One great learning from Perry Kaufman is to use the efficiency ratio to measure the noise of the market. Kaufman’s Efficiency Ratio was invented in the 1970s to measure how noisy the market is, and from his book Trading Systems and Methods, 5th edition, Chapter 1.
Here’s the formula for the n-day Efficiency Ratio.
\[ ER = \frac{|P_t-P_{t-n}|}{\sum_{i = t-n}^{i = t}|P_i-P_{i-1}|} \]
The idea is simple. A trend with high efficiency ratio is smooth and linear. Conversely, a trend with low efficiency ratio is choppy.
As we see from the formula, the efficiency ratio will be based on different factors:
The timeframe: In lower timeframe prices tend to fluctuate more
The length of the window
We will examine the efficiency ratio across the following asset classes (or proxy ETFs)
Equity:
US: IYY, SPY, QQQ, IWM
Asia: FXI, EWJ, VNM, INDA, EWY, EWT
Europe: EWQ, EWI, EWG, EWU
South America: ARGT, EWW, EWZ
Emerging markets: ACWX, EEM
Bonds: SHY(1-3 years TBond), TLT (20+ Year Treasury Bond)
Commodities: GC, SI, HG, CL, NG, HO, RB, CT, ZC, ZS, ZL, ZW, SB
Forex: 6A, 6B, 6C, 6E, 6J, 6S, 6N, DX
library(quantmod)Loading required package: xtsLoading required package: zoo
Attaching package: 'zoo'The following objects are masked from 'package:base':
as.Date, as.Date.numericLoading required package: TTRRegistered S3 method overwritten by 'quantmod':
method from
as.zoo.data.frame zoo library(ggplot2)efficiency_ratio <- function(close, n = 20) {
close <- na.omit(close) # Remove NAs
close_lag <- lag(close, n)
# Numerator
close_minus_close_lag <- abs(close - close_lag)
# Denominator
d <- abs(diff(close))
ds <- rollapply(d, n, sum)
return(mean(close_minus_close_lag / ds, na.rm = TRUE))
}universe <- c(
"IYY", "SPY", "QQQ", "IWM",
"FXI", "EWJ", "VNM", "INDA", "EWY", "EWT",
"EWQ", "EWI", "EWG", "EWU",
"ARGT", "EWW", "EWZ",
"ACWX", "EEM",
"ZT=F", "ZF=F", "ZN=F", "ZB=F",
"GC=F", "SI=F", "HG=F", "CL=F", "NG=F", "HO=F", "RB=F", "CT=F", "ZC=F", "ZS=F",
"ZL=F", "ZW=F", "SB=F",
"AUDUSD=X", "GBPUSD=X", "CADUSD=X", "EURUSD=X", "USDJPY=X", "CHFUSD=X", "NZDUSD=X", "DX=F"
)
asset_class <- c(
"Equity", "Equity", "Equity", "Equity",
"Equity", "Equity", "Equity", "Equity", "Equity", "Equity",
"Equity", "Equity", "Equity", "Equity",
"Equity", "Equity", "Equity",
"Equity", "Equity",
"Bonds", "Bonds", "Bonds", "Bonds",
"Commodities", "Commodities", "Commodities", "Commodities", "Commodities", "Commodities",
"Commodities", "Commodities", "Commodities", "Commodities",
"Commodities", "Commodities", "Commodities",
"Forex", "Forex", "Forex", "Forex", "Forex", "Forex", "Forex", "Forex"
)start_date <- "2025-01-01"
end_date <- "2025-03-31"
getSymbols(Symbols = universe,
src = "yahoo",
index.class = "POSIXct",
from = start_date,
