Original paper

SSRN-id869447.pdf299.4KB

Abstract

Guo and Savickas [2005] show that aggregate stock market volatility and average idiosyncratic stock volatility jointly forecast stock returns. In this paper, we quantify the economic significance of their results from the perspective of a portfolio manager. That is, we evaluate the performance, e.g., the Sharpe ratio and Jensen's alpha, of a mean-variance manager who tries to time the market based on those variables. We find that, over the period 1968-2004, the associated market-timing strategy outperforms the buy-and-hold strategy, and the difference is statistically and economically significant.

Keywords: Stock return predictability, Market timing, Stock market volatility, Idiosyncratic volatility

Trading rules

Measure the market's volatility from the preceding quarter by using squared daily excess stock market returns.
Ascertain individual stock variance for each company in the S&P 500 by employing a regression that utilizes Fama and French factors (like Market, Size, and Book-to-Market ratios).
Weight and sum residuals from regression based on each stock’s market cap to obtain summary idiosyncratic variance.
Forecast the next quarter's stock market excess return using a regression that incorporates both market volatility and the summarized idiosyncratic variance as independent variables.
Set equity weight in the portfolio based on expected excess stock market return, expected stock market variance, and investor’s risk aversion coefficient.
Adjust the portfolio composition every three months.

Python code

Backtrader

import backtrader as bt
import numpy as np
import pandas as pd
from sklearn.linear_model import LinearRegression

class MarketTimingStrategy(bt.Strategy):
    def __init__(self):
        self.quarterly_timer = 0

    def next(self):
        self.quarterly_timer += 1
        if self.quarterly_timer % 63 == 0:  # Rebalance every quarter (approx. 63 trading days)
            market_returns = self.data.close.pct_change()
            excess_market_returns = market_returns - self.data.close.get(size=252).mean()
            # Calculate market variance for the previous quarter
            market_variance = np.square(excess_market_returns[-63:]).sum() / 63
            # Determine idiosyncratic variance for each stock in the S&P 500
            idiosyncratic_variances = []
            market_caps = []
            for stock_data in self.datas:
                stock_returns = stock_data.close.pct_change()
                excess_stock_returns = stock_returns - stock_data.close.get(size=252).mean()
                # Fama-French factors
                market_factor = excess_stock_returns - excess_market_returns
                size_factor = stock_data.size
                book_to_market_factor = stock_data.book_to_market
                X = np.column_stack((market_factor, size_factor, book_to_market_factor))
                y = excess_stock_returns
                # Regression analysis
                model = LinearRegression()
                model.fit(X, y)
                residuals = y - model.predict(X)
                idiosyncratic_variance = np.square(residuals).sum() / len(residuals)
                idiosyncratic_variances.append(idiosyncratic_variance)
                market_caps.append(stock_data.market_cap)
            # Weight and sum residuals
            weights = np.array(market_caps) / sum(market_caps)
            summary_idiosyncratic_variance = np.dot(weights, idiosyncratic_variances)
            # Estimate expected excess stock market return for the upcoming quarter
            X = np.column_stack((market_variance, summary_idiosyncratic_variance))
            y = excess_market_returns
            model = LinearRegression()
            model.fit(X, y)
            expected_excess_return = model.predict(X)
            # Set equity weight in the portfolio
            risk_aversion_coefficient = 1  # Modify as needed
            equity_weight = expected_excess_return / (risk_aversion_coefficient * market_variance)
            # Rebalance portfolio
            for i, stock_data in enumerate(self.datas):
                self.order_target_percent(stock_data, target=equity_weight[i])

cerebro = bt.Cerebro()
# Add data feeds for S&P 500 stocks here
cerebro.addstrategy(MarketTimingStrategy)
results = cerebro.run()

Market Timing with Aggregate and Idiosyncratic Stock Volatilities

Original paper

Abstract

Trading rules

Python code

Backtrader