Factor Validation

Check whether RSI or anything similar has predictive power by building zero investment portfolio

In quantitative finance, testing whether an technical indicator like RSI (Relative Strength Index) carries predictive power is done by constructing a Zero-Investment (Long-Short) Portfolio or calculating the Information Coefficient (IC) between the factor value at time t and future stock returns at time t+1.

Here is how the quantitative methodology works in practice:

1. Rank & Segment: At the end of each period (e.g., monthly/daily), calculate the 14-day RSI for all stocks in the universe (Nifty 50).

2. Form Portfolios: * Mean-Reversion Thesis: Go Long oversold stocks (lowest RSI) and Short overbought stocks (highest RSI).

   • Momentum Thesis: Go Long high-RSI stocks and Short low-RSI stocks.

3. Measure Performance: The return of the Long-Short portfolio is the Factor Premium. If the average premium over time is significantly positive (t-statistic > 2.0), the factor has predictive power.

Python Code Implementation (Pandas + yfinance)

Below is a complete, working script that downloads data for Nifty 50 stocks, computes 14-day RSI, forms a monthly Long-Short (Zero-Investment) Factor Portfolio, and evaluates its statistical significance.

Python

import numpy as np
import pandas as pd
import yfinance as yf

# 1. Define Nifty 50 Tickers (Yahoo Finance format: '.NS')
nifty50_tickers = [
    "RELIANCE.NS",
    "TCS.NS",
    "HDFCBANK.NS",
    "ICICIBANK.NS",
    "INFY.NS",
    "BHARTIARTL.NS",
    "ITC.NS",
    "SBIN.NS",
    "LTIM.NS",
    "LT.NS",
    "HINDUNILVR.NS",
    "AXISBANK.NS",
    "KOTAKBANK.NS",
    "M&M.NS",
    "TATAMOTORS.NS",
    "NTPC.NS",
    "MARUTI.NS",
    "POWERGRID.NS",
    "SUNPHARMA.NS",
    "TITAN.NS",
    "ULTRACEMCO.NS",
    "BAJFINANCE.NS",
    "ADANIENT.NS",
    "TATASTEEL.NS",
    "JSWSTEEL.NS",
    "GRASIM.NS",
    "ASIANPAINT.NS",
    "COALINDIA.NS",
    "NESTLEIND.NS",
    "TECHM.NS",
    "HCLTECH.NS",
    "HDFCLIFE.NS",
    "WIPRO.NS",
    "SBILIFE.NS",
    "DRREDDY.NS",
    "BAJAJFINSV.NS",
    "TATACONSUM.NS",
    "DIVISLAB.NS",
    "EICHERMOT.NS",
    "CIPLA.NS",
    "BPCL.NS",
    "HEROMOTOCO.NS",
    "APOLLOHOSP.NS",
    "INDUSINDBK.NS",
    "BEL.NS",
    "TRENT.NS",
    "BAJAJ-AUTO.NS",
    "SHRIRAMFIN.NS",
    "ONGC.NS",
    "ADANIPORTS.NS",
]


# 2. Function to Calculate 14-Day RSI
def compute_rsi(prices, window=14):
    delta = prices.diff()
    gain = (delta.where(delta > 0, 0)).rolling(window=window).mean()
    loss = (-delta.where(delta < 0, 0)).rolling(window=window).mean()
    rs = gain / loss
    return 100 - (100 / (1 + rs))


# 3. Download Historical Daily Price Data
print("Downloading stock data...")
data = yf.download(nifty50_tickers, start="2018-01-01", end="2024-01-01")[
    "Adj Close"
]

# 4. Calculate RSI for all stocks
rsi_df = data.apply(compute_rsi)

# 5. Resample to Monthly Frequency (End of Month)
# Factor Signal (RSI) measured at Month End
monthly_rsi = rsi_df.resample("ME").last()

# Calculate Forward 1-Month Return for each stock
monthly_prices = data.resample("ME").last()
forward_returns = monthly_prices.pct_change().shift(-1)  # Return of NEXT month

