Andrea Frazzini and Lasse Pedersen and others in the last decade have offered an approach to asset pricing that builds on the possibility of limits on leverage (Frazzini and Pedersen, 2014; Asness, Frazzini, and Pedersen, 2012). They show that limits to leverage flatten the capital markets line. More important, as a test of theory against reality, this line of thinking is consistent with investment performance across a broad set of markets.
Frazzini and Pedersen argue that limits to true leverage force investors to find other less efficient ways to take on the higher risk often associated with higher returns. Constrained investors buy assets with a high beta to the overall market—assets with returns likely to move up or down more than the market basket. Instead of moving out along the capital markets line to create the most efficient risk and return, constrained investors move out along Markowitz's efficient frontier.
The tendency for constrained investors to overinvest in high beta assets raises the price for these assets and lowers their expected return. Underinvestment in low beta assets lowers their price and raises their expected return. This distortion, Frazzini and Pedersen argue, leads to the flat capital markets line—stronger returns in lower risk assets, weaker returns in higher risk assets.
To test their theory, Frazzini and Pedersen build a series of portfolios that buy assets with a low beta and sell short assets with a higher beta.1 The portfolios balance their holdings so if markets go up or down, portfolio value should hold steady. Betting-against-beta becomes less about taking market risk and more about buying undervalued assets and selling overvalued assets. If constrained investors shape asset performance by underinvesting in low beta and overinvesting in high beta assets, Frazzini and Pedersen's betting-against-beta portfolios will produce excess returns that get stronger as limits to leverage become more binding. There is an exception to the rule, however. If limits to leverage become so binding that every investor becomes constrained, then leveraged investors get forced to deleverage and betting-against-beta unravels.
Frazzini and Pedersen first show that splitting up assets into portfolios with low beta and high beta produces the predicted result: as portfolio beta runs from low to high, portfolio alpha steadily declines. The list of markets where this pattern holds is impressive: US equities, international equities, Treasury debt, corporate debt, commodities, foreign exchange, indexes for equities, corporate debt, and credit default swaps.
Frazzini and Pedersen then build betting-against-beta portfolios in each market starting with US equities. Using returns from January 1926 to March 2012, their analysis shows that betting-against-beta delivers average monthly excess returns of 0.70%. They further test their strategy by comparing it to the performance of the US equity market basket and find that average excess return rises to 0.73%. They compare it to the performance of a portfolio built on the factors that Fama and French highlight—the market, company size, and book value—and still find excess return of 0.73%. And when they add strategies built on momentum and liquidity, excess return drops to 0.55% but still stands well above the returns predicted by CAPM.
In international equities, betting-against-beta adds average monthly excess return of 0.64%, beats the international equity market basket by 0.64%, exceeds returns on the Fama and French factors by 0.65%, and outperforms more elaborate models by 0.28% to 0.30%. The results suggest limits to leverage in equity markets worldwide.
The US Treasury market might seem to offer the most efficient pricing in the world because of its relatively simple cash flows, the general uniformity of the debt, average daily trading of hundreds of billions of dollars, a global audience of investors, and ready financing, but predictions made by betting-against-beta show up in Treasury debt, too. Investors targeting a particular yield may find it easier to buy 10-year or longer debt than to buy one-year or shorter debt and leverage their position. In Treasury debt, measuring asset beta against a market index is equivalent to measuring asset maturity or duration, a measure of interest rate sensitivity. Building portfolios of low and high beta debt still shows alphas that decline steadily with portfolio beta. Sharpe ratios decline steadily from short- to long-maturity bonds. And betting-against-beta from 1952 to 2012 delivers average monthly excess returns of 0.17%.
In markets for corporate bonds, in credit default swaps, and across indexes for equity, the bonds of different countries, foreign exchange, and commodities, betting-against-beta has delivered excess return. Limits to leverage seem to shape returns across a broad range of assets.
Finally, Frazzini and Pedersen look for evidence of limits to leverage in the investment portfolios of a sample of individuals, mutual funds, private equity funds, and in the portfolio of Berkshire Hathaway, the company famously run by investor Warren Buffett (Frazzini, Kabiller, and Pedersen, 2018). Individuals face clear regulatory limits to borrowing against stocks, and the Investment Company Act of 1940, which sets the guidelines for mutual funds, sets clear limits to leverage, too. Mutual funds also often have to hold cash to pay out investors redeeming their shares, which also limits their leverage. Private equity funds, however, often issue debt in the capital markets to buy target companies, and Berkshire Hathaway, which operates as an insurance company, borrows by taking in insurance premiums from its clients. Betting-against-beta predicts individuals and mutual funds would hold high beta portfolios, and private equity and insurers would hold low beta portfolios. Frazzini and Pedersen, in fact, find that individuals and mutual funds from 1980 to 2012 held stock portfolios with betas significantly higher than the market basket beta of 1.0, and private equity and Berkshire Hathaway held portfolios with betas significantly lower than 1.0.
More Betting-Against-Beta
J. Benson Durham at the Federal Reserve Bank of New York noticed Frazzini and Pedersen's surprising results with betting-against-beta in the US Treasury market and decided to repeat the test and extend the analysis to 10 other global government bond markets (Durham, 2015). In the US Treasury market, widely assumed to be one of the most efficient in the world, Durham found betting-against-beta from 1962 through 2013 delivered better returns—more return for each measure of risk—than either the overall Treasury market itself or even the overall US equity markets. He tried the same test in the government bond markets for Germany, France, the Netherlands, Belgium, Italy, Spain, Japan, the UK, Canada, and Switzerland. Betting-against-beta only delivered better returns than the overall bond market in Italy, but it beat the equity markets in all countries. The results for government bonds beyond the US Treasury market could reflect a relatively smaller proportion of investors who are limited by leverage in those markets. In the US, a larger share of investment coming from individuals, mutual funds, and foreign portfolios averse to leverage may explain the good results from betting-against-beta in the US Treasury market.
A Natural Experiment
Finally, the market over time has run through a natural experiment that puts Frazzini and Pedersen's thinking to the test, thanks to the Federal Reserve. The Securities Exchange Act of 1934 gives the Fed the right under Regulation T to set a minimum amount of equity, or margin, and, consequently, the maximum amount of debt an individual can use to buy common stock on credit on a US exchange. From October 1934 to January 1974, the Fed changed the minimum margin requirement 22 times, allowing it to range from 40% of the market value of stock purchased to 100%. Each change in required margin shifted the limits on leverage across the entire US stock market. Each change put Frazzini and Pedersen to the test.
In Espoo, Finland, on the Baltic Sea, Petri Jylhä, a professor at the Aalto University School of Business, noticed the Fed's natural experiment as a way to test Frazzini and Pedersen. As the Fed's margin requirement moved higher, Jylhä recognized, the capital market line should get progressively flatter. If that happened, it would give further support to the case for betting-against-beta.
Jylhä started by showing that the Fed typically changed margin requirements in response to a surge or drop in credit, raising margin requirements
