Rethinking MS Part III: Kaufman's Efficiency Ratio
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Welcome to Rethinking Market Structure — Part 3. I’ve laid out my thoughts on the third update of the "OMSF Learning Space" tutorial below. If you grab the chart, you’ll jump into the tutorial right at the location that matches this text. If you already have the OMSF Learning Space on your chart, an update icon should appear in the indicator's status line.
In this update, we introduced Kaufman's Efficiency Ratio (KER) to find out whether our market structure indicators (Pivots & OMSF) produce arbitrary price levels or actually correlate with objective measurements.
1. KAUFMAN'S EFFICIENCY RATIO
Definition:
- The Kaufman Efficiency Ratio (KER) measures price displacement within a specific timeframe (number of bars = KER length / including direction) divided by the sum of all individual price displacements per unit time (difference between the current and previous bar).
export dir_kaufman_eff_ratio(int kerLen) =>
float direction = close - close[kerLen]
float volatility = math.sum(math.abs(close - close[1]), kerLen)
float ker = volatility != 0 ? (direction / volatility) : 0.0
[ker]
- KER = +1.0 (Perfect Efficiency): The market moves like a laser beam upwards (-1.0 downwards). Every single candle closes in the direction of the trend. There is not a single counter-move within the lookback window. The distance traveled equals the net displacement exactly.
- KER = 0.0 (Pure Chaos / Noise): The market is chopping around wildly (the sum of all individual moves up and down in the denominator is much larger than the price difference over n candles), or the market ends up near its starting level after n candles (making the numerator extremely small).
2. VALIDATING THE PIVOT-TRENDFILTER USING KER
What does "validation" mean?
If we want to prove that Pivot Highs/Lows represent significant turning points and are thus relevant for determining trend direction, our pivot conditions should align with other trend-relevant measurements.
We assume KER measures market / trend structure because:
- The formula contains the direction of price change (indicating trend direction).
- We expect more clear upward moves in an uptrend, and more clear downward moves in a downtrend.
- TradingView authors like andrew888 and DojiEmoji use KER directly as a trend filter.
3. PIVOT-TRENDFILTER VALIDATION - RESULTS
Note: I am not presenting formal statistical proof here. Doing so would require aggregating data across multiple assets and timeframes and subjecting it to rigorous statistical testing. My observations stem from manually scanning table values in the OMSF Learning Space, but they nevertheless point to a mathematically systematic relationship between our Pivot Filter and KER:
Stability of the Pattern
For indices on the 1-hour chart and higher with settings of (Pivot Length: 10, KER Period: 14), the data reveals the following pattern:
- In an Uptrend (Long): An average KER of around +0.2
- In a Downtrend (Short): An average KER of around -0.1
Market Asymmetry
In liquid Forex markets (e.g., EUR/USD or USD/CHF), the asymmetry between Long and Short conditions disappears. Here, the average KER is:
- Approximately +0.13 in an Uptrend versus -0.13 in a Downtrend.
- A similar phenomenon can be observed on minute charts of equity markets.
If we assume KER reflects trend structure, these observations suggest that classic Pivot points are not arbitrary chart marks, but indicate structural turning points in the market. I draw this conclusion because:
- Table values across different asset classes (Forex vs. Indices) speak for a correlation between KER(14) and the Pivot filter.
- They mirror frequently reported differences between equity indices and Forex markets: Stock markets exhibit a structural long bias (they ride the escalator up, but take the elevator down – corrections are sharp, volatile, and mathematically less linear). Forex markets, on the other hand, show their classic tendency toward mean reversion (returning to the average).
4. KER AND OMSF
To maintain the comparative framework from OMSF Learning Space –Chapters 1 and 2, I built an equivalent trend filter based on OMSF ( Chapter 4b). The OMSF Filter switches
- to a Long condition as soon as a valid OMSF Low is logged and an upmove is present,
- or to a Short condition when an OMSF High is confirmed and a downmove is present.
- Yields lower values in default settings than for Pivot conditions, meaning KER discriminates less clearly here.
- However, across assets and timeframes, a clear stability in results as well as the distinct difference between Forex pairs and equity indices remains evident.[.
Why are OMSF Long/Short conditions not as clearly distinguished by KER as Pivots?
Answering this question reveals how OMSF actually works:
- Agility vs. Inertia (Standard Mode): In Exercise 2 of the Learning Space, you can visually overlay both filters. You will see that in default settings, OMSF provides a finer structure, switching to a downward condition more frequently within an overarching upward phase. The longer and more lagging the KER, the more frequently KER and OMSF run out of sync, which depresses the average KER.
