Without risk none of us would make any money in the markets, but managing trading risk as a financial executive is a lot more complicated than one might like.

Often risk limits are set arbitrarily and impacted by trader performance, units traded, the typical risk per trade, and whether the risk per trade is statistically appropriate. If the risk is too low, that means you constantly see your stops hit and exceed your limits, only for the market to turn back in your favor. If the risk is too high, you will stay in losing positions too long, and give up too much on profitable exits.

Proper stops cannot be placed purely on one's comfort level, or budget, but are dictated by market conditions and volatility.

STEP 1

Understanding Trader Performance Risk and Percent Chance of Loss

Everything else being equal, a trader with a good track record has a lower probability of losing the risk limit than a trader with a poor one.

Corporate traders are often inexperienced, as I was when I was transferred into international energy trading from engineering in 1983 (just as the crude oil contract was introduced). So it's not always a valid assumption professional traders are competent or well-trained. Back then, energy traders only used fundamentals (defined as research combined with speculation), and setting risk limits as a gross value made sense. The best computing power we had on the trading floor was an Intel 8086 beige-box desktop, and streaming data evaluation--available on today's Bloomberg terminals--was not within reach.

Many years later, computing power can push lots of streaming data through very sophisticated algorithms evaluating risk in portfolios, even if they contain thousands of securities, in the blink of an eye. Thus we can set risk limits and control risk in a much more granular and nuanced way. It's not a question of either fundamentals or technicals. Today, there's no excuse not to do both.

This first step involves understanding the math that underlies basic risk calculations, and how they are impacted by trader performance. Here are the key formulae, derived from game theory.

A = RL / (In(P) / [ln(1 - W) - ln(W * R)])

RL = A * (ln(P) / [ln(1 - W) - ln(W * R)])

P = EXP ({RL * [ln(1 - W) - ln(W * R)]}/A)

Where:

A = Amount of Risk per Trade

RL = Risk Limit, or Total Capital Willing to Lose

P = Percent Chance of Losing RL

W = Percentage of Time "Win"

R = Win-to-Loss Ratio

Let's assume the risk limit is $100,000. The trader will be "shut down" if that much is lost. However, there's a big difference between a 25 percent chance of losing $100,000, versus a more tolerable 0.25 percent.

The question becomes how much of a chance is being taken of losing "everything". W is the percent of times a profit is made. So if 100 trades are taken and 55 are winners, the W value is 55 percent, or 0.55. R is the ratio of the average wins, say $10,000, and the average losses, say $5,000, with R, then the win to loss ratio equal to 2.0.

Using various inputs with a range of P values produces the...