Background: Alpha and Beta

In quantitative investing, Alpha (α) represents "excess returns" and Beta (β) represents "market benchmark returns." Understanding the relationship between these two is core to building hedging strategies and risk management.

1. Core Concept Definitions

1.1 Beta (β): Systematic Risk and Returns

Beta measures the volatility sensitivity of a portfolio relative to the market (benchmark). It reflects the portion of profit you receive from "market appreciation" and also reflects the structural risk you bear.

Formula: $\beta_i = \frac{\mathrm{Cov}(r_i, r_m)}{\mathrm{Var}(r_m)}$
- $r_i$ : Asset return
- $r_m$ : Market benchmark return
Benchmark values:
- β = 1: Moves with the market (e.g., S&P 500 index fund)
- β > 1: Aggressive (typically growth stocks, tech stocks)
- β < 1: Defensive (typically utilities, consumer staples)
- β < 0: Negative correlation (rare, e.g., inverse leveraged ETFs)
- β ≈ 0: Market Neutral, returns don't fluctuate with the market.

1.2 Alpha (α): Excess Returns

Alpha is the pure profit after risk adjustment (excluding Beta's influence). It's viewed as the investment manager's "skill" or the model's "secret sauce."

Modern definition: Returns that cannot be explained by known factors (such as market cap, value, momentum).
Current state: As market efficiency improves, traditional Alpha is gradually decaying (Alpha Decay) and evolving into benchmark returns.

2. CAPM Model and Formula

The classic Capital Asset Pricing Model (CAPM) reveals the composition of returns:

E(R_i) = R_f + \beta_i (E(R_m) - R_f) + \alpha_i

$R_f$ : Risk-free rate
$E(R_m) - R_f$ : Market risk premium
Essence of Alpha: The difference between actual return and CAPM-predicted return.

3. Evolution: From Alpha to Smart Beta

Modern quantitative investing further decomposes returns:

Traditional Beta: Pure market movement.
Smart Beta (Factor Returns): Between α and β. Returns obtained through systematic exposure to certain factors (e.g., Size, Value, Momentum).
Pure Alpha: True excess skill (e.g., high-frequency arbitrage, alternative data mining, AI deep pattern recognition).

Dimension	Beta (β)	Smart Beta	Alpha (α)
Source of Returns	Overall market performance	Factor exposure	Unique information/algorithms
Cost	Very low (index funds)	Relatively low	High (hedge funds)
Scalability	Very high	High	Limited
Transparency	Fully transparent	Rules are transparent	Black box/non-public

4. US vs China Market Differences

Characteristic	A-Share (China) Market	US Stock Market
Alpha Environment	Alpha-rich. Many retail investors, inefficient pricing.	Beta-driven. High institutionalization, Alpha hard to find.
Difficulty	Higher but relatively stable (high volatility).	Extremely high (highly efficient market).
Neutral Strategies	Effective but limited by hedging instrument costs.	Extremely rich tools, excellent liquidity.

5. Python Implementation: Calculating Alpha and Beta

Using statsmodels for linear regression:

import numpy as np
import pandas as pd
import statsmodels.api as sm

def calculate_alpha_beta(portfolio_returns, market_returns, rf_rate=0.02/252):
    """
    Calculate daily Alpha and Beta
    """
    # 1. Calculate excess returns
    y = portfolio_returns - rf_rate
    x = market_returns - rf_rate

    # 2. Linear regression: y = alpha + beta * x
    x = sm.add_constant(x)
    model = sm.OLS(y, x).fit()

    alpha = model.params[0]
    beta = model.params[1]

    return alpha, beta

# Example usage
# alpha_daily, beta = calculate_alpha_beta(returns_df['strategy'], returns_df['benchmark'])
# print("Daily Alpha:", alpha_daily, "Beta:", beta)

6. What Top Quantitative Funds Pursue

Renaissance (Medallion Fund): Famous for low Beta, extremely high Alpha. Their logic is to find "statistical arbitrage" opportunities that don't move with the market.
Market Neutral Strategies: By going long an Alpha portfolio while shorting a corresponding amount of index futures (Beta approaches zero), stable profits can be achieved regardless of whether the market goes up or down.

Summary: For retail investors, focus on long-term growth from Beta; for quantitative researchers, the core task is mining Alpha signals with predictive power from raw data.