Example: Bollinger Bands

This walkthrough follows the worksheet bollinger_bands.clj. It runs on the bundled sample dataset; open it in Gorilla REPL with make start (see Get Started), or paste the code into lein repl.

You will use: moving-avg, moving-sd, order with :remaining, and the evaluation report.

The idea

Bollinger Bands draw an envelope around the price:

• Middle band: the 20-day simple moving average (SMA) of the closing price.
• Upper band: the SMA plus 2 standard deviations of the price over the same 20 days.
• Lower band: the SMA minus 2 standard deviations.

The bands widen when the price is volatile and narrow when it is calm. A mean-reversion trader reads a close below the lower band as "oversold", likely to bounce back, and a close above the upper band as "overbought". The strategy here:

• Buy 10 shares whenever the price closes below the lower band.
• Sell the whole position whenever the price closes above the upper band.

It trades AAA (10001) and CCC (10003). The bands need 20 closes, so nothing happens before 1990-01-29, the 20th trading day. CCC's five days without prices in February mean its bands are missing for a while after them, too.

Setup

(load-dataset "resources/sample-data/main" "main" add-aprc)
(init-portfolio "1990-01-02" 10000)

The dataset is already furnished by add-aprc. No more modification is needed.
"Date range: 1990-01-02 ~ 1990-03-30"
"Date: 1990-01-02 Cash: $10000"

The strategy

bollinger-bands handles one security on the current day. moving-avg and moving-sd return nil until 20 prices are available, and when with and skips those days.

(defn bollinger-bands [permno]
  (let [price (get-permno-price permno)
        sma   (moving-avg permno 20)
        sd20  (moving-sd permno 20)]
    (when (and price sma sd20)
      (let [upper (+ sma (* 2 sd20))
            lower (- sma (* 2 sd20))]
        (when (< price lower)
          (order permno 10))                   ; buy 10 more shares
        (when (> price upper)
          (order permno 0 :remaining true))))))  ; sell everything

The main loop runs it for both securities each day, records the metrics and moves the clock. On 1990-03-29, the last full day of the sample, end-order sells what is left.

(while (< (compare (get-date) "1990-03-29") 0)
  (bollinger-bands "10001")
  (bollinger-bands "10003")
  (update-eval-report)
  (next-date))
(end-order)

What happened

Six closes crossed a band. These are the values on those days:

Day	Security	Close	Lower band	Upper band	Signal	What the order did
1990-01-30	AAA	47.77	48.06	52.29	Buy	Bought 10 on 1990-01-31 at 48.05
1990-03-19	AAA	45.67	46.15	49.53	Buy	Bought 10 on 1990-03-20 at 44.69
1990-03-20	AAA	44.69	45.51	49.90	Buy	Bought 10 on 1990-03-21 at 44.85
1990-03-20	CCC	19.24	18.04	19.23	Sell	Nothing: no CCC held
1990-03-21	AAA	44.85	45.03	49.98	Buy	Bought 10 on 1990-03-22 at 44.91
1990-03-21	CCC	19.82	17.90	19.45	Sell	Nothing: no CCC held

Each order fills at the close of the trading day after its signal. CCC's two sell signals do nothing, because "sell down to 0 shares" (:remaining true) on a position of 0 shares has nothing to trade. AAA never closed above its upper band, so its position was only sold by end-order:

(print-order-record)

|      :date | :permno | :price | :aprc | :quantity |
|------------+---------+--------+-------+-----------|
| 1990-01-31 |   10001 |  48.05 | 48.05 |      10.0 |
| 1990-03-20 |   10001 |  44.69 | 45.15 |      10.0 |
| 1990-03-21 |   10001 |  44.85 | 45.31 |      10.0 |
| 1990-03-22 |   10001 |  44.91 | 45.37 |      10.0 |
| 1990-03-29 |   10001 |  43.87 | 44.32 |  -40.1025 |

The last sale is 40.1025 shares, not 40. AAA paid a dividend on 1990-02-15 and dividends are reinvested by default, so the first 10 shares grew to 10.1025. The adjusted price (:aprc) is above the raw price after that date for the same reason (see Prices: raw and adjusted).

(print-portfolio)

| :asset | :price | :aprc | :quantity | :tot-val |
|--------+--------+-------+-----------+----------|
|   cash |    N/A |   N/A |       N/A |  9934.30 |

Evaluation report

The report starts on 1990-01-31, the day of the first fill. Its first ten rows:

(print-eval-report 10)

|      :date | :tot-value |    :vol |  :r-vol | :sharpe | :r-sharpe | :pnl-pt | :max-drawdown |
|------------+------------+---------+---------+---------+-----------+---------+---------------|
| 1990-01-31 |     $10000 | 0.0000% | 0.0000% |  0.0000 |    0.0000 |      $0 |       0.0000% |
| 1990-02-01 |      $9996 | 0.0083% | 0.0083% | -3.3101 |   -3.3101 |     $-4 |       0.0400% |
| 1990-02-02 |      $9995 | 0.0082% | 0.0082% | -3.3240 |   -3.3240 |     $-4 |       0.0410% |
| 1990-02-05 |     $10000 | 0.0128% | 0.0128% |  0.3485 |    0.3485 |      $0 |       0.0410% |
| 1990-02-06 |     $10008 | 0.0199% | 0.0199% |  2.6432 |    2.6432 |      $8 |       0.0410% |
| 1990-02-07 |     $10000 | 0.0258% | 0.0258% |  0.0228 |    0.0228 |      $0 |       0.0849% |
| 1990-02-08 |      $9994 | 0.0275% | 0.0275% | -1.1350 |   -1.1350 |     $-5 |       0.1409% |
| 1990-02-09 |     $10002 | 0.0309% | 0.0309% |  0.4252 |    0.4252 |      $2 |       0.1409% |
| 1990-02-12 |      $9998 | 0.0313% | 0.0313% | -0.2709 |   -0.2709 |     $-1 |       0.1409% |
| 1990-02-13 |      $9999 | 0.0308% | 0.0313% | -0.0665 |   -0.0675 |      $0 |       0.1409% |

With only $480 invested in February, the daily changes are tiny compared with the $10,000 portfolio, so the volatility is a few hundredths of a percent.

Takeaways

• The strategy ended with $9,934.30, a loss of $65.70. AAA kept falling through March, and buying each dip below the lower band added to a losing position. Mean reversion assumes the price comes back; in a steady downtrend it does not.
• Signals can repeat on consecutive days. Here, three days in a row below the band bought 30 shares. To buy once per dip, check whether you already hold the security, for example with (get-in @portfolio ["10001" :quantity]).
• Try it: change the 2 standard deviations to 1.5, or trade BBB (10002) instead, and compare the evaluation reports. Remember that BBB's split on 1990-03-01 halves its raw price, which the bands will see as a crash.