to = end_date,
adjust = TRUE) [1] "IYY" "SPY" "QQQ" "IWM" "FXI" "EWJ"
[7] "VNM" "INDA" "EWY" "EWT" "EWQ" "EWI"
[13] "EWG" "EWU" "ARGT" "EWW" "EWZ" "ACWX"
[19] "EEM" "ZT=F" "ZF=F" "ZN=F" "ZB=F" "GC=F"
[25] "SI=F" "HG=F" "CL=F" "NG=F" "HO=F" "RB=F"
[31] "CT=F" "ZC=F" "ZS=F" "ZL=F" "ZW=F" "SB=F"
[37] "AUDUSD=X" "GBPUSD=X" "CADUSD=X" "EURUSD=X" "USDJPY=X" "CHFUSD=X"
[43] "NZDUSD=X" "DX=F" efficiency_ratios <- c()
for (symbol in universe) {
efficiency_ratios <- c(efficiency_ratios, efficiency_ratio(Cl(get(symbol)), n = 20))
}
result <- data.frame(
symbol = universe,
asset_class = asset_class,
efficiency_ratio = efficiency_ratios
)
ggplot(result, aes(x = reorder(symbol, -efficiency_ratio), y = efficiency_ratio, fill = asset_class)) +
geom_bar(stat = "identity") +
theme(axis.text.x=element_text(angle=45, hjust=1))
start_date <- "2024-03-01"
end_date <- "2025-03-31"
getSymbols(Symbols = universe,
src = "yahoo",
index.class = "POSIXct",
from = start_date,
to = end_date,
adjust = TRUE) [1] "IYY" "SPY" "QQQ" "IWM" "FXI" "EWJ"
[7] "VNM" "INDA" "EWY" "EWT" "EWQ" "EWI"
[13] "EWG" "EWU" "ARGT" "EWW" "EWZ" "ACWX"
[19] "EEM" "ZT=F" "ZF=F" "ZN=F" "ZB=F" "GC=F"
[25] "SI=F" "HG=F" "CL=F" "NG=F" "HO=F" "RB=F"
[31] "CT=F" "ZC=F" "ZS=F" "ZL=F" "ZW=F" "SB=F"
[37] "AUDUSD=X" "GBPUSD=X" "CADUSD=X" "EURUSD=X" "USDJPY=X" "CHFUSD=X"
[43] "NZDUSD=X" "DX=F" efficiency_ratios <- c()
for (symbol in universe) {
efficiency_ratios <- c(efficiency_ratios, efficiency_ratio(Cl(get(symbol)), n = 20))
}
result <- data.frame(
symbol = universe,
asset_class = asset_class,
efficiency_ratio = efficiency_ratios
)
ggplot(result, aes(x = reorder(symbol, -efficiency_ratio), y = efficiency_ratio, fill = asset_class)) +
geom_bar(stat = "identity") +
theme(axis.text.x=element_text(angle=45, hjust=1))
start_date <- "2019-01-01"
end_date <- "2024-12-31"
getSymbols(Symbols = universe,
src = "yahoo",
index.class = "POSIXct",
from = start_date,
to = end_date,
adjust = TRUE) [1] "IYY" "SPY" "QQQ" "IWM" "FXI" "EWJ"
[7] "VNM" "INDA" "EWY" "EWT" "EWQ" "EWI"
[13] "EWG" "EWU" "ARGT" "EWW" "EWZ" "ACWX"
[19] "EEM" "ZT=F" "ZF=F" "ZN=F" "ZB=F" "GC=F"
[25] "SI=F" "HG=F" "CL=F" "NG=F" "HO=F" "RB=F"
[31] "CT=F" "ZC=F" "ZS=F" "ZL=F" "ZW=F" "SB=F"
[37] "AUDUSD=X" "GBPUSD=X" "CADUSD=X" "EURUSD=X" "USDJPY=X" "CHFUSD=X"
[43] "NZDUSD=X" "DX=F" efficiency_ratios <- c()
for (symbol in universe) {
efficiency_ratios <- c(efficiency_ratios, efficiency_ratio(Cl(get(symbol)), n = 20))
}
result <- data.frame(
symbol = universe,
asset_class = asset_class,
efficiency_ratio = efficiency_ratios
)
ggplot(result, aes(x = reorder(symbol, -efficiency_ratio), y = efficiency_ratio, fill = asset_class)) +
geom_bar(stat = "identity") +
theme(axis.text.x=element_text(angle=45, hjust=1))
