Indicators

This page introduces the functions that calculate technical indicators. Unless stated otherwise, they calculate the indicator for the current date of the global date pointer, from the trading price (the closing price by default).

The examples ran on the bundled sample dataset with the date pointer at 1990-02-19, except the second parabolic-SAR call and the ATR and keltner-channel examples, which ran on 1990-02-20, and the MACD examples, which show their own steps.

Which Indicator Does What

Indicator	Kind	What it tells you	Typical use
moving-avg	Trend	The average price over the last n days	Crossovers such as the Golden Cross
moving-sd	Volatility	How much the price varied over the last n days	Bollinger Bands
EMA	Trend	An average that weights recent days more	Faster trend signals
MACD	Trend	The gap between a short and a long EMA, and its signal line	Buy when MACD crosses above its signal line
parabolic-SAR	Trend	A stop level that trails the price and flips with the trend	Trailing stops
ROC	Momentum	The percentage change over n days	Buy strength, sell weakness
RSI	Momentum	Recent gains against recent losses, from 0 to 100	Below 30 oversold, above 70 overbought
ATR	Volatility	The average daily trading range	Sizing positions and stops
keltner-channel	Volatility	Bands two ATRs around the EMA	Breakouts

Good to know: every indicator returns nil until there is enough history, and works on the raw trading price, so a stock split looks like a sudden drop. EMA, MACD and RSI keep their own state and update it every trading day once you have called them; parabolic-SAR and ATR instead take yesterday's value as an argument.

Trend Indicators

moving-avg

Calculate the simple moving average of a security over the last n trading days, including today.

Argument	Type	Function	Remarks
permno	String	The target security
n	Positive Integer > 1	Length of the moving window including today

Return

A number, or nil unless the security has a price on all n days.

Example

=> (moving-avg "10001" 10)
48.217

moving-sd

Calculate the moving (sample) standard deviation of a security's price over the last n trading days, including today. Together with moving-avg it gives Bollinger Bands; see the bollinger_bands.clj worksheet.

Argument	Type	Function	Remarks
permno	String	The target security
n	Positive Integer > 1	Length of the moving window including today

Return

A number, or nil unless the security has a price on all n days.

Example

=> (moving-sd "10001" 10)
0.5631666420045367

EMA

Calculate the exponential moving average of a security. The first call returns the EMA-CYCLE-day moving average. After that, the backtester updates the EMA every trading day according to its definition, as long as the run continues. This update is automatic. On a day without a price, it keeps its last value.

Argument	Type	Function	Remarks
permno	String	The target security

Relevant Parameter

EMA-CYCLE: the cycle of the EMA (20 by default).

Return

A number, or nil if the first moving average cannot be computed yet.

Example

=> (EMA "10001")
48.4835

EMA-generator

Create an EMA function for another cycle.

Argument	Type	Function	Remarks
cycle	Positive Int	The cycle of the EMA

Return

An EMA function with the same usage as EMA, using the given cycle.

Example

=> (def EMA10 (EMA-generator 10))
=> (EMA10 "10001")
48.217
=> (def EMA20 (EMA-generator 20))
=> (= (EMA20 "10001") (EMA "10001"))
true

MACD

Calculate the moving average convergence / divergence of a security. After the first call, it is updated automatically every trading day, even while it still returns nil.

Argument	Type	Function	Remarks
permno	String	The target security

Relevant Parameters

MACD-SIGNAL: the cycle of the signal line (9 by default)

MACD-SHORT: the cycle of the short EMA (12 by default)

MACD-LONG: the cycle of the long EMA (26 by default)

Return

A vector [MACD, signal, short EMA, long EMA]. The short and long EMAs are of the security's price, MACD = short EMA − long EMA, and the signal line is the MACD-SIGNAL-day EMA of MACD, seeded with the mean of its first MACD-SIGNAL values.

nil until the signal line has been seeded. With the default cycles, that takes 26 closes for the long EMA and then 9 MACD values from the days it has been tracked; so call MACD once early in the run, as below, to get the first value on the 34th close.

Example

=> (init-portfolio "1990-01-02" 10000)
=> (MACD "10001") ;; not enough prices yet, but now tracked every day
nil
=> (while (< (compare (get-date) "1990-02-28") 0) (next-date))
=> (MACD "10001")
[-0.4655478988484276 -0.6167045545421674 48.08274496033748 48.548292859185906]

MACD-generator

Create a MACD function for other cycles.