- Hybrid Method: OMSF reacts fundamentally immediately (fast, candle-based) to directional changes (see Chapter 2, OMSF Learning Space). When OMSF switches to "Downmove," for instance, KER still measures a large portion of the previous upmove depending on its period length. On smaller structures below the compression threshold (where price moves very little), OMSF responds to momentum.
3 Modes of OMSF for Illustration
- Pure Momentum Mode: Setting the compression threshold extremely high (e.g., 10 ATR) makes OMSF react exclusively to momentum. The clearer KER averages show that KER and OMSF align better in this mode, as OMSF now frequently switches into the matching condition during an ongoing movement.
- Reversal Mode (Excessive Price Movement): Increasing the momentum threshold so high that it is never breached (e.g., 10 ATR) and setting the compression threshold = 4 makes OMSF react solely to reversal signals after large moves (i.e., when KER is extremely positive/negative). The signs of the table values for OMSF reverse completely! This means our filter now runs in exact opposition to KER.
- Without Filter: OMSF reacts immediately to every reversal. Shortening the KER length (e.g., to 9) sharpens the discrimination of OMSF conditions by avg. KER. The shorter the KER length, the more inevitably KER looks right into a fresh impulse and reaches values closer to the extremes (+1 or -1). Note that here we leave the domain of trend filtering and move toward pure impulse/momentum measurement.
Analyzing KER provides, in my view, strong evidence that both market structure indicators deliver relevant price levels. However, they represent different lenses through which to view the markets, allowing traders to find their optimal application depending on individual market understanding. I reach this conclusion because despite all differences (methodology, degree of differentiation by avg. KER), the distinction between stock markets and Forex pairs holds true across all settings and variants.
Both systems have their advantages:[
- The strength of Pivot levels lies in their robustness, making them exceptionally well-suited for describing overall market structure. Due to their confirmation lag (right length), Pivots align better with KER, which similarly looks backward due to its lookback period. Thus, by tweaking KER length and Pivot lengths, both measurements can be well synchronized.
- The advantage of OMSF lies in its agility, driven by the integration of direct reversal signals and momentum measurement, which in turn limits its alignment with KER.
Parameter Variation
In Chapter 4a of the Learning Space, we extended the KER length and the Pivot confirmation duration (right lengths), thereby expanding the analyzed chart window. I found a sweet spot for high KER averages in Pivot conditions with a KER period of 27 and right Pivot lengths of 17. This allows us to look at a longer chart section (i.e., the longer-term trend direction) while ignoring short-term volatility or minor corrections. Even with KER(50) and a Right Length = 35, we still get solid KER discrimination between Pivot conditions. Beyond that, judging alignment visually becomes increasingly difficult, as KER mathematically flattens with higher periods, causing average values to drop.
- By tailoring efficiency measurement to the wavelength of our Pivot structure, we can: ... evaluate the quality of the Pivot trend. The closer we get to the extreme points (+1, -1), the cleaner the current trend. One could attempt to filter out false Pivot signals using KER thresholds.
- ... use KER as an early warning system for changes in Pivot conditions, since KER is measured continuously and complements discrete Pivots effectively.
For OMSF, I only found meaningful alignment with longer KERs in "Reversal Mode" (see above; note KER asynchrony in this mode). By increasing the compression threshold (3–4 ATR), we observe a relatively good fit with KER lengths of 27–35. Shorter KER lengths naturally fit standard OMSF better, where direct reactions to price reversals and momentum are decisive.
In Exercise 2 of the Learning Space, you can visually stack both filters. In default settings, OMSF appears to act as a subordinate structure to the Pivot structure. For example, OMSF could be used to time entries into an overarching trend movement. In fact, many ideas emerge for combining all three methods (including KER) to construct more complex trend indicators.
Despite all differences and lower overall discrimination by avg. KER, the "OMSF Filter" on indices displays the exact same Long/Short asymmetry as the Pivot Filter—an asymmetry that vanishes in Forex markets. This means classic Pivots and the OMSF structure capture the same objective market structure. Both describe real market dynamics; they simply use different coordinate systems.
So far, this series has been quite theoretical. But in our next and (for now) final update of the Learning Space (Chapter 5), we will tackle the question everyone is most interested in: What real trading potential do both structure indicators offer?
To answer this, we will look at MFE (Maximum Favorable Excursion) and MAE (Maximum Adverse Excursion) and their ratio to roughly estimate the trading potential and risk inherent in both methods.
Don't hesitate to share criticism or questions—both are highly appreciated! Otherwise, I look forward to seeing you in the next update.
Cheers, arni
