the next three to six months;

2. A European embargo of Iran, which could threaten a spike in oil prices, since much oil is shipped through the Persian Gulf; and

3. A downturn in European markets lead by the FTSE 100 and then the CAC 40 and the DAX. Nothing says we can't profit from European woes and spats.

Now, form your own expectations and go trade! The only way you'll lose is if you are wrong. I'll leave the rest to your imagination. Happy scalping!

*Somnath Basu is a professor of finance at California Lutheran University and the director of its California Institute of Finance. Dr. Basu also serves as a professor of the Helsinki School of Economics' executive MBA program. He's involved with financial planning organizations including the National Endowment for Financial Education, the CFP Board of Standards, the International CFP Board and the Financial Planning Association.*