Determining Optimal Risk
by Ed Seykota and Dave Druz
Seasoned traders know the importance of risk management. If you risk little, you win little. If you risk too much, you eventually run to ruin. The optimum, of course, is somewhere in the middle. Here, Ed Seykota of Technical Tools and Dave Druz of Tactical lnvestment Management, using subject matter and materials that they have used in lectures and workshops around the US, present a method to measure risk and return.
Placing a trade with a predetermined stop-loss point can be compared to placing a bet: The more money risked, the larger the bet. Conservative betting produces conservative performance, while bold betting leads to spectacular ruin. A bold trader placing large bets feels pressure — or heat — from the volatility of the portfolio. A hot portfolio keeps more at risk than does a cold one. Portfolio heat seems to be associated with personality preference; bold traders prefer and are able to take more heat, while more conservative traders generally avoid the circumstances that give rise to heat.
In portfolio management, we call the distributed bet size the heat of the portfolio. A diversified portfolio risking 2% on each of five instrument & has a total heat of 10%, as does a portfolio risking 5% on each of two instruments.
Our studies of heat show several factors, which are:
1，Trading systems have an inherent optimal heat.
2，Setting the heat level is far and away more important than fiddling with trade timing parameters.
3，Many traders are unaware of both these factors.
COIN FLIPPING
One way to understand portfolio heat is to imagine a series of coin flips. Heads, you win two; tails, you lose one is a fair model of good trading. The heat question is: What fixed fraction of your running total stake should you bet on a series of flips?
This puzzle has been presented in numerous workshops and lectures. The participants generally come up with some amazingly complex ways to arrive at a solution. Overall, the simplest way is to notice that:
1 In the long run, heads and tails balance.
2 The order of heads and tails doesn't matter to the outcome.
3 The result after n sets of head/tail cycles is just the result of one head/tail cycle raised to the nth power (see sidebar, "Coin flipping math").
So we can get our answer simply by making a table of results of just one head/tail cycle.
Figure 1 represents such a heat test. It shows an optimal bet size of 25%, at which point one head/tail cycle delivers 12.5% profit, after a 50% gain and a 25% drawdown. As is typical of heat tests, at low heat, performance rises linearly with bet size. At high heat, performance falls as losses dominate, because drawdowns are proportional to heat squared (see Figures 2 and 3). In practice, a trader may prefer to bet the coin at less than optimal heat, say 15% to 20%, taking a slightly smaller profit to avoid some drawdown-induced stress.
The results of the 12-year simulation recall the coin flips described previously. Return initially rises with increasing heat and then falls as drawdowns dominate.
Heat tests show profitability and volatility over a range of bet sizes. Heat tests can help traders communicate with their investors about and ultimately align on betting strategy before trading begins.Otherwise, investors may become disenchanted with traders who trade well yet ultimately deliver either too little or too much heat.
FIGURE 1: The percent bet is the percentage bet of the running stake. The "Win-on heads" is always 200% of the bet. The "Lose-on tails" is the bet The final total shows the result of one cycle. Beyond a 25% bet (lower half of table) the final total begins to suffer.
FIGURE 2: Plotting the return versus the heat illustrates that the optimal amount bet is 25% of the stake. The curve has a peak (point of zero slope) at 25%
FIGURE 3: Plotting the drawdown versus the heat of heads you win two, tails you lose one bet illustrates that the drawrdown rises with the amount bet.
ACTUAL HEAT TEST
To study actual portfolio betting strategies, we fired up our system testing engine and simulated a trading system over a range of heats. The engine trades all instruments simultaneously (see sidebar, "System test"). The engine rolls deliveries forward to stay with the most active deliveries.
The results of the 12-year simulation recall the coin flips described previously. Return initially rises with increasing heat and then falls as drawdowns dominate. This heat test shows optimal performance for heat around 140% (about 28% per each of five instruments), at which point the system delivers about 55% return per annum (see Figure 4) with average drawdown around 40% per annum (see Figure 5) and maximum drawdown over 90%. In actual practice, few investors would have the stomach for such an optimum. Most would prefer less drawdown and less gain. In any event, heat testing can provide a focus for traders and their investors and help align on critical issues of bet sizing, return and drawdown before beginning new trading relationships.
FIGURE 4: The optimal level of heat is near 140%; then increasing heat causes losses to dominate.
FIGURE 5: As heat is increased, the size of the drawdowns reaches maximum of over 90%.
Ed Seykota, who was interviewed in Market Wizards, operates Technical Tools, a purveyor of historical and daily financial data. Dave Druz, a computer programmer, heads Tactical Investment Management, a commodity trading advisory firm and commodity pool operator to the Tactical Futures Funds.