Anomalies in Investment Management: Quality, Low Beta, and Buffett's Alpha

Introduction

• The lecture will cover anomalies related to the CAPM (Capital Asset Pricing Model).
• CAPM was the main explanation for differences in expected returns across assets for a long time.
• Anomalies are deviations from what CAPM predicts.
• Size, value, and momentum are well-known factors/anomalies.
• The lecture focuses on:
  • Quality: Investing in profitable and growing companies.
  • Betting-against-beta (BAB): Investing in safe assets.
• These factors will be used to analyze Warren Buffet’s performance.

Quality Investing (QMJ)

• CAPM World: Portfolio choice would be a mix of cash and the market portfolio.
• Multi-Factor World: Portfolio design involves deciding between "bargains" (cheap companies) and high-quality firms.
• Warren Buffett's perspective: "It’s far better to buy a wonderful company at a fair price than a fair company at a wonderful price."
• Measuring Company Quality: Measured using profitability, growth, and safety.
• Profitability: Profits per unit of book value.
• Growth: Five-year growth of the profitability measure.
• Safety: Market beta or fundamental risk.

Measuring Profitability

• Focus on the permanent component of profitability.
• Uses an average of different profitability measures to reduce noise:
  • Gross profits over assets.
  • Return on assets.
  • Return on equity.
  • Cash flows over assets.
  • Gross margin.
• Formula: $Profitability = \frac{1}{5}(zGPOA + zROA + zROE + zCFOA + zGMAR)$, where $zX$ is the z-score of measure $X$.

Measuring Growth and Safety

• Growth is measured using a 5-year window focusing on changes in profitability measures:
  • Formula: $Growth = \frac{1}{5}(z\Delta GPOA + z\Delta ROE + z\Delta CFOA + z\Delta GMAR)$, where $\Delta X$ represents the five-year difference of measure $X$.
• Safety is measured using market and fundamental variables:
  • Low beta (BAB).
  • Low leverage (LEV).
  • Low ROE volatility (EVOL).
  • Formula: $Safety = \frac{1}{3}(zBAB + zLEV + zEVOL)$

Measuring Overall Quality

• Quality is measured as follows: $Quality = z(Profitability + Growth + Safety)$, where $z(X)$ is the z-score of measure $X$.
• The following cross-sectional regression can be run to test if higher quality implies higher value:
  • $log \, MB<em>{i,t} = a + b \, Quality</em>{i,t} + controls + \epsilon_{i,t}$

Empirical Evidence of Quality on Prices/Returns

• High-quality firms have high prices.
• Construct portfolios sorted on quality to test the effect on alpha.
• If prices fully reflect differences in quality, there should be no effect on alpha.
• The 4-factor Fama-French-Carhart model is used: $r<em>t = \alpha + \beta</em>{MKT} \, MKT<em>t + \beta</em>{SMB} \, SMB<em>t + \beta</em>{HML} \, HML<em>t + \beta</em>{UMD} \, UMD<em>t + \epsilon</em>t$
• High-quality firms tend to have high returns.

Quality-Minus-Junk (QMJ) Factor

• QMJ factor has a positive alpha.
• Constructed as the intersection of six value-weighted portfolios formed on size and quality.
• Stocks are assigned to two size-sorted portfolios based on market capitalization at the end of each calendar month:
  • U.S. securities: the median NYSE market equity.
  • Other markets: the 80th percentile by country.
• Conditional sorts are used, first sorting on size, then on quality.
• Portfolios are value-weighted, refreshed, and rebalanced every calendar month.

Why Does Quality Affect Returns?

• Theory suggests quality should affect prices rather than returns because expected returns should depend only on a company’s risk.
• News about quality should immediately affect prices.
• If prices do not incorporate news about quality right away, it would predict returns, which would be a failure of market efficiency.

Betting Against Beta (BAB)

• Empirically, the Security Market Line (SML) is too flat.
  • Low-beta stocks have positive alpha.
  • High-beta stocks have negative alpha.
• Fisher Black explained this based on borrowing constraints:
  • Low risk aversion investors want a portfolio with high beta but may be leverage constrained.
  • Leverage-constrained investors bid up the price of high-beta stocks, leading to a negative alpha.
  • Low-beta stocks will have lower prices and positive alpha.

Betting Against Beta Strategy

• Construct a trading strategy by going long on low-beta stocks and short on high-beta stocks.
• Buying and selling in the same proportion creates a portfolio with positive alpha but negative beta.
• To fix this, the portfolio is rescaled to have zero beta:
  • $rBAB<em>{t+1} = \frac{1}{\beta</em>L t} (r<em>L t+1 − r</em>f) − \frac{1}{\beta<em>H t} (r</em>H t+1 − r<em>f)$, where \betaL t < \beta_H t.
• Works well in practice by computing market betas, constructing low/high-beta portfolios, and longing low-beta while shorting high-beta.
• Notion of “market portfolio” may be asset-specific when extending beyond stocks.
• The table shows beta-sorted calendar-time portfolio returns in US equities from 1926-2012.
• Stocks are ranked in ascending order based on their estimated beta at the end of the previous month and assigned to decile portfolios based on NYSE breakpoints.
• BAB factor: stocks are assigned to low-beta and high-beta portfolios and weighted by the ranked betas, then rescaled to have a beta of one at portfolio formation.

Application of BAB on Bonds

• BAB strategy can also apply to bonds.
• The BAB Sharpe ratio varies by asset class. Construct the BAB factor, securities are assigned to one of two portfolios: low beta and high beta. Securities are weighted by the ranked betas and the portfolios are rebalanced every calendar month. Both portfolios are rescaled to have a beta of one at portfolio formation. The BAB factor is a self-financing portfolio that is long the low-beta portfolio and shorts the high-beta portfolio. Sharpe ratios are annualized.

Warren Buffett's Performance

• Standard formulation of the Efficient Market Hypothesis (EMH) implies no one can beat the market (alphas equal zero).
• Michael Jensen suggested Warren Buffet might be luck.
• Buffet responded that many winners come from the same "intellectual village" - Graham-and-Doddsville.
• Average excess return of 19% in 35 years compared to market 6.1%.
  • A dollar invested in 1976 would have been worth $1500 35 years later.
  • Volatility was also higher: 25% compared to market volatility of 15%.
  • Buffet had a better Sharpe ratio: 0.76 compared to the market’s 0.4.
  • Berkshire Hathaway had a beta of only 0.7.
• Berkshire's Information Ratio is greater than both that of other common stocks and mutual funds.

Buffett's Leverage

• $L<em>t = \frac{TotalAssetsMarketValue</em>t − CashMarketValue<em>t}{EquityMarketValue</em>t}$
• Frazzini et al (2013) estimates Berkshire leverage as 1.6:1.
• Buffet was able to secure a reliable source of funds.
  • Berkshire issued the first-ever negative-coupon security in 2002.
  • Utilized insurance companies and derivatives.

Buffett's Investment Style

• Return of his private and public holdings (before leverage) is about 10-12%.
  • Factor regression: $r<em>{t} − r</em>{f,t} = \alpha + \beta<em>1 MKT</em>t + \beta<em>2 SMB</em>t + \beta<em>3 HML</em>t + \beta<em>4 UMD</em>t + \beta<em>5 BAB</em>t + \beta<em>6 QMJ</em>t + \epsilon_t$
• Berkshire demonstrates the exposure to quality companies owning stocks (1976-2011).
• Buffett on quality: “Whether we’re talking about socks or stocks, I like buying quality merchandise when it is marked down.”
• “Ben Graham taught me 45 years ago that in investing it is not necessary to do extraordinary things to get extraordinary results.”