start_date <- "2014-01-01"
end_date <- "2024-12-31"
getSymbols(Symbols = universe,
src = "yahoo",
index.class = "POSIXct",
from = start_date,
to = end_date,
adjust = TRUE) [1] "IYY" "SPY" "QQQ" "IWM" "FXI" "EWJ"
[7] "VNM" "INDA" "EWY" "EWT" "EWQ" "EWI"
[13] "EWG" "EWU" "ARGT" "EWW" "EWZ" "ACWX"
[19] "EEM" "ZT=F" "ZF=F" "ZN=F" "ZB=F" "GC=F"
[25] "SI=F" "HG=F" "CL=F" "NG=F" "HO=F" "RB=F"
[31] "CT=F" "ZC=F" "ZS=F" "ZL=F" "ZW=F" "SB=F"
[37] "AUDUSD=X" "GBPUSD=X" "CADUSD=X" "EURUSD=X" "USDJPY=X" "CHFUSD=X"
[43] "NZDUSD=X" "DX=F" efficiency_ratios <- c()
for (symbol in universe) {
efficiency_ratios <- c(efficiency_ratios, efficiency_ratio(Cl(get(symbol)), n = 20))
}
result <- data.frame(
symbol = universe,
asset_class = asset_class,
efficiency_ratio = efficiency_ratios
)
ggplot(result, aes(x = reorder(symbol, -efficiency_ratio), y = efficiency_ratio, fill = asset_class)) +
geom_bar(stat = "identity") +
theme(axis.text.x=element_text(angle=45, hjust=1))
efficiency_ratios <- c()
for (symbol in universe) {
efficiency_ratios <- c(efficiency_ratios, efficiency_ratio(Cl(get(symbol)), n = 40))
}
result <- data.frame(
symbol = universe,
asset_class = asset_class,
efficiency_ratio = efficiency_ratios
)
ggplot(result, aes(x = reorder(symbol, -efficiency_ratio), y = efficiency_ratio, fill = asset_class)) +
geom_bar(stat = "identity") +
theme(axis.text.x=element_text(angle=45, hjust=1))
start_date <- "2004-01-01"
end_date <- "2024-12-31"
getSymbols(Symbols = universe,
src = "yahoo",
index.class = "POSIXct",
from = start_date,
to = end_date,
adjust = TRUE) [1] "IYY" "SPY" "QQQ" "IWM" "FXI" "EWJ"
[7] "VNM" "INDA" "EWY" "EWT" "EWQ" "EWI"
[13] "EWG" "EWU" "ARGT" "EWW" "EWZ" "ACWX"
[19] "EEM" "ZT=F" "ZF=F" "ZN=F" "ZB=F" "GC=F"
[25] "SI=F" "HG=F" "CL=F" "NG=F" "HO=F" "RB=F"
[31] "CT=F" "ZC=F" "ZS=F" "ZL=F" "ZW=F" "SB=F"
[37] "AUDUSD=X" "GBPUSD=X" "CADUSD=X" "EURUSD=X" "USDJPY=X" "CHFUSD=X"
[43] "NZDUSD=X" "DX=F" efficiency_ratios <- c()
for (symbol in universe) {
efficiency_ratios <- c(efficiency_ratios, efficiency_ratio(Cl(get(symbol)), n = 20))
}
result <- data.frame(
symbol = universe,
asset_class = asset_class,
efficiency_ratio = efficiency_ratios
)
ggplot(result, aes(x = reorder(symbol, -efficiency_ratio), y = efficiency_ratio, fill = asset_class)) +
geom_bar(stat = "identity") +
theme(axis.text.x=element_text(angle=45, hjust=1))
It is interesting to see that the findings is different from what Kraufman suggested in his book (p. 13). It could be due to the fact that the market is always changing.
In past 5 years, futures market are trending and linear, while emerging market and small-caps are choppy. It could be a good insights to design relevant trading strategies.