Original paper

SSRN-id2577963.pdf111.0KB

Abstract

Traditional capital structure theory predicts that reducing banks’ leverage reduces the risk and cost of equity but does not change the weighted average cost of capital, and thus the rates for borrowers. We confirm that the equity of better-capitalized banks has lower beta and idiosyncratic risk. However, over the last 40 years, lower risk banks have not had lower costs of equity (lower stock returns), consistent with a stock market anomaly previously documented in other samples. A calibration suggests that a binding ten percentage-point increase in Tier 1 capital to risk-weighted assets could double banks’ risk premia over Treasury bills.

Keywords: Bank, Banks, Banking, Regulation, Capital, Requirements, Leverage, Tier 1, Capitalization, Anomaly, Risk

Trading rules

Use the CRSP database for choosing stocks.
Calculate the 12-month moving beta for each stock compared to the MSCI US Equity Index.
Arrange stocks from lowest to highest based on their calculated beta.
Classify stocks into either low beta or high beta groupings.
Distribute stock weights in accordance to their beta rankings.
Adjust the portfolio compositions every month.
Normalize both portfolios to maintain a beta value of one at their inception.
Construct a cost-neutral, beta-neutral Betting-Against-Beta strategy: taking a long position in low-beta and a short position in high-beta.
Consider simple modifications (e.g., long bottom beta decile, short top beta decile) to enhance performance.

Python code

Backtrader

Here’s a Backtrader Python code implementing the trading rules you described:

import backtrader as bt
import backtrader.feeds as btfeeds
import pandas as pd

class BetaRanking(bt.Strategy):
    params = (
        ('lookback', 252),
        ('rebalance_freq', 21),
        ('num_long', 10),
        ('num_short', 10)
    )

    def __init__(self):
        self.betas = {}
        self.rankings = []
        self.rebalance_day = 0
        # Compute beta for each stock
        for d in self.datas:
            self.betas[d._name] = bt.indicators.Beta(d, self.data0, period=self.params.lookback)

    def next(self):
        self.rebalance_day += 1
        if self.rebalance_day % self.params.rebalance_freq != 0:
            return
        self.rankings = sorted(
            self.datas,
            key=lambda d: self.betas[d._name][0]
        )
        longs = self.rankings[:self.params.num_long]
        shorts = self.rankings[-self.params.num_short:]
        for d in longs:
            self.order_target_percent(d, target=1.0 / self.params.num_long)
        for d in shorts:
            self.order_target_percent(d, target=-1.0 / self.params.num_short)
        for d in self.datas:
            if d not in longs and d not in shorts:
                self.order_target_percent(d, target=0.0)

if __name__ == '__main__':
    cerebro = bt.Cerebro()
    # Add strategy
    cerebro.addstrategy(BetaRanking)
    # Load CRSP database
    # Replace this part with your actual CRSP data
    for stock_data in CRSP_data:
        data = btfeeds.PandasData(dataname=stock_data)
        cerebro.adddata(data)
    # Load MSCI US Equity Index data
    msci_data = btfeeds.PandasData(dataname=pd.read_csv('msci_us_equity_index.csv', parse_dates=['date'], index_col='date'))
    cerebro.adddata(msci_data, name='msci_us_equity_index')
    # Set initial capital and run
    cerebro.broker.setcash(100000.0)
    cerebro.run()

This code implements a Backtrader strategy that calculates rolling betas for each stock relative to the MSCI US Equity Index, ranks stocks based on their betas, and rebalances the portfolio monthly. Remember to replace the data loading part with your actual CRSP data and the MSCI US Equity Index data in a suitable format.

Do Strict Capital Requirements Raise the Cost of Capital? Bank Regulation, Capital Structure, and the Low Risk Anomaly

Original paper

Abstract

Trading rules

Python code

Backtrader