Original paper

SSRN-id3076181.pdf2595.9KB

Abstract

We define “deep value” as episodes where the valuation spread between cheap and expensive securities is wide relative to its history. Examining deep value across global individual equities, equity index futures, currencies, and global bonds provides new evidence on competing theories for the value premium.

Following these episodes, the value strategy has:

(1) high average returns;

(2) low market betas, but high betas to a global value factor;

(3) deteriorating fundamentals;

(4) negative news sentiment;

(5) selling pressure;

(6) increased limits to arbitrage; and

(7) increased arbitrage activity.

Lastly, we find that deep value episodes tend to cluster and a deep value trading strategy generates excess returns not explained by traditional risk factors.

Keywords: value investing, market efficiency, bubbles, behavioral finance, over-reaction, demand pressure, arbitrage, noise

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

Deep Value

Original paper

Abstract

Trading rules

Python code

Backtrader