Aug

24

Summiting mount kenyaI have been learning about ski mountaineering and climbing. One aspect of safety is setting anchors and belay points called protection. When starting up a steep pitch where falling and injury or death is possible in case of a mistake, the climber creates an anchor by tying a loop around a rock or putting pitons or nuts in a crack which will hold the rope tied to the climber to limit how far he can fall. As the climber climbs higher, the rope is shortened, and new protection is placed limiting the fall length. In case of a fall, there is some give in the system to avoid too hard a shock.

In climbing there are other "stops". One is the summit…goal reached, or back home. The other stop is time. If the climber has not reached the summit by enough time to return home by dark or before bad weather hits, its time to stop and turn around.

The trading applications are obvious, and in both cases it appears to be an art. Phil has stated that stops do not improve performance, but merely lower deviation of return. Senator has always advocated using stops. What is unclear to me is some scientific way to determine the optimum stop. Time stops seem common. Profit stops are too common. The difficult question is the use to trailing stops and the distance or adjustment and size. I've never seen a satisfactory analysis. Adjustment for volatility seems a must. Chair has advocated adjusting or limiting leverage, rather than stops as "protection".

Advice sought.

George Parkanyi writes:

This is very timely, because I just set three rows of stops in August trying to catch the down-leg (short) while keeping my risk low, and I got taken out of the meat of my position all three times– FOMC fake-out, sheared right before the 20-point drop, and sheared again this morning before the market settled down again. Arggh. Luckily still made a little something on the scraps, but basically managed to completely miss the move. (Please feel free to point and laugh.)

Sometimes taking a larger position (and risk) and commensurately narrowing your stops can pay off big, but there's something to be said for taking smaller positions and more forgiving stops (and a longer holding period to adjust reward to risk). While I was frantically trying to catch the equities just so, my relatively smaller short oil position (whose stop I had not touched) was plodding along building up nicely, looking over now and then going "What's YOUR problem?" Maybe you do a hybrid. I don't know.

So, what looks good on the long side then? Bargain-hunting in the long bonds perhaps?

Phil McDonnell comments:

There are many interesting themes in this discussion so I will address a few.

First a few basics assuming a random walk - if you use stops:

1. Your expectation will not change. You will neither make or lose more money assuming a random walk.

2. Your variance will be reduced (a good thing)

3. Your probability of having a loss as least as great as the stop will DOUBLE! Suppose the odds are about 16% that a stop loss set at 1 std deviation will be exceeded to the downside. If you use a stop loss at that price point, the probability it will be hit is 32%. The reason is the Reflection Principle of Statistics which essentially says that every path that reaches that point has an equal and opposite path that reflected back from that point. There are some graphs in my book Optimal Portfolio Modeling (Chapter 4) which illustrate this point.

4. If you use profit targets the preceding points are reversed.

5. On Friday I posted a 9 minute video with charts to theStreet.com which discusses my use of stop profits with respect to options. It is in the Options Profits section but people can get a free trial at the site.

In my opinion it is possible to optimize a stop loss or profit target provided you first specify an objective function that you want to optimize. My preference would be something that includes both risk and reward like a Sharpe Ratio. In one sense a stop loss and a stop profit are much alike. They both double the odds of winding up there. But a loss is more important in the sense of compounding your money. A 25% loss needs a 33% gain to break even. But this information is captured by taking the log as your weighting function. The trick is to take the log at the portfolio level and not the trade level.

Optimizing stops can easily be done in Excel using the solver. But I am not saying that such optimization will always be productive. Essentially it is a search for an anomaly just like a trading system. Just like a trading system it requires a significance test and sufficient data. Adding the stop parameters brings one that much closer to the slippery slope of data mining and curve fitting.

Nick White's interesting point about information is spot on. If you compare the formulas in my book to the formulas developed by Claude Shannon the father of Information Theory they are essentially identical. Yet mine were derived from first principles and compound interest math. As an aside the formulas in list member Ralph Vince's book are essentially the same math even though when you look at them Ralph does not use logs (mostly) so on the surface they appear different from the formulas Shannon and I wrote, but they are not.

To me this says that the market pays for information. That explains the beautiful symmetry between the formulas of Information Theory and portfolio optimization.
 


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  1. douglas roberts dimick on August 25, 2010 3:47 pm

    Market Dimensionality Revisited

    The Theory of Quantitative Relativity favors the position of the Chair. See my article on dimensionality of market trading…

    “The state of a system makes the system’s history irrelevant. The state of the system contains all of the information needed to calculate responses to present and future inputs without reference to the past history of inputs and outputs; present inputs and the sequence of future inputs allow computation of all future states (and outputs). Some dynamic systems are modeled best with state equations while others are modeled best with state machines.”

    http://www.dailyspeculations.com/wordpress/?p=4353

    Any given electronic exchange market is a dynamic system. Therefore, in that one of any state of any such operating system presents variance in state equations and transitions, quantification of stops cannot be so correlated to rules-based state excitations due to lack of an invariant to constrain declared objects (e.g, target price or profit) of any given class (or conditions constituting both strategy and order execution protocols).

    George’s three strikeouts account is exemplary.

    So how and why have strategies successfully — however one so chooses to quantify this adverb — employed stops?

    “Exponential divergence of sequences of iterates explains the connection between chaos and unpredictability: a small error in the supposed initial state of the system will tend to correspond to a large error later in its evolution. It is often possible, however, to make precise and accurate statements about the likelihood of a future state in a chaotic system.”

    As with quantitative impressions, we are referring here to probabilities of output during any given state or state transition of the operating systematics constituting the electronic exchange process.

    Accordingly, albeit this elaborate form or gambling (ahem, speculation), hedging via adjusting and limiting leverage appears optimal to achieve “[t]opological mixing (or topological transitivity)” relative to state output and state transitioning.

    dr

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