Introduction to BRAIN

Introduction to Alphas #

For official materials, click here

Equity long-short market neutral strategy

Goal: minimize exposure to the market in general, and profit from a change in the spread between two stocks

1. Inside simulation #

Key settings: Delay, Decay

When you click “simulate”

Step 1: Evaluate the expression for each stock to generate the alpha vector for the given date.

Step 2: From each value in the vector, subtract the average of the vector values in the group. Sum of all vector values = 0. (Neutralization)

Step 3: The resulting values are scaled or ‘normalized’ such that the absolute sum of the alpha vector values is 1. These values can be called as normalized weights.

Step 4: Using normalized weights, the BRAIN simulator allocates capital (from a fictitious book of $20 million) to each stock to construct a portfolio.

Step 5: Calculate next day PnL based on observed stock returns the next day.

Step 6: Perform the operations in Step 1 to Step 5 for each date in a several-year history span also called the In-sample period (IS) to get daily PnL generated for each day.

Step 7: Calculate the cumulative PnL of the alpha from the start of the in-sample period to get the PnL chart of the alpha.

If Decay is used $$ \text{Decay_linear}(x,n)=\frac{x_t\times n+x_{t-1}\times (n-1)+\cdots+x_{t-n-1}}{n+(n-1)+\cdots+1} $$

2. Simulation results #

Most important: Information Ratio (IR) $$ IR=\frac{mean(returns)}{std(returns)} $$

Need to be high and consistent over years $$ Sharpe=IR\times \sqrt{252} $$ Turnover (tvr)

Represents the cost of trading $$ tvr=\frac{\text{Value traded}}{\text{Value held}} $$ The lower the turnover the better (< 40%)

Usually delay-0 alphas have higher turnover

3. OS test #

Base tests

  • Check weight: ensures diversify

  • Subuniverse value

    • Definition: the Sharpe in the next smallest standard universe (e.g. the subuniverse of Sector is Industry)

    • Pass when greater than

      • Delay 1 $$ \sqrt{252}\times \max(0.065, 0.15\times \frac{S_{sub}}{S_{max}}) $$

      • Delay 0 $$ \sqrt{252}\times \max(0.065, 0.25\times \frac{S_{sub}}{S_{max}}) $$

      Where $S_{sub}$ is the sub-universe size, $S_{max}$ is the largest universe size

    • Tips: Always check in the next smallest universe first

  • Superuniverse value

    • Definition: … next largest …

    • Pass when greater than

    $$ 0.7\times \text{Sharpe of alpha} $$

  • Ranked sharpe

    • Definition: Sharpe of the alpha after applying the Rank and Power operators (exp=3) to each side of the alpha, each side is then rescaled to its original size

    • Example, $$ \alpha_t=[0.3,-0.1,0.2,0.5]\xrightarrow{Rank}[3,1,2,4]\xrightarrow{Power}[3^3, 1^3, 2^3, 4^3]=\alpha_t' $$

      $$ \xrightarrow{rescale}\alpha_t’’=\mu_t+\frac{\alpha_t’-\mu_t’}{\sigma_t’}\cdot \sigma_t $$

    • Pass if

      • Sharpe is positive
      • Meet one of the following
        • Ratio of ranked Sharpe to original $\geqslant 0.5$
        • Rank Sharpe $> 0.15$

  • Bias test

    • Definition: Detect any forward bias
    • [di-delay] in python code is required

  • Correlation test

    Pass if one of the following criteria is met

    • PnL correlation with any external WebSim alpha is $< 0.7$
    • Alpha’s PnL, positions or trade correlation with any external WebSim alpha in the same group is $<0.4$
    • Alpha has 10% higher Sharpe than any alpha in the same group with PnL, positions or trade correlation above the 0.7 threshold

  • ISSharpe

    • Definition: filters random noise from true alpha
    • aim for consistent performance across years and maximize sharpe

Performance tests

  • OSSharpe
    • Separates random noise from true alpha, alpha must meet the Sharpe requirement for different intervals to pass this test
  • New high test
    • Reaches a new high in cumulative PnL

Basic Operators #

For official materials, click here

Step sum & IndNeutralize

group_neutralize(volume / (ts_sum(volume, 60) / 60), sector)

ts_sum(vector, n): n < 512

group_neutralize(alpha x, specified grouping)

Improvement:

ts_step(20) * volume / (ts_sum(volume, 60) / 60)

Weight 20 on current, 19 on yesterday, and so on. This prevent sudden changes.

Product rank & Signed power operators

- (today's price - yesterday's price)

Rank(- (close - Ts_Product(close, 5))^(0.2))

SignedPower(x, e): $\text{Sign}(x)\times |x|^e$

Correlation & Rank operator

- ts_corr(rank(close), rank(volume / adv20), 5)

ts_corr(x, y, n): correlation of x and y for past n days

  1. If the close price and volume ratio have increased more than the other stocks in the universe, the correlation will be positive. (Market hasn’t absorbed the price information)
  2. If the close price and volume ratio have fallen more than the other stocks in the universe, the correlation will be positive. (Market hasn’t absorbed the price information)
  3. If the close price has increased and the volume ratio has fallen as compared to other stocks in the universe, the price trend will likely continue. (Market react intensively)
  4. If the close price has fallen and the volume ratio has increased as compared to other stocks in the universe, the price trend will likely revert. (Market react intensively)

Scale & GroupMean operators

Scale: to combine two ideas

scale(X): make the sum of vector X to be 1

Neutralize: $x-\text{mean}(x)$