Math, Investing and life what do they have in common

PROBABILITY AND LIFE
By Melvin J. Howard

When I was going to school it was not cool to be smart as a matter of fact I use to hide my papers if I got a “A” But I liked school especially high school some of the teachers let me express myself instead of trying to put me in a category. But it was not until 7 years ago that I started to discover that math given the right variables could give you a probable outcome to just about anything. I am still testing my theory but I have to say for me so far its been a remarkable ride. Events can be quantitatively described as probable or improbable when compared to the total number of possible outcomes. But when the total number of outcomes cannot be specified, there are no grounds for calculation. Intuitively, it seems like a very improbable event that I would unexpectedly meet a old Swiss girlfriend in a British airport. But how can I quantify this probability? Do I include all of the other people I have ever known and the total number of people in British airports? Improbable events occur coincidences even though they occur with low probability. Given a high number of possible improbable events, it is highly probable that some of them will occur. We only notice the "coincidences" that do occur, not the ones which do not occur. The occurrence of improbable events do not necessarily require paranormal or supernatural explanations.

Additionally, some coincidences are more probable than we might expect due to our lack of appreciation of actual probabilities. The probability of two people not having the same birthday is 364/365 (multilpying the 364 days remaining for the second person times the 1/365 probability of the birthday of the first person). 1 - 364/365 => 0.275% chance of having the same birthday. But for 23 people there is a greater than 50% chance that at least two of them will have the same birthday because
P(same birthday) ;= 1 - (364/365)(363/365)...(343/365) > 0.5

Although flipping a coin or rolling dice are treated as random processes they are not. Whether a coin comes up heads or tails is determined by the trajectory of the coin, the speed of rotation, the angle of rotation, air resistance, material characteristics of the surface on which the coin is thrown, the force of gravity in the location, etc. The same can be said for a roll of dice. There are so many variables, the variables are so hard to measure and the interaction of the variables is so complex that the flipping of a coin or rolling of dice are practically speaking "random". Said another way, the processes can be treated epistemologically as being random although metaphysically they are not -- they are deterministic.

In 1961 a research meteorologist at MIT named Edward Lorenz was using a set of equations to model weather on a computer when he discovered that rounding his initial numbers to three decimal places produced dramatically different results from those obtained by using six decimal places. Systems so sensitive to small variations in initial conditions have been called "chaotic", but they are more accurately described as pseudo-random -- just as so-called random numbers generated by computer are called pseudo-random. Again, the phenomena are metaphysically deterministic, but their unpredictability renders them epistemologically random no different from rolling dices or flipping coins.

In arguing against the Copenhagen Interpretation of Quantum Mechanics Albert Einstein made the infamous remark, "God does not play dice with the universe." I call the remark not logical because it is usually quoted to display how irrational Einstein's beliefs were when it came to spookiness at a distance. Which Einstein could not get his head around when it came to quantum physics. Neils Bohr, Werner Heisenberg and others in the Copenhagen School proposed that randomness is a metaphysical condition of subatomic particles, whereas Einstein argued that randomness as a phenomenon is an artifact of our ignorance of underlying deterministic processes & forces limitations on our knowledge. Probability bridges the gap between descriptive statistics (average, standard deviation, histograms, etc.) and inferential statistics (decision-making statistics).
Decision-making is based on the probability of an event occuring times the payoff of the event -- a cost/benefit decision. More formally:
Expected value = probability X payoff It would seem advantageous to wager $1 on the chance of winning $10 by rolling a snake-eye (one) with a single die because the expected value is probability X payoff = (1/6) X $10 = $1.67
which is greater than the $1 cost. But there is a 5/6 chance of losing the $1, which could be critical if you need the money to buy bus-fare. Non-monetary factors are often important in cost/benefit calculations -- with benefits more often being more difficult to quantify and calculate than costs.