Argument	Type	Function	Remarks
signal-cycle	Positive Int	The EMA cycle of the signal line
short-cycle	Positive Int	The EMA cycle of the short line
long-cycle	Positive Int	The EMA cycle of the long line

Return

A MACD function with the same usage as MACD, using the given cycles. Generators with the same cycles return the same function.

Example

=> (init-portfolio "1990-01-02" 10000)
=> (def MACD51020 (MACD-generator 5 10 20))
=> (MACD51020 "10001")
nil
=> (while (< (compare (get-date) "1990-02-28") 0) (next-date))
=> (MACD51020 "10001")
[-0.23347193957126677 -0.31630965090941965 48.056297547397676 48.28976948696894]

parabolic-SAR

Calculate Wilder's parabolic stop and reverse (SAR), one trading day per call. Pass the result of the previous day's call back in on the next trading day.

Needs the daily low and high columns :BIDLO and :ASKHI in the dataset.

Argument	Type	Function	Remarks
permno	String	The target security
state	Map / nil	The map returned by the previous day's call	nil on the first day: the trend is then read from today's price against the previous one.

Relevant Parameters

SAR-AF-STEP: the starting acceleration factor and its increment (0.02 by default)

SAR-AF-MAX: the cap of the acceleration factor (0.2 by default)

Return

A map {:sar :trend :ep :af}: the stop level, the trend (:up or :down), the extreme point of the current trend, and the acceleration factor, which grows by SAR-AF-STEP on every new extreme.

Example

=> (def sar (parabolic-SAR "10001" nil))
=> sar
{:sar 49.79, :trend :down, :ep 47.32, :af 0.02}

=> (next-date)
=> (parabolic-SAR "10001" sar)
{:sar 49.7406, :trend :down, :ep 47.2, :af 0.04}

Momentum Indicators

ROC

Calculate the rate of change of a security's price over the last n trading days.

Argument	Type	Function	Remarks
permno	String	The target security
n	Positive Integer	The time window

Return

The rate of change as a decimal (today's price / the price n trading days ago − 1), or nil if there are fewer than n earlier days or either price is missing.

Example

=> (ROC "10001" 10)
-0.014546965918536903

RSI

Calculate the Relative Strength Index of a security over RSI-CYCLE days. The first call seeds it with the simple average gain and loss; after that it is updated every trading day with Wilder's smoothing. This update is automatic. Through days without a price it keeps its last value, and the change across the gap counts as one day's change.

Argument	Type	Function	Remarks
permno	String	The target security

Relevant Parameter

RSI-CYCLE: 14 by default.

Return

A number between 0 and 100, or nil unless the security has a price on all of the first RSI-CYCLE days.

Example

=> (RSI "10001")
45.56962025316458

RSI-generator

Create an RSI function for another cycle.

Argument	Type	Function	Remarks
cycle	Positive Int	The time window

Return

An RSI function with the same usage as RSI, using the given cycle.

Example

=> (def RSI10 (RSI-generator 10))
=> (RSI10 "10001")
36.27992633517498
=> (def RSI14 (RSI-generator 14))
=> (= (RSI14 "10001") (RSI "10001"))
true

Volatility Indicators

ATR

Calculate the average true range of a security, Wilder-smoothed from the previous value: (previous ATR × (n − 1) + today's true range) / n. The true range is the largest of high − low, |high − previous close| and |low − previous close|.

Needs the daily low and high columns :BIDLO and :ASKHI in the dataset.

Argument	Type	Function	Remarks
permno	String	The target security
n	Positive Integer	The smoothing window
prev-atr	Number	The previous day's ATR	On the first day, seed it with, e.g., today's high − low.

Return

A number.

Example

=> (ATR "10001" 14 0.5)
0.5114285714285712

;; carry the ATR from day to day
(def atr (atom (- (get-permno-by-key "10001" :ASKHI)
                  (get-permno-by-key "10001" :BIDLO))))
;; then, on each trading day:
(swap! atr #(ATR "10001" 14 %))

keltner-channel

Calculate the Keltner Channel of a security: the EMA as the middle line, with bands two ATRs above and below it.

Argument	Type	Function	Remarks
permno	String	The target security
window	Positive Integer	The ATR smoothing window
prev-atr	Number	The previous day's ATR	As for ATR

Return

A vector [middle upper lower].

Example

=> (keltner-channel "10001" 14 0.5114285714285712)
[48.38030952380952 49.42439115646258 47.33622789115646]