Signal Processing, Applied to Markets

A price chart is a signal.

That sounds like a figure of speech until you take it literally. Engineers have spent seventy years pulling real signals out of noisy ones, in radar, in audio, in medical imaging, and they did not do it by averaging the last two hundred readings. They did it by separating what was in the recording by speed, keeping the part that carried information and discarding the part that did not.

That is the idea underneath everything THOR runs. This is how it works, at the level of the idea rather than the settings.

Noise has a definition

In finance the word noise gets used loosely. It usually means "the part of the move I did not like." In engineering it has a definition, and the definition is what makes it useful.

A signal is the part of a recording that carries information. Noise is everything else riding in the same recording.

Put a microphone in a coffee shop. It captures your voice and the espresso machine in one waveform. Nothing in that file is labeled. There is no column marking which sample belongs to the voice. A machine that wants to keep one and drop the other has to work it out from the shape of the wave over time, and it can, because the two things move at different speeds.

Three speeds, stacked in one line

A market series has the same layering.

There is a drift that runs for years. There is a cycle that runs for weeks and months. There is a jitter that arrives every session and reverses by Thursday. All three are stacked into the single line you look at on a screen, and your eye cannot pull them apart because your eye only ever sees the sum.

A filter can pull them apart, because speed is a property you can select on.

Splitting the series

So the first real move is to split the series by speed. A low frequency component that holds the slow drift. A high frequency component that holds the chop.

Neither half is the answer on its own.

The slow part is always late, and that is not a tuning problem. Slow is what late means. The fast part is mostly noise by construction. What is worth having is the band in between, the one that describes the character of the market as it is now rather than as it was two quarters ago.

Take the series, remove the slow drift, and what is left behind is a wave. It rises, it rolls over, it falls, it troughs. Not a line with a slope. A wave with a shape.

Once you are looking at a wave, the question changes. You stop asking whether price is above some average. You start asking whether the wave has turned.

Decomposition instead of more indicators

It is worth saying what this replaces, because the alternative is familiar to anyone who has looked at a trading screen.

The common approach to a noisy series is to add instruments to it. A moving average, then a second one at a different length, then a momentum oscillator, then a volatility band, then a rule about what to do when three of the four agree. Each instrument is computed from the same price, so each carries the same noise, and stacking them mostly stacks the noise with it. Agreement between four views of one series is not four pieces of evidence.

Decomposition is the other approach. Rather than adding readings on top of the series, split the series itself into parts that move at different speeds, then decide which part is the one worth acting on. One decision gets made, about one component, for a stated reason. That is a smaller and more honest claim than a committee of indicators voting.

Why not a moving average

This is where the approach separates from most trend systems, and it is worth being precise about why.

A moving average crossing is a comparison between price and a lagging copy of price. It cannot say anything until enough history has accumulated to drag the average through the current price. The delay is not a flaw in the setting, it is the definition of the tool.

Shorten the window and you get whipsawed, because now the copy is close enough to the price to be pushed around by noise. Lengthen it and you arrive after the move, because now the copy is smooth and slow. There is no setting that escapes it. The structure of the instrument is the problem.

A turn is a different kind of object. A turn is a change in the direction of the wave, and it belongs to the signal itself rather than to a comparison against a delayed version of it.

What counts as a turn

A single observation pointing the other way is not a turn, it is one observation.

The requirement is persistence. The change of direction has to hold before it counts as a change of state. That one requirement does most of the practical work, because it is what stops a system from trading every headline, and it is why the approach produces few position changes rather than many.

It also sets up the honest trade, which comes later in this piece.

The output is a state, not a forecast

What comes out of the process is not a prediction.

It is a state. Either conditions support owning equity risk or they do not, and when they do not, the allocation moves toward money market funds, cash alternatives, or other ETFs.

We detect, we do not predict. Nobody here has a view on where the S&P 500 closes next quarter, and no part of the process asks for one. The system reads the character of the signal now and holds that state until the signal turns.

That distinction matters in practice. A forecast has to be right about the future. A state only has to be an accurate description of the present, which is a much smaller thing to ask of any model.

Where it is weak

Every method has a place where it struggles, and a manager who will not name theirs is not worth listening to.

This one is strongest in markets with real persistence, up or down, where turns form cleanly. It is weakest in flat markets that chop sideways and mean revert, where turns form and then fail.

That is a known cost of the design, and it is deliberate. The method accepts more small false turns in exchange for staying clear of the large sustained declines. If you want the arithmetic behind that preference, it is the oldest one in the business. A 40% loss needs a 67% gain to get back to even, and the small false turns cost a fraction of that.

Anyone evaluating a systematic approach should ask for the weak environment by name, then look at what it cost in that environment. A method with no weak environment has not been described honestly.

One engine, two indexes

The same process, pointed at different universes, produces different results.

Pointed at the three large U.S. equity indexes it rotates among them, with the freedom to hold none of them, and that is the THOR SDQ Rotation Index, which THOR Index Rotation tracks.

Pointed at the sectors of the S&P 500, held in equal weight rather than by market capitalisation, it produces a low volatility profile that is not built from the same crowded mega caps that dominate a cap weighted index. That is the THOR Equal Weight Low Volatility Index, which THOR Low Volatility tracks.

Two published indexes, two different universes, one process underneath both of them. Index construction and index methodology are documented, which is the point. A rules based index is a description you can read and check, rather than a manager’s discretion you have to take on trust.

What to ask

If you are evaluating any systematic manager, including this one, four questions get you most of the way:

1. What is the input, and what does the process do to it before a decision is made? 2. What triggers a change of state, and what specifically prevents a single observation from triggering one? 3. What are the possible states, and where does the money sit in each of them? 4. In which environment does this perform worst, and what did that cost the last time it happened?

Answers to those four describe a process. Anything that cannot answer them is describing a track record instead.

Educational content only. This is not investment advice and it is not a recommendation regarding any security. Index construction is described here in general terms and simplified for explanation. Investing involves risk, including possible loss of principal.

Past performance does not guarantee future results.