Single Period Optimization (SPO)

What We Need

In order to backtest a portfolio using SPO, we'll need:

• Forecast stock returns over the time periods we wish to backtest: forecast_returns
• Actual stock returns over the time periods we wish to backtest: actual_returns
• Start and end dates: start_date and end_date

For TradingCost, we'll need:

• Actual stock prices over the time periods we want to backtest: actual_prices
• Forecast volume (perhaps an average of the last year for each asset, for simplicity) over the time periods we want to backtest: forecast_volume
• Forecast standard deviation in returns (perhaps the standard deviation of the last year for each asset, for simplicity) over the time periods we want to backtest: forecast_std_dev
• Forecast (half) trading spreads for each asset (we are using 2.5bps for all assets for simplicity in this example) over the time periods we want to backtest: half_spread

For ShortHoldingCost: we'll need:

• Forecast short borrowing rates for each asset (we are using 40bps for all assets for simplicity in this example) over the time periods we want to backtest: short_rates

In order to make this example as easy as possible, we've prepared, and will use, actual returns and prices and forecast returns, volumes, standard deviations, spreads, and short rates from 2017 - 2018 for a universe of 319 stocks.

Sample Code For a SPO Backtest

Set up modules and load data:

import pandas as pd
import investos as inv
from investos.portfolio.cost_model import *
from investos.portfolio.constraint_model import *

actual_returns = pd.read_parquet("https://investos.io/example_actual_returns.parquet")
forecast_returns = pd.read_parquet("https://investos.io/example_forecast_returns.parquet")

# For trading costs:
actual_prices = pd.read_parquet("https://investos.io/example_spo_actual_prices.parquet")
forecast_volume = pd.Series(
    pd.read_csv("https://investos.io/example_spo_forecast_volume.csv", index_col="asset")
    .squeeze(),
    name="forecast_volume"
)
forecast_std_dev = pd.Series(
    pd.read_csv("https://investos.io/example_spo_forecast_std_dev.csv", index_col="asset")
    .squeeze(),
    name="forecast_std_dev"
)
half_spread_percent = 2.5 / 10_000 # 2.5 bps
half_spread = pd.Series(index=forecast_returns.columns, data=half_spread_percent)

# For short holding costs:
short_cost_percent = 40 / 10_000 # 40 bps
trading_days_per_year = 252
short_rates = pd.Series(index=forecast_returns.columns, data=short_cost_percent/trading_days_per_year)

Run SPO:

strategy = inv.portfolio.strategy.SPO(
    actual_returns = actual_returns,
    forecast_returns = forecast_returns,
    costs = [
        ShortHoldingCost(short_rates=short_rates, exclude_assets=["cash"]),
        TradingCost(
            actual_prices=actual_prices,
            forecast_volume=forecast_volume,
            forecast_std_dev=forecast_std_dev,
            half_spread=half_spread,
            exclude_assets=["cash"],
        ),
    ],
    constraints = [
        MaxShortLeverageConstraint(limit=0.3),
        MaxLongLeverageConstraint(limit=1.3),
        MinWeightConstraint(limit=-0.03),
        MaxWeightConstraint(limit=0.03),
        LongCashConstraint(),
        MaxAbsTurnoverConstraint(limit=0.05),
    ],
    cash_column_name="cash"
)

portfolio = inv.portfolio.BacktestController(
    strategy=strategy,
    start_date='2017-01-01',
    end_date='2018-01-01',
    hooks = {
        "after_trades": [
            lambda backtest, t, u, h_next: print(".", end=''),
        ]
    }
)

backtest_result = portfolio.generate_positions()
backtest_result.summary

When backtest_result.summary is executed, it will output summary backtest results:

# Initial timestamp                         2017-01-03 00:00:00
# Final timestamp                           2017-12-29 00:00:00
# Total portfolio return (%)                               5.6%
# Annualized portfolio return (%)                         5.68%
# Annualized excess portfolio return (%)                  2.61%
# Annualized excess risk (%)                              2.47%
# Information ratio (x)                                   1.06x
# Annualized risk over risk-free (%)                      2.47%
# Sharpe ratio (x)                                        1.05x
# Max drawdown (%)                                        1.05%
# Annual turnover (x)                                    12.88x
# Portfolio hit rate (%)                                  60.0%

What a difference trading costs make vs our previous RankLongShort example!

If you have a charting library installed, like matplotlib, check out BaseResult for the many backtest_result metrics you can plot!

Next: Reporting

Next, let's explore the backtest performance reporting available to you through backtest_result (an instance of BaseResult): Analyzing Backtest Results.