Get Rich Bot Problem¶
You've developed an algorithmic stock trading bot to strike it rich 
, but you want to backtest it before
putting it into production. You have price data on 10 stocks, each tracked at 8 regular time intervals.
import numpy as np
rng = np.random.default_rng(1234)
prices = [rng.normal(rng.lognormal(3, 1), size=8).round(2) for i in range(10)]
prices = np.vstack(prices)
print(prices) # (1)!
# [[ 4.1 4.78 4.19 4.9 6.95 2.56 4.99 2.37]
# [ 27.81 29.65 27.46 28.84 27.06 26.17 28.76 30.06]
# [ 32.79 34.06 34.56 34.98 32.63 34.49 34.14 33.76]
# [ 19.67 19.73 21.68 20.61 19.87 17.86 19.48 19.85]
# [ 4.24 6.39 5.32 3.87 4.23 5.27 6.68 4.06]
# [ 98.02 96.79 99.02 99.94 98.28 99.15 98.19 98.49]
# [107.11 105.01 109.01 105.19 107.06 106.71 106.13 106.41]
# [ 17.89 16.34 15.88 17.53 18.79 16.91 18.75 16.96]
# [ 96.28 95.84 96.26 94.48 95.42 93.75 93.54 96.24]
# [ 18.31 17.43 16.53 20.2 18.68 17.48 17.33 18.96]]
- Element (i,j) represents the price of stock i at time j.
For each stock, your algorithm suggests the best time to buy the stock and the best time to sell the stock.
trade_idxs = [np.sort(rng.choice(8, size=2, replace=False)) for i in range(10)]
trade_idxs = np.vstack(trade_idxs)
print(trade_idxs) # (1)!
# [[0 1]
# [3 6]
# [2 4]
# [1 5]
# [0 3]
# [2 7]
# [2 3]
# [1 3]
# [3 6]
# [1 4]]
- Element (i,0) represents the time to buy stock i. Element (i,1) represents the time to sell stock i.
trade_idxs identifies the index of the buy price and sell price for each stock. So, the holding periods look like this.
| trade_idxs | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|:-----------|------:|------:|------:|-------:|------:|------:|------:|------:|
| [0 1] | 4.1 | 4.78 | ----- | ----- | ----- | ----- | ----- | ----- |
| [3 6] | ----- | ----- | ----- | 28.84 | 27.06 | 26.17 | 28.76 | ----- |
| [2 4] | ----- | ----- | 34.56 | 34.98 | 32.63 | ----- | ----- | ----- |
| [1 5] | ----- | 19.73 | 21.68 | 20.61 | 19.87 | 17.86 | ----- | ----- |
| [0 3] | 4.24 | 6.39 | 5.32 | 3.87 | ----- | ----- | ----- | ----- |
| [2 7] | ----- | ----- | 99.02 | 99.94 | 98.28 | 99.15 | 98.19 | 98.49 |
| [2 3] | ----- | ----- | 09.01 | 105.19 | ----- | ----- | ----- | ----- |
| [1 3] | ----- | 16.34 | 15.88 | 17.53 | ----- | ----- | ----- | ----- |
| [3 6] | ----- | ----- | ----- | 94.48 | 95.42 | 93.75 | 93.54 | ----- |
| [1 4] | ----- | 17.43 | 16.53 | 20.2 | 18.68 | ----- | ----- | ----- |
Given prices and trade_idxs, calculate the average price of each holding period.