Original paper

SSRN-id1567012.pdf360.6KB

Abstract

We find that the positive relation between aggregate accruals and one-year-ahead market returns documented in Hirshleifer, Hou and Teoh [2009] is driven by discretionary accruals but not normal accruals. The return forecasting power of aggregate discretionary accruals is robust to choices of sample periods, return measurements, estimation methods, business condition and risk premium proxies, and accrual models used to isolate discretionary accruals. Our extensive analysis shows that aggregate discretionary accruals, in sharp contrast to aggregate normal accruals, contain little information about overall business conditions or aggregate cash flows and display little co-movement with ICAPM-motivated risk premium proxies. Our findings imply that aggregate discretionary accruals likely reflect aggregate fluctuations in earnings management, thereby favoring the behavioral explanation that managers time aggregate equity markets to report earnings.

Keywords: Aggregate Discretionary Accruals, Return Predictive Regressions, ICAPM-Motivated Risk Premium Proxies, Managerial Market Timing

Trading rules

Utilize the S&P 500 Index and three-month Treasury Bill yields as references for equity market returns and no-risk rates.
Annually ascertain accruals for all companies in the S&P 500 by the end of April, using: BS_ACC = (ΔCA – ΔCash) – (ΔCL – ΔSTD – ΔITP) – Dep

ΔCA: annual change in current assets
ΔCash: change in cash and cash equivalents
ΔCL: change in current liabilities
ΔSTD: change in debt included in current liabilities
ΔITP: change in income taxes payable
Dep: annual depreciation and amortization expense

Determine the value-weighted sum of accruals.
Figure out the term differential by gauging the difference between the 10-year Treasury Bond yield and the yield of a 1-month Treasury Bill.
Employ the consolidated accruals and the term difference in a regression analysis (with a data set spanning 15 years) to forecast next year’s mean and variance of excess stock market returns
Allocate capital to the equity market based on the predicted average-variance proportion of equity returns, and allocate any residual funds to Treasury Bills.
Maintain portfolio for twelve months and rebalance annually at the end of April

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):
    params = (
        ('rebalance_month', 4),
        ('lookback_years', 15)
    )

    def __init__(self):
        self.yearly_data = []

    def next(self):
        if self.data.datetime.date().month == self.params.rebalance_month and len(self.yearly_data) >= self.params.lookback_years:
            regression_data = pd.DataFrame(self.yearly_data)
            X = regression_data[['aggregate_accruals', 'term_spread']].values
            y = regression_data['excess_return'].values
            model = LinearRegression().fit(X, y)
            forecast = model.predict([self.aggregate_accruals, self.term_spread])
            mean_variance_ratio = forecast[0] / forecast[1]
            equity_weight = mean_variance_ratio / (1 + mean_variance_ratio)
            cash_weight = 1 - equity_weight
            self.order_target_percent(self.data0, equity_weight)
            self.order_target_percent(self.data1, cash_weight)
            self.yearly_data.pop(0)
        if self.data.datetime.date().month == self.params.rebalance_month:
            bs_acc = (self.delta_ca - self.delta_cash) - (self.delta_cl - self.delta_std - self.delta_itp) - self.dep
            aggregate_accruals = np.average(bs_acc, weights=self.data0.close)
            term_spread = self.data2.close[0] - self.data1.close[0]
            excess_return = self.data0.close[0] - self.data1.close[0]
            self.yearly_data.append({
                'aggregate_accruals': aggregate_accruals,
                'term_spread': term_spread,
                'excess_return': excess_return
            })
            self.delta_ca = 0
            self.delta_cash = 0
            self.delta_cl = 0
            self.delta_std = 0
            self.delta_itp = 0
            self.dep = 0

    def notify_fund(self, cash, value, fundvalue, shares):
        self.delta_ca += cash
        self.delta_cash += cash
        self.delta_cl += cash
        self.delta_std += cash
        self.delta_itp += cash
        self.dep += cash

cerebro = bt.Cerebro()
# Add S&P 500 index data
cerebro.adddata(data0)
# Add 3-month T-Bill yield data
cerebro.adddata(data1)
# Add 10-year Treasury Bond yield data
cerebro.adddata(data2)
cerebro.addstrategy(MarketTimingStrategy)
cerebro.run()

Please note that this code assumes that you have already prepared the S&P 500 index, 3-month T-Bill yield, and 10-year Treasury Bond yield data feeds (data0, data1, and data2). Also, the code does not handle the calculation of accruals for each company in the S&P 500, as that requires individual company data. You would need to preprocess the data to calculate the aggregate accruals before running the Backtrader strategy.

Predicting Stock Market Returns with Aggregate Discretionary Accruals

Original paper

Abstract

Trading rules

Python code

Backtrader