One of the most important issues in finance concerns the relationship between risk and expected return. John Lintner, William Sharpe and Jack Treynor are generally given most of the credit for introducing the first formal asset pricing model, the capital asset pricing model (CAPM), which was developed in the early 1960s. The CAPM provided the first precise definition of risk and how it drives expected returns.
The CAPM looks at risk and return through a “one-factor” lens, meaning the risk and the return of a portfolio are determined only by its exposure to market beta. Market beta is the measure of the equity-type risk of a stock, mutual fund or portfolio relative to the risk of the overall market. The CAPM was the financial world’s operating model for about 30 years.
However, like all models, it was by definition flawed or wrong, explaining only about two-thirds of the differences in returns of diversified portfolios. If such models were perfectly correct, they would be laws, like we have in physics.
More Than Beta
In their 1992 paper, “The Cross-Section of Expected Stock Returns,” Eugene Fama and Kenneth French proposed that, along with the market factor of beta, exposure to the risk factors of size and value explain the cross section of expected stock returns. The Fama-French model greatly improved upon the explanatory power of the CAPM, accounting for more than 90% of the differences in returns between diversified portfolios.
The three-factor model became the new powerhouse working model in finance. Later, the Carhart momentum factor was added, and we had a four-factor model. Today there’s a factor model battle going on, with a few additional factors competing for inclusion. Among these other factors are investment, profitability and quality.
The bottom line is that beta is only one measure of risk, and there are many others currently being “thrown around,” such as the higher moments of volatility (skewness, kurtosis and downside volatility).
Does Beta Make Sense As A Risk Measure?
With this in mind, Javier Estrada and Maria Vargas, authors of a November 2015 paper, “Black Swans, Beta, Risk, and Return,” sought to answer the question of whether beta is a good measure (if not the only one) of risk.
Their hypothesis was that, while markets are more complex than indicated by the CAPM, it “seems highly unlikely that expected returns are unrelated to the risks of doing badly in bad times.” Clearly, an asset that performs badly in bad times is a risky asset. Thus, investors should demand (expect) a risk premium as compensation.
To test their hypothesis, Estrada and Vargas explored whether high-beta portfolios of countries and industries fall more than low-beta portfolios when negative “black swans” hit the market. They defined a black swan as a month where the market rose or fell by at least 5%.
Five percent might seem like a low hurdle to define a black swan. However, you want to make sure you have enough data. If the authors had defined blacks swans as monthly returns in the world market of at least 10%, they would have had only 15 events (eight negative and seven positive) between January 1973 and December 2009 relevant for countries, and only six events (four negative and two positive) between January 1998 and December 2009 relevant for industries.
The authors also sought to answer the question of whether beta is a valuable tool for portfolio selection. In pursuit of an answer, Estrada and Vargas explored if a strategy that reacts to positive and negative black swans by investing in portfolios selected on the basis of beta would outperform a passive investment in a world market portfolio.
Their study covered the period 1970 through 2009 and included 47 countries (23 developed and 24 emerging) and 57 industries. The benchmark passive index was the MSCI World (equity) Market Index. Due to the availability of data, between January 1970 and December 1987, Estrada and Vargas used a world market portfolio consisting only of developed markets. From January 1988 through December 2009, they used a world market portfolio consisting of developed as well as emerging markets.
The authors tested an investable strategy that reacts to negative black swans by investing in high-beta portfolios (based on country and industry indexes) and to positive black swans by investing in low-beta portfolios.