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For example, if typical recent volatility levels on IMM Japanese yen futures for our specified trading time frame suggest that stop-loss orders should be no less than $1,500 from entry price, then the Japanese yen is probably an appropriate trading vehicle if our equity under management were $100,000, because one contract would represent 1.5 percent risk of total equity under management (generally considered an acceptable level of per-position risk). On the other hand, if our equity under management were $15,000, then taking a position in the Japanese yen would represent an unacceptable level of price risk, because one contract would now represent 10 percent risk of total equity under management.
Just as there are no absolute answers regarding the placement of stoploss orders, neither are there any absolute answers regarding maximum levels of total per-position risk. The issue is made even more complicated by the fact that certain assets and/or trading systems may have positive or negative correlations to existing positions currently held in our trading accounts. If open positions have a positive correlation to our potential entry signal, prudent price risk management might suggest that we avoid trade execution despite our having adequate funds for the trade on a stand-alone basis. For example, if we currently held an open long position in Chicago Board of Trade (CBOT) soybeans, our purchase of CBOT soybean meal might represent excessive risk due to the strong positive correlation between these markets. By contrast, if we held the same long CBOT soybeans position and received a sell signal in CBOT soybean meal, because of this same strong positive correlation between these assets, it might be prudent to take the soybean meal trade even if that trade’s stand-alone risk seemed excessive.
Aside from these correlation considerations, a good general rule of thumb is to limit per-position exposure to somewhere between 1 and 2 percent of our total equity under management. Why 1 to 2 percent? Because our goal is to ensure that our account will be able to survive long enough to return to profitability after enduring our worst equity drawdown. Remember the 37.5 percent trading account stop-loss level? Well, the lower our percentage of equity stop-loss on a per-trade basis, the lower the probability of triggering the 37.5 percent trading account stop-loss level. If we assume
MECHANICAL TRADING SYSTEMS
$100,000 in equity under management and set our per-trade stop-loss level at 4 percent, it would mean that 12 consecutive losses3 would trigger our trading account stop loss (see maximum consecutive loss columns of Tables 3.9 and 3.10). By contrast, if we had $100,000 in equity under management and set our per-trade stop-loss level at 1 percent, it would translate into having to endure 47 consecutive losses before activating our 37.5 percent trading account stop loss.
Finally, the ability to quantify per-position risk in relation to equity under management is particularly useful for traders utilizing leveraged instruments, such as futures and/or options. This is due to the fact that per-po-sition risk in relation to total equity under management negates questions of leverage and margin, and instead allows the manager to trade as many contracts as desired, so long as they do not exceed the 1 to 2 percent limit on a per-position basis.
VOLUMETRIC PRICE RISK MANAGEMENT: MARTINGALE AND ANTI-MARTINGALE STRATEGIES
Stop-loss price risk management is not, in and of itself, a sufficient risk management methodology and should be complemented by a robust system of designating stop-loss levels per volumetric position(s) taken. This twotiered approach to price risk management allows us to answer these questions: How much I am willing to risk on a per unit basis (stop-loss limit level)? and How many units I am willing to trade on a per account basis (volumetric limit level)?
Although there are infinite varieties of volumetric price risk management strategies, all of them can be broken down into two basic philosophies of position sizing: Martingale and anti-Martingale. Martingale is a method in which the volumetric size of the risks assumed are doubled after every losing trade. The theory is that if we merely continue to double our position size after every loss, eventually we will regain everything lost in addition to the original stake. The problem with Martingale is that a string of consecutive losses will result in bankruptcy. If our beginning position size risked $1,000, 11 consecutive losses utilizing a Martingale strategy would result in a drawdown in account equity of over $1 million. A review of the performance tables 3.9, 3.10, and 4.4 shows that, although a rarity, 11 consecutive losses will occur for some moderately successful trading systems.
Although a “pure” Martingale position sizing methodology is defined as the doubling of volumetric exposure after every loss, participants in the financial markets commonly employ other, equally lethal varieties of such adding-to-losses strategies. The most popular of these strategies—typically employed on the long side of the equities markets—is known as averaging