Optimizing stops

March 27, 2016 09:00 AM

One trading system has smaller average profits than losses and a greater number of wins. Another features bigger average profits and smaller but more numerous losses. Which will be the better system? To help decide, let’s consider some extreme methodologies.

The Martingale system is designed to all but guarantee an ultimate winning bet. That we’re now talking gambling rather than trading is irrelevant as the concept is applicable to both. The player starts with one unit. If the wager pays off, the next bet is the same basic unit. If it loses instead, the next bet is doubled. If that bet loses, it’s redoubled to four units. If that loses, you bet eight, then 16 and so on. Wherever there’s a win in the sequence, one unit profit is netted out and the next play reverts to the single unit. 

The bets must all be of the same roughly 50-50 win chance variety, such as on the craps table’s pass or don’t pass lines. The driver is obvious — a single loss can happen at any time, but consecutive losses are more unlikely and a huge string of them is really improbable. The appeal is also clear — if you think in terms of sequences rather than individual bets, you will enjoy a string of one-unit profits. You will not lose.
Until you do. Maybe your bankroll only extended to a sixth loss? Or maybe your next double would exceed table limits? The strategy counts on many small wins, but the more expansive “many” becomes, the more likely the possibility of total ruin.

The “black swan,” as such anomalies are now known, occurs more frequently than we might expect in the financial markets. We shouldn’t be surprised when the mutation materializes in a sheer sea of trials. A normal statistical bell curve has skinny tails at both ends representing the unlikeliest events. One that reflects human emotion, probably the most plentiful element in the trading world, becomes skewed. The unlikely becomes more likely. The tails get fatter. It has been theorized that 9/11, Black Monday (Oct. 19, 1987) and the flash crash of 2010 should each occur maybe once every several thousand years. We saw at least three within a quarter century.

Martin Gladwell’s book, “What the Dog Saw” includes a chapter recounting the fortunes of two huge traders with diametrically opposing strategies. Day after day, Nicholas Taleb watched his low probability long options expire worthless. It wasn’t a surprise; the plan was to endure consistent losses during all the normal days to hit a huge windfall the one day the market got insanely wild. Taleb knew such days would arrive far more frequently than anyone could imagine. He could therefore accomplish what would be psychologically impossible for the rest of us — hang with a steadily eroding account to get mega wealthy when the black swan hit. Taleb placed tremendous value on the inevitability of a market shock.

Victor Niederhoffer did the opposite. He discounted the low (but not non-existent) risk of ruin that is an ever-present part of speculation, pretty much as we all do whenever we put on a position. He was in effect taking the other side of Taleb’s trades, collecting small sums by shorting the ever deteriorating improbable options. Option traders know this as “picking up nickels in front of the steamroller.” Lots of nickels — the trick is to never get flattened.

Niederhoffer got flattened. It was fall 1997, and a crisis in Asia caused a 69.5-point drop in S&P 500 futures. It was the very day Nicholas Taleb enjoyed an upside explosion in his account equity.

How does this relate to whether to use large or small stops? If you make it easier to take profits and harder to get stopped out, you’re betting more on normal market behavior and downplaying the infrequent anomaly. If you make stops tight and hope that enough trades will survive and travel far in your direction, you’re figuring outliers will occur more frequently rather than less.

The two-trader tale had a clear winner/loser outcome. Non-extreme trading isn’t so lopsided. System development is a game of constant weighing and balancing; it is possible to make your stops too tight. Often, however, you can assume less risk without significantly hurting your bottom line.

“No-stop system” (above) shows a profitable inter-day mini index futures system that has no stops. The exits occur only when the condition is no longer met for staying long or short. Not unexpectedly, the makeup of the trades significantly changes when you impose an arbitrary stop as “Fixed stops” (below) demonstrates. 

Stop effect

You might expect that at the very least, the net profits would significantly shrink as stops are tightened. That’s often not true. “Optimized stops” (below) shows the same system in the S&Ps with optimized stops ranging from $500 to $5,000 in $500 increments. (The left column numbers should be multiplied by 10,000 to produce the stop increments.) A $1,000 stop (second row) generates a bottom line a mere $580 less than the original stop-less system. Stops of $3,000 and higher have performance summaries identical to the original. With a $2,500 loss limit, your net equity would actually increase to $40,202.