Successful Trading
I believe that there are three essential components to successful trading:
(1) Money management
(2) Risk management
(3) Forecasting ability

Money-management is absolutely essential. A trader should know how much his/her assets total at every moment. And (associated with risk management) a trader should know exactly how much money will be lost if everything goes completely wrong (as often happens). In short, always look both ways before entering the market look up and look down!! I know of too many cases of traders who have lost everything on a single trade. It is only possible to lose everything on a single trade by risking everything on a single trade. A trader may make big money a few times by doing this, but as a policy it is a recipe for disaster. Conservative money managers will never risk more than 5% of total capital on a single trade. The market is very efficient in transferring money from the impatient investor to the patient investor I know this from personal experience.Concerning risk-management, protective stops are a powerful tool for self-discipline in daytrading. Stops should never be below round numbers on long positions and above round numbers on short positions to reduce the chance of being stopped-out at the same time as other investors (who have a fondness for round numbers). Round numbered stops typically increase slippage, ie, extra loss beyond the stop due to a bad fill of the stop order. Fast price movements increase slippage.

Stops are also a way to get yourself cut to pieces if they are too close to your current position. The market must have some slack to make excursions up and down on the way to your desired destination. More often than not, when I am worrying about what my stop should be, it is a sign that I should exit my position (sell-out if long, buy-out if short). I always prefer to be in control of when I exit my position. Stops have probably cost me more money than they have saved me because of sudden & temporary spikes in price. (There was a significant exception.) Excessive confidence in one's forecasting ability is dangerous. A good forecaster who is right more often than wrong, who always knows how much money she/he has available and who does not risk too much money on any one trade is most likely to succeed.

Day-trading

Day-trading is very risky and the odds are stacked against the amateur day-trader. Over 80% of day-traders in stocks lose money in a bull market a much higher percentage in a sideways or bear market. The on-line day-trading companies were devastated by the 2000/2001 bear market. The futures market is even more risky. The very few of those who enter the futures market with less than $10,000 remain in the market for a full year. Even without trading on margin, a trader automatically loses money on every trade because of commissions & fees, bid/ask price-spread and a small gouge from the broker (personal observation and my opinion). A high volume of trading in which the trader is right on half the trade volume automatically means a loss.

There is a great temptation to buy when there is a sudden run-up in price and sell when there is a sudden fall. (Sudden falls are more frequently sudden and rises more frequently gradual, in my opinion.) Generally this is a bad policy. In fact, there are many contrarians who sell on run-ups and buy on run-downs -- and advise strongly against adding to a position that is currently proving profitable. My most conservative form of daytrading is to buy on a low where the market has sold-off strongly for a couple of days and has been relatively flat for a couple of hours. I prefer to do this when I have enough margin to hold the position overnight, if necessary (not day-trading, literally, but a good time for entering a position). Less conservatively, I will look for what I expect will what I call a monotonic-upday, ie, a day when the price movement is primarily upward with little downward excursion. This may be a Monday after a period of deep selling or the Friday after American Thanksgiving. Although it is normally bad practice to add to a profitable position, it can be conservative if I feel confident of my forecast because my risk only increases in increments and if I am right I am still limiting my loss with stops. For example, I would enter the market with an S&P 500 contract on the open (9:30am), with a 4-point or 6-point stop (allowing for the fact that the first half-hour of trading is the most volatile). If the market moves up 2 or 3 points I will buy another contract and raise my stop. 10 o'clock is a very volatile time, so if I can get beyond then I would narrow my stop to 3 points and continue the process. If I have patience to last-out the day I may attempt to do so, but normally the afternoons can be saggy & risky, so it is most prudent to sell-out earlier -- even though the last hour or half-hour often shows a final up-surge.
My most aggressive day-trading is on the day of the FOMC meetings. Typically the market rises in the morning of those meetings. At the time of the 2:15 pm announcement of the interest rate move (and bias) the market is usually very volatile (after being very unvolatile shortly before). It is usually most prudent to say on the sidelines for the first 15 minutes, at least. By 3 pm a trend is usually established that generally lasts at least until 3:45 pm. Buying or selling to follow that trend can be very profitable. Of course, if you are heavily margined and an earthquake hits you can be in deep trouble if you are not watching CNBC and not ready to exit the position at a moment's notice. I try to day-trade only rarely, when I believe the opportunity is exceptional. Oddly, I normally take a position in the futures market where I have ample margin to cover the most extreme of market movements -- buy-&-hold or sell-&-hold -- not what you normally see in futures traders. When I do day-trade futures indices I find it essential to continually monitor charts of the indexes (to follow trends) and the numbers themselves.

