Original paper

SSRN-id3054017.pdf1324.4KB

Abstract

We show that returns to value strategies in individual equities, industries, commodities, currencies, global government bonds, and global stock indexes are predictable in the time series by their respective value spreads. In all these asset classes, expected value returns vary by at least as much as their unconditional level. A single common component of the value spreads captures about two-thirds of value return predictability and the remainder is asset-class-specifc. We argue that common variation in value premia is consistent with rationally time-varying expected returns, because (i) common value is closely associated with standard proxies for risk premia, such as the dividend yield, intermediary leverage and illiquidity, and (ii) value premia are globally high in bad times.

Keywords: Value Premium, Value Spread, Global Asset Pricing, Return Predictability, Alternative Assets, Common and Asset-Class-Specific Value

Trading rules

Set the investment scope to primarily include the largest stocks, making up 75% of the total market cap based on the CRSP data.
To gauge a firm's value, leverage industry-adjusted book-to-market metrics (represented as BM).
Monthly, organize stocks into value-weighted decile portfolios, based on their BM ranking.
Define the portfolio with the highest value as decile 10 and the one with the lowest value as decile 1.
Determine the value spread by evaluating the difference in the average value indicators between the high and low portfolios.
Construct a timing strategy for individual stock value by establishing a value spread that's standardized in the current month, using only past data.
Standardize the spread by dividing the difference of two accumulative values by the standard deviation of $VS_{1:t-12}$ .
Limit the standardized indicator to a range of ±2.
Check if the average value difference over the preceding year is historically significant.
Depending on the signal $VS_t$ , the linear timing strategy either goes long or short, and adjustments are made monthly.

Python code

Backtrader

import backtrader as bt
from scipy.stats import zscore

class LinearTimingStrategy(bt.Strategy):
    def __init__(self):
        self.inds = {}
        self.stocks = []
        total_market_cap = 0  # total market capitalization in the CRSP file
        # get the largest stocks whose market capitalizations cumulate to 75% of total market capitalization
        self.stocks = [s for s in self.datas if s.market_cap > 0]
        self.stocks.sort(key=lambda s: s.market_cap, reverse=True)
        for s in self.stocks:
            total_market_cap += s.market_cap
            if total_market_cap >= 0.75 * total_market_cap:
                break
        # use industry-adjusted book-to-market ratios to measure the value of each firm
        for s in self.stocks:
            bm = s.book_value / s.market_cap
            bm_ind_adj = bm / s.industry_bm
            self.inds[s] = {'bm_ind_adj': bm_ind_adj}
        self.add_timer(monthdays=[1,])  # rebalance monthly on first day of each month

    def next(self):
        # get the value signal of each stock
        value_signals = [self.inds[s]['bm_ind_adj'] for s in self.stocks]
        # form value-weighted decile portfolios each month by sorting on BM i,t,Ind.adj.
        deciles = {}
        for i in range(1, 11):
            decile_size = len(self.stocks) // 10
            decile = sorted(self.stocks, key=lambda s: self.inds[s]['bm_ind_adj'])[i*decile_size:(i+1)*decile_size]
            deciles[i] = decile
        # define the value and growth portfolios
        value_portfolio = deciles[10]
        growth_portfolio = deciles[1]
        # calculate value spread as the difference between the average value signal in the high and low portfolio
        value_spread = sum(self.inds[s]['bm_ind_adj'] for s in value_portfolio) / len(value_portfolio) - \
                       sum(self.inds[s]['bm_ind_adj'] for s in growth_portfolio) / len(growth_portfolio)
        # standardize the value spread using historical information
        value_spreads = [value_spread]
        for i in range(1, 12):
            prev_month_start = self.datetime.date().replace(month=self.datetime.date().month-i, day=1)
            prev_month_end = prev_month_start.replace(day=bt.num2date(bt.date2num(prev_month_start)).daysinmonth)
            prev_month_spread = (sum(self.inds[s]['bm_ind_adj'][prev_month_start:prev_month_end] for s in value_portfolio) / \
                                len(value_portfolio)) - \
                               (sum(self.inds[s]['bm_ind_adj'][prev_month_start:prev_month_end] for s in growth_portfolio) / \
                                len(growth_portfolio))
            value_spreads.append(prev_month_spread)
        std_signal = zscore(value_spreads)[-1]  # the standardized signal of the most recent month
        # cut off the standardized signal at ±2
        std_signal = max(-2, min(2, std_signal))
        # invest VSt,His dollars long or short accordingly to the signal and rebalance monthly
        for s in self.stocks:
            if self.inds[s]['bm_ind_adj'] > std_signal:
                self.order_target_percent(s, target=0.1)
            elif self.inds[s]['bm_ind_adj'] < std_signal:
                self.order_target_percent(s, target=-0.1)
            else:
                self.order_target_percent(s, target=0)  # do not hold the stock

Value Return Predictability Across Asset Classes and Commonalities in Risk Premia

Original paper

Abstract

Trading rules

Python code

Backtrader