Strategy lab / 151 Trading Strategies

Strategy lab

Every strategy from 151 Trading Strategies and all 101 Formulaic Alphas as formulas you can edit and backtest on ten years of daily stocks, ETFs, futures, forex and crypto data. Free, in your browser.

Options58

Stocks21

Exchange-traded funds8

Fixed income15

Indexes5

Volatility7

Foreign exchange6

Commodities6

Futures7

Structured assets6

Convertibles2

Tax arbitrage3

Miscellaneous assets4

Distressed assets7

Real estate8

Cash5

Cryptocurrencies2

Global macro4

Infrastructure1

3.18StocksBacktest

Statistical arbitrage – optimisation

Turn expected returns into holdings by maximising the Sharpe ratio subject to dollar neutrality. With a diagonal covariance matrix this reduces to weights proportional to expected return over variance.

In the paper

w = \frac{1}{λ} [C^{- 1} E - \frac{ν ^{T} C ^{- 1} E}{ν ^{T} C ^{- 1} ν} C^{- 1} ν], ν = (1, \dots, 1)

Note. Uses a diagonal covariance matrix; a full risk model would also neutralise correlated exposures.

Formula

Edit anything; the result updates as you type. Lines like window = 20 become sliders.

…lose / delay(close, 5…d / stddev(returns, 60…ddev(returns, 60) ^ 2

Market

AssetsLoading…

Period

PortfolioDemean the signal each day and scale so longs and shorts each total 50%.RebalanceCosts0 bpSector-neutral

Loading market data and running the strategy…

Hypothetical backtests on daily closes with no slippage unless you add costs. Survivorship bias applies: the stock list is today’s large caps. For learning, not investment advice. Data: Yahoo Finance via yfinance.

Source: 151 Trading Strategies
Section: 3.18 · Stocks
Asset class: Stocks
In the lab: Full backtest

Statistical arbitrage – optimisation (3.18)

Key equation

w = \frac{1}{λ} [C^{- 1} E - \frac{ν ^{T} C ^{- 1} E}{ν ^{T} C ^{- 1} ν} C^{- 1} ν], ν = (1, \dots, 1)

Lab formula

// Expected returns from sector mean reversion, scaled by 1 / variance
expected = -indneutralize(log(close / delay(close, 5)), IndClass.sector)
expected / stddev(returns, 60) ^ 2

Uses a diagonal covariance matrix; a full risk model would also neutralise correlated exposures.

How the backtest works

The formula is evaluated for every asset on every day. Its values become positions at that day’s close, using the portfolio rule you pick, and earn the next day’s close-to-close return. Costs are charged in basis points on the amount traded. Everything runs in your browser on daily data from Yahoo Finance, adjusted for splits and dividends.

More in Stocks

Source: Kakushadze, Z. and Serur, J. A. (2018). 151 Trading Strategies. Palgrave Macmillan. SSRN 3247865. Summaries are our own.