Low risk

Investors are assumed to be risk averse in nature, meaning that they seek to minimize the risk they have to endure in order to obtain certain expected return. Variance is a measurement of stock risk. Markowitz (1952) concludes expected return being desirable thing whereas variance undesirable thing in investing. This composition led to Modern Portfolio Theory (MPT) according to which investors maximize the expected returns at a given level of market risk, therefore enabling investor to form so-called “efficient frontier” of possible allocation choices of the portfolio. With this in mind, there has been some anomalous returns generated with low risk stocks that violate the basic assumptions of MPT. The total risk of specific stock can be decomposed into systematic or market risk and idiosyncratic risk or firm-specific risk. Previous researches have proven that by allocating capital into low risk stocks, measured either by beta coefficient or variance of returns, an investor could have earned abnormal risk-adjusted returns.

Beta coefficient (b) of CAPM is a firm specific coefficient of risk, which measures a company’s exposure to market risk.

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Black, Jensen and Scholes (1972) found out that the expected linear relationship between stock returns and beta of CAPM was inconsistent. They noticed that excess return of a stock did not always implicitly result in equally high beta coefficient, thus security market line appeared to be too flat compared to one implied by the CAPM. The time-series regression results they obtained between 1947 and 1965 indicated that high beta securities had significantly negative intercepts whereas low-beta securities had significantly positive intercepts, meaning that low-beta stocks had outperformed high-beta stocks.

Blitz and Vliet (2007) examined low-volatility anomaly among large cap stocks between 1986 and 2006 in U.S, Japan and Germany. The results showed that stocks with low volatility generate higher risk-adjusted returns. The difference in average returns between top and bottom decile portfolios, thus extreme high volatility and extreme low volatility, was 5.9% annually. Another compelling fact was that the annual alpha spread of global low and high volatility portfolios was 12%. Moreover, the Sharpe ratios and Fama-French alphas seemed to steadily decline in volatility. The authors also found that low risk portfolio has a low beta of 0.56 with a positive annualized alpha of 4%. Furthermore, betas increased monotonically for the consecutive decile portfolios. This indicated that beta and volatility are related risk measures, thus beta coefficient obviously negatively related with future stock returns. Blitz and Vliet (2007) offered also explanations for the irrationality that investors tend to overpay for risky stocks. According to their reasoning, leverage restrictions, inefficient two step investment processes and behavioral biases of private investors could be explanations for this phenomenon.

Cederburg and O’Doherty (2016) suggested investors to approach a possible bet against beta strategy with caution. Their empirical results indicated, not only that the differences in conditional alphas across high- and low-beta portfolios are substantially smaller in economic magnitude and statistically insignificant, but also that differences in risk-adjusted returns between high- and low-beta portfolios are largely due to biases in unconditional performance

measures. Bali et al. (2017) explained that beta anomaly is mainly driven by the demand of lottery like stocks. Investors tend to be fascinated by illiquid stocks with high probability of substantial short-term upward movements. These movements were at least partially generated by beta. Massive demand of these lottery-like stocks pushes their prices up, thus expected future returns decrease, which leads to poor performance of these high beta stocks.

Beta anomaly disappeared, after controlling the returns for this lottery demand. Moreover, Liu, Stambaugh and Yuan (2018) argued that beta anomaly is caused by idiosyncratic volatility (IVOL) of individual assets. Relation between IVOL and alpha is positive among underpriced stocks and negative among overpriced, high beta, stocks. Their empirical evidence suggested, that this strong negative relation combined with the positive IVOL-beta correlation produces beta-anomaly. Beta anomaly was insignificant after controlling results for either IVOL or excluding overpriced stocks with high IVOL.

Frazzini and Pedersen (2014) proved that betting against beta has generated abnormal returns between 1926 and 2012. They formed BAB (betting against beta) factor which took a long position on low beta stocks and short position on high beta stocks. In addition to this, researchers levered the low beta portfolio and de-levered the high beta portfolio in order to generate a market neutral BAB factor. Although BAB factor generated risk-adjusted excess returns, in order to profit from the BAB factor, one had to lever up the low beta portfolio until preferred risk-return feature. Interestingly, authors claim that Warren Buffett’s company Berkshire Hathaway bets against beta by buying low beta stocks instead of low volatility stocks and then applies leverage into portfolio.

Baker, Bradley and Wurgler (2011) investigated the returns generated by low risk by forming low risk portfolios based on beta and lagged volatility of stocks. Authors summarize, that it makes no different, whether risk is defined as beta or volatility and moreover, whether including only large cap stocks or all of them in the portfolio formation.

Low risk portfolio consistently outperformed high risk portfolio over the period between 1968 and 2008 in the U.S. stock market. In their research, over the beforementioned period 1 dollar in low volatility portfolio resulted in 10,12 dollars when taking inflation into consideration whereas one dollar in high volatility portfolio declined into less than 10 cents.

Furthermore, one dollar in low beta portfolio resulted in 10,28 dollars and one dollar in high beta portfolio decreased into 64 cents.