# 6. Backtest Long-Short Zero-Investment Factor Portfolio
long_returns = []
short_returns = []
factor_premiums = []
dates = []

# Loop over each month (excluding last row due to look-ahead shift)
for date in monthly_rsi.index[:-1]:
    rsi_signal = monthly_rsi.loc[date].dropna()
    fwd_ret = forward_returns.loc[date].dropna()

    # Get common stocks present in both signal and return
    common_stocks = rsi_signal.index.intersection(fwd_ret.index)

    if len(common_stocks) < 10:
        continue

    sig = rsi_signal[common_stocks]
    ret = fwd_ret[common_stocks]

    # Mean-Reversion Strategy:
    # Long Quintile 1 (Lowest RSI = Oversold)
    # Short Quintile 5 (Highest RSI = Overbought)
    q1_threshold = sig.quantile(0.20)
    q5_threshold = sig.quantile(0.80)

    long_basket = ret[sig <= q1_threshold]
    short_basket = ret[sig >= q5_threshold]

    long_ret = long_basket.mean()
    short_ret = short_basket.mean()

    # Zero-Investment Factor Return (Long - Short)
    f_rsi = long_ret - short_ret

    dates.append(date)
    long_returns.append(long_ret)
    short_returns.append(short_ret)
    factor_premiums.append(f_rsi)

# 7. Evaluate Predictive Power & Statistical Significance
results = pd.DataFrame(
    {
        "Long_Return": long_returns,
        "Short_Return": short_returns,
        "RSI_Factor_Premium": factor_premiums,
    },
    index=dates,
)

avg_premium = results["RSI_Factor_Premium"].mean()
std_premium = results["RSI_Factor_Premium"].std()
t_stat = (avg_premium / std_premium) * np.sqrt(len(results))
annualized_return = avg_premium * 12
annualized_vol = std_premium * np.sqrt(12)
sharpe_ratio = (
    annualized_return / annualized_vol if annualized_vol != 0 else np.nan
)

print("\n--- RSI FACTOR VALIDATION RESULTS ---")
print(
    f"Average Monthly Factor Premium (Long-Short): {avg_premium:.4%} per month"
)
print(f"Annualized Premium: {annualized_return:.2%}")
print(f"t-Statistic: {t_stat:.2f}")
print(f"Sharpe Ratio: {sharpe_ratio:.2f}")

if t_stat > 2.0:
    print(
        "\nConclusion: RSI has STATISTICALLY SIGNIFICANT PREDICTIVE POWER at the 95% confidence level."
    )
elif t_stat < -2.0:
    print(
        "\nConclusion: Reverse-RSI (Momentum) has STATISTICALLY SIGNIFICANT PREDICTIVE POWER."
    )
else:
    print(
        "\nConclusion: RSI does NOT show statistically significant predictive power (t-stat between -2 and +2)."
    )

Key Takeaways from this Validation Test

1. t-Statistic Rule of Thumb: * A t-statistic > |2.0| indicates that the RSI factor premium is statistically different from zero (not random luck).

2. Information Coefficient (IC): * You can also measure predictive power using Spearman rank correlation between RSI at t and returns at t+1:

   $\text{IC}_t = \text{Corr}\big(\text{Rank}(\text{RSI}_t), \text{Rank}(\text{Return}_{t+1})\big)$

   IC at time t is the correlation between:

   the rank of RSI at time t, and the rank of next period’s return (time t+1). In simple words: it checks whether stocks with higher RSI today tend to have higher (or lower) returns in the next period.

   • An average IC > 0.05 is considered a good predictive factor in quantitative equity management.

3. Common Pitfalls to Avoid:

• Look-ahead Bias: Always ensure factor inputs (RSI at month-end) use price data up to month-end, and returns are evaluated for the subsequent period (t+1).

• Transaction Costs & Slippage: A zero-investment portfolio requires rebalancing, which incurs brokerage costs and impact cost, especially in shorting.