Investment+Profit Basics Gambling+Trading Avoiding ruin Optimizing Return Transaction costs

Basics Here you will repeatedly meet the concept of probability. The underlying mathematical theory for which was established by the French mathematician Blaise Pascal (1623-1662). His original intent head been to rank the different hands of a game of cards. If events occur at random, the only way to quantify them is to calculate their relative probability. A single random event cannot be predicted and even with low numbers of events, their individual probabilities will not matter much, if the differences between them are small. However, the observed number of certain events will approach the expected number the more events occur. So if the probabilities are in your favour you will win in the long run. Probabilities are solid data. Some economic sectors like the insurance industry or the licensed gambling industry like state lotteries and casino owners and renters of gambling machines can rely on the calculated or empirical probabilities. Gambling + Trading Uncertain return on investment is a trait not confined to gambling only. Any free enterprise runs a certain risk of failure likewise trading at the financial markets with equities, foreign exchange and commodities incurs risks. The outlooks for risk and reward can be computed, provided the trading habits follow certain fixed trading rules consequently. The rules must be clear cut and consistent, but this is not enough. The chances of trading success have to be found out empirically that is with historical data and many buy/sell transactions to make the results trustworthy and statistically significant. Avoiding Ruin Only if the conditions for success in the long run are met it can be desirable to run the risk of variable returns. Many people misunderstand probabilities and therefore expect them to be meaningful in short time series, which will more likely then not lead to ruin. Probabilities are reliable only in the long run, therefore the first aim must be to stay in business. So for each trade only a small proportion of the available capital should be at risk. Many traders fail because they are too greedy, that is they bet too much money on a single trade . Not to bet too much on a single occasion sounds like a good advice, but how much is too much and can a bet be too small? These question will be dealt with in the next section. Optimizing return It is understandable that the proportion of money to be risked on each trade should grow with the likelihood of success. If the amount to be gained and the amount to be lost were identical, then there would exist a simple formula for optimizing return. Information theory gives us the answer: 2p - 1 is the optimal bet. Here p is the probability to win. Therefore, if the probability of winning was 50%, then p=0.5 and in that particular case the term (2*0.5)-1 = 0. This means, you should bet nothing. However, if the probability of winning was 55%, then term (2*0.55)-1 = 0.1 and in that case the optimal strategy would be to bet 10% of the available trading capital. Average individual gains and average individual losses are not identical as a rule. This holds particularly for trading systems in the financial markets. In that case the formula for optimizing return becomes somewhat more complicated xxx[(R + 1) * p] - 1 xxx_____________ xxxxxxxxR Here the term R is the ratio of the average single gain devided by the average single loss. The variable p denotes the probability of winning. If individual gains and individual losses were of equal size and occurred at equal probabilities, the numerator would become zero and therefore nothing should be risked. However if the numerator became positive it would be advantageous to bet a certain amount of trading capital. A positive numerator can only appear, if R > 1 and/or p >0.5 Consequently it would be possible to win, even if a single gain was smaller than a single loss, provided the probability of winning was greater accordingly. Likewise a trading system could be profitable even if losses were more frequent then winners, provided the individual loss was small in comparison to a single gain. Transaction Costs The optimizing formula assumes that a trade or a bet was free of charge. That is not the case as a rule. Traders have to pay transaction costs for each trade. For a valid calculation these fees have to be considered as well.