Trading Psychology and Emotions

Holding positions in the market can be extremely emotionally involving. And, of course, the larger the position (the more at risk) the greater the emotional involvement. Every uptick causes joy and every downtick causes grief. It is enough to cause otherwise intelligent people to spend hours staring mesmerized at changing numbers. The craving for emotional involvement may be the same as gambler's excitement. But I am not a gambler and I hate gambling I know the odds are against me. I never buy lottery tickets and I don't randomly trade. When I commit money in the future's market I always do so on the basis of some theory I have about how the market will move and why. Nonetheless, some of those theories can be pretty flimsy, so I try to make the amount of money I commit correspond to my intensity of certainty (knowing that I am often wrong). I am right more often than wrong but have been terribly wrong too many times. I continue to learn, but continue to find new mistakes I can make.

A professional investor friend of mine has said that many people lose money in the market because being in the market is motivated by reasons other than making money or avoiding losses such as talking to their friend about trading or the emotional involvement of trading. "When in doubt, stay out" is good advice. I experience great grief when I am out of the market and am watching the market make big moves that could have been making money for me. I wonder at times if that emotional grief isn't greater than the grief I experience when I have a position and am losing money. A run-up in price inspires optimism (an emotional buy-signal) even though it is bad policy to buy into a run-up (similar to selling into a sudden price decline).

(Contrarians are wired backwards.) Like many traders I have great difficulty taking a loss from a losing position. For some people this difficulty is associated with too much ego-involvement in their trading decision. They took a position on the basis of some belief and are unwilling to admit having made an error. In my case, however, it is more that I cannot truly accept the fact that I have already taken a loss as if my unrealized loss is not real and that by holding the position the market may move in my favor. Moreover, I reason like a contrarian that if the market has already moved so far in one direction a reversal is more likely (when prices have fallen, buyers are attracted and vice versa). When I realize that I have walked into a propeller and am being cut to pieces, I have all the rationality of a deer who stares transfixed into the headlights of an on-rushing car. The worst position is to be feeling sick with grief and to be passively/helplessly hoping the price will make a move for the better. Such emotions are a sign of poor money management too much has been risked. Programmed or mechanical trading would remove the emotion from decision-making, but it would not remove the emotion from profitting or losing. Futures traders often blame their failures on lack of self-discipline. By this theory, one should not enter a position without having a well-defined exit price and one should have the discipline to act on the plan (or use stops to enforce the decision).

I do have non-monetary, emotional incentives for my involvement in the market and I don't believe this is a bad thing. Years ago I made a conscious decision to start exercising and meditating as a means of reducing my anxiety. I wanted to experience my emotions fully and to learn to deal with them. I can say similar things about trading. Also, I am one of those people for whom market behavior is a fascinating puzzle and I am arrogant enough to believe that I have the capacity to solve that puzzle. I go from mistake to mistake, thinking that I am approaching the point where I will run out of mistakes and consistently make more money than I lose.
I believe that I have learned a great deal about myself by trading and I believe that I have grown as a person in learning to control my impulsiveness and impatience. Unlike Keynes, who arrogantly proclaimed that "The market can be irrational longer than I can stay solvent", I have learned humility in the face of my many false forecasts. Life & survival is a process of risk management. I believe the market is teaching me wisdom & good judgement that has helped me (and, hopefully, others) in managing many many areas of life. I still have lots to learn. I still become too giddy & reckless when successful and dysfunctional from despair (or desperate & reckless) when I fail. I suppose this comes from my manic side in me. The learning is on a very deep level of personality much deeper than factual knowledge because in many cases I already know the mistakes but have not gain enough mastery over myself so as to not make them. Which is what life is all about no matter the profession Doctor, Lawyer, Judge, Fireman, CEO to homemaker. We all make mistakes the question is do you learn from them?