Besides expectancy, most traders have problems understanding risk. For instance, a historian by education, (former) head of a regional investing company with assets over a million dollars by summer 1997 was sure that "risk doesn't exist so it cannot be measured" and also sure that "one shouldn't sell shares at a loss". What can one say about amateurs then… Risk does exist and it can be measured. It is considered that risk is a volatility measured as the standard deviation of the changes of actives traded. This holds true for investing risk, speculative risk is more adequately defined as standard deviation of capital changes. By both those definitions risk is heavily underestimated. According to Murphy's laws, the worst is yet to come; We shall employ the following definition: risk is the amount of money we are ready to lose before withdrawing from a losing trade.

Before opening a position it is necessary to define the point where we close the position wit a loss to save capital - the so-called stop loss1, or where we open an opposite position, having made sure of our mistake concerning the market direction - the so-called stop-and-reverse. The difference between the entry point and the stop loss point multiplied by the number of lots is the starting risk or 1 R2, independent of how and in which units we measure the stop level, be it dollars, percents, volatility units or six-packs. This definition of risk is not equal to the first definition - the risk may be many times the 1 R if the stops are not executed due to lack of discipline3, gaps against the position or unexpectedly high slippage. The profit, then, can be defined in units of risk per share or in multiples of R. In terms of multiples the basis rule of speculation will be formulated as: keep losses at the level of 1 R as long as possible and let profits reach many times R.

The expectancy in multiples of R will mean how much can we win or lose per unit of risk in an average trade. To calculate expectancy in terms of multiples of R we must place the results of our trades in a table with the following columns:

The Profit or Loss must take into account broker commissions and slippage. Multiple of R is calculated by dividing the second column by the third. Then to calculate expectance it is enough to add up the values of the fourth column and divide by the number of trades. This method is also works with "intuitive" trading.

So, we do have a winning strategy - what next?

We can open a brokerage account and bet all our capital with the maximal leverage.

Here the most important thing - the money management begins. To clear the situation here is a pair of facts. Ralph Vince invented a game, where bet size was the only moveable parameter. He chose forty doctors of sciences (i.e. not the dumbest people at least) as players, none of which were professional traders or studied statistics. The doctors played a game where 100 random trades were generated, one by one. Every one began at $1000, and before every trade one had to make a single decision - how much (up to 50% of the capital) to bet. 60% of the time the players won their bet, and 40% of the time they lost their bet. This game has an expectancy of 20 cents per dollar risked, i.e. in the long run the player can receive 1 dollar 20 cents per dollar. The academicals made their 100 bets, enough to resolve the expectancy. Making the same trades, they finished the game with different results. Guess how much of them increased their starting capital? Two of forty. 95% of doctors lost money playing a game with a positive expectation!1

Van Tharp made an even more striking example. In an Asian Tour for Dow Jones Telerate TAG (Technical Analysis Group) he gave lectures in 8 cities before 50-100 listeners each time, most of them professional traders for large companies or banks that traded shares, bonds or exchange rates on Forex. In an analogous game over a half of highly professional traders lost!2 Another personal example - a trader offered a similar game to a friend employed by Charles Schwab as a leading analyst. At the first level the distribution of multiples of R with an expectancy of 0,45 and 60% profitable trades. To get to the second level one had to make 50% profit in 100 trades. The result was "I cannot get to level 2 in a day!"3. In 1991 Brinson, Singer and Beebower published a research of the efficiency of 82 portfolio managers in a 10-year period, which showed that 91,5% of all profit was generated by asset distribution3. The asset distribution meant the division of capital between cash, shares and bonds. Only 8,5% of profit was due to buying and selling the right stocks and bonds at the right time.

Let us play the game described by Vince. If there was no risk, i.e. we knew the result of each trade beforehand, it would make sense to bet all the capital each time. So every player would have gained $1000 ..(1.2 ^100)=$82,817,974,522.01 .

In reality, if we bet all $1000 on the first trade, we have a 40% risk to lose all at the first attempt. Even if we win and have $2000, betting all on the next trade would be exactly as insane.

Now suppose we bet $200 at a time. So if five first trades are losing, we again lose all. The probability of such an event is small, just over 1%. But are we ready for such a "small" risk, if we can lose all the money? Suppose we lose in the first two trades (16% probability), so we'd lose 40% of the capital. Beginning from the next trade we must gather 67% of profit just ot restore the starting capital. This effect is called "asymmetric leverage"5.

Table 2 shows that loses of over 50% need improbably large profits just to recover; so if we risk relatively large sums and lose our chances to end up wit a profit are negligible.

So, we do have a winning strategy - what next?

We can open a brokerage account and bet all our capital with the maximal leverage.

Here the most important thing - the money management begins. To clear the situation here is a pair of facts. Ralph Vince invented a game, where bet size was the only moveable parameter. He chose forty doctors of sciences (i.e. not the dumbest people at least) as players, none of which were professional traders or studied statistics. The doctors played a game where 100 random trades were generated, one by one. Every one began at $1000, and before every trade one had to make a single decision - how much (up to 50% of the capital) to bet. 60% of the time the players won their bet, and 40% of the time they lost their bet. This game has an expectancy of 20 cents per dollar risked, i.e. in the long run the player can receive 1 dollar 20 cents per dollar. The academicals made their 100 bets, enough to resolve the expectancy. Making the same trades, they finished the game with different results. Guess how much of them increased their starting capital? Two of forty. 95% of doctors lost money playing a game with a positive expectation!1

Van Tharp made an even more striking example. In an Asian Tour for Dow Jones Telerate TAG (Technical Analysis Group) he gave lectures in 8 cities before 50-100 listeners each time, most of them professional traders for large companies or banks that traded shares, bonds or exchange rates on Forex. In an analogous game over a half of highly professional traders lost!2 Another personal example - a trader offered a similar game to a friend employed by Charles Schwab as a leading analyst. At the first level the distribution of multiples of R with an expectancy of 0,45 and 60% profitable trades. To get to the second level one had to make 50% profit in 100 trades. The result was "I cannot get to level 2 in a day!"3. In 1991 Brinson, Singer and Beebower published a research of the efficiency of 82 portfolio managers in a 10-year period, which showed that 91,5% of all profit was generated by asset distribution3. The asset distribution meant the division of capital between cash, shares and bonds. Only 8,5% of profit was due to buying and selling the right stocks and bonds at the right time.

Let us play the game described by Vince. If there was no risk, i.e. we knew the result of each trade beforehand, it would make sense to bet all the capital each time. So every player would have gained $1000 ..(1.2 ^100)=$82,817,974,522.01 .

In reality, if we bet all $1000 on the first trade, we have a 40% risk to lose all at the first attempt. Even if we win and have $2000, betting all on the next trade would be exactly as insane.

Now suppose we bet $200 at a time. So if five first trades are losing, we again lose all. The probability of such an event is small, just over 1%. But are we ready for such a "small" risk, if we can lose all the money? Suppose we lose in the first two trades (16% probability), so we'd lose 40% of the capital. Beginning from the next trade we must gather 67% of profit just ot restore the starting capital. This effect is called "asymmetric leverage"5.

Table 2 shows that loses of over 50% need improbably large profits just to recover; so if we risk relatively large sums and lose our chances to end up wit a profit are negligible.