The net profit isn’t even the best performance criterion, however. If you instead optimize for return on account (far right column), you’ll get performance in more relative terms — not only a profit projection, but what kind of pain you had to endure getting there during the worst period. The ROA divides the net profit by the worst drawdown. The resulting figure is a percentage your account would have increased had your startup been the drawdown amount. On the top line, your assumed startup capital would have been $6,245 and your ultimate $27,115 net profit would have represented a 434.19% increase (far right column).

Why is this a better statistic than merely knowing your profit? If you don’t delve below the surface, a $100,000 profitable system is always going to appear better than one that produced $40,000 in the same period. But what if you knew that the former system had a $70,000 worst drawdown while the latter had an $8,000 one? You would have done better tripling your position size on the second system. You’d have superior results on both ends — a $120,000 vs. a $100,000 net profit, and a combined drawdown of only $24,000 vs. $70,000. Judging by return on account, your best result would have been the 780% increase stemming from a mere $1,500 stop.

The ROA figures alone demonstrate a robust system. Remember, they represent a percentage increase off an assumed worst drawdown startup. That’s a 645% equity rise in the S&Ps, and a whopping 1,322% in the Russell. The least accommodating market more than doubled its money and the next to worst figure was a more than four-fold improvement. This isn’t bad over an 11-year period.

But the ROA isn’t the only formidable performance measure. Only one drawdown just barely exceeds $10,000. All but one has percentage profits over 50%. Average trades are all triple digit — most far into that realm. We’ve demonstrated that wide losses are not a necessary price to pay for impressive stats.

“No stops vs. $1,000 stops” (below) further illustrates this. The dual row sets are identical versions of the same system other than reporting no stops on the top lines and $1,000 stops on the bottom. Three out of the five markets barely gave up any net profit. While the Russell saw a 17% equity decrease, its ROA was almost totally unaffected. Three out of the five markets actually increased their ROAs.

The role of stops

Charlie Wright, mechanical system fund manager and author, said in my book “Market Beaters” that his testing proved that, ultimately, “indicators don’t matter.” This flies in the face of where systems developers tend to focus. For them, the Holy Grail would be the discovery of the definitive entry signal. As Wright observed, however, markets only provide a finite range of potentially profitable entry points which is why, for example, trend-followers tend to enter and exit at similar levels regardless of signals. He maintained that any “edge” is derived from “the back end” of the trade — risk management.

Let’s consider an extremely simple intraday system that shows a bias in 15-minute bars. At the end of the first bar, or 8:45 a.m. Central time, if the close is greater than the open, buy; if less than the open, go short. Use a $200 money management stop — if not hit, exit on the close. “Simple system” (below) shows the result in the mini midcap from the start of 2005 through Dec. 24, 2015. Each trade represents a single mini contract. For this education-only demonstration, no slippage/commission is deducted.

Intraday strategies often trigger off first bar activities, but is that really the magic driver here? The first chart in “Optimized results” (below) is an optimized study in the midcap. It shows how many 15-minute bars pass before entering in the direction relative to the daily open. The numerically sequenced far left columns correspond to a time of day between 8:45 a.m. and 11:00 a.m. One equals 8:45, two equals 9:00, three is 9:15, etc. Clearly a quick first bar entry is not the relevant driver here; in fact, the time of day doesn’t seem to matter much at all.

Interestingly, neither does the only other system rule. The second table in “Optimized results” shows an optimization of going long when under the opening price, short if over it — the complete opposite of the optimized results in the first table. The opposite logic doesn’t show the same level of overall profit or unanimous winners, but most of its rows are positive. Wouldn’t you assume that none would be profitable given the profitability of every mirror image system line?

In short, it’s not the time of day that’s producing the 15-minute system bias. It’s not particularly the direction you follow relative to the opening. Though following the momentum is better than fading it, both sides can show profit as everything else remains equal. 

The real key to success is the tight $200 stop. It’ll get hit a lot, but when it doesn’t, the potential is near-unlimited.

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