Efficient markets theory has been challenged by the finding that relatively simple investment strategies are found to generate statistically significantly higher returns than the market portfolio. Well-known examples are the value, size and momentum strategies, for which return premiums have been documented in US and international stock markets. Market efficiency is also challenged, however, if some simple investment strategy generates a return similar to that of the market, but at a systematically lower level of risk.
An interesting study in this regard is the empirical analysis of the characteristics of minimum variance portfolios in Clarke, de Silva & Thorley (CST, 2006). These authors find that minimum variance portfolios, based on the 1,000 largest US stocks over the 1968-2005 period, achieve a volatility reduction of about 25%, whilst delivering comparable, or even higher, average returns than the market portfolio. We present a simple alternative approach to constructing portfolios with similar risk and return characteristics. Specifically, we create decile portfolios that are based on a straightforward ranking of stocks on their historical return volatility. Contrary to CST, we effectively only use the diagonal of the historical covariance matrix with this approach. We find that portfolios consisting of stocks with the lowest historical volatility are associated with Sharpe ratio improvements which are even larger than those in CST, and statistically significant positive alpha.
A related study in this regard is Ang, Hodrick, Xing & Zhang (AHXZ, 2006), who report that US stocks with high volatility earn abnormally low returns over the 1963-2000 period. These authors focus on a very short term (1 month) volatility measure, while in our study we concentrate on long-term (past 3 years) volatility, which implies a much lower portfolio turnover. Furthermore, we do not only find that high risk stocks are exceptionally unattractive, but also that low risk stocks are particularly attractive.
Ranking stocks on their historical volatility bears a resemblance to ranking stocks on their historical CAPM beta. Theoretically this follows from the fact that the beta of a stock is equal to its correlation with the market portfolio times its historical volatility and divided by the volatility of the market portfolio. Empirically we also observe that portfolios consisting of stocks with a low (high) volatility exhibit a low (high) beta as well. Since the earliest tests of the CAPM researchers have shown that the empirical relation between risk and return is too flat, e.g. Fama & MacBeth (1973). Similarly, others such as Black, Jensen & Scholes (1972) report that low beta stocks contain positive alpha. In their seminal paper, Fama and French (1992) show that beta does not predict return in the 1963-1990 period, especially after controlling for size. In our sample we also find alpha for portfolios ranked on beta, but considerably less than for portfolios ranked on volatility.
Our main contributions to he existing literature are as follows. Firstly, we document a clear volatility effect: low risk stocks exhibit significantly higher risk-adjusted returns than the market portfolio, while high risk stocks significantly underperform on a risk-adjusted basis. Secondly, our findings are not restricted to the US stock market, but apply to both the global and regional stock markets. The alpha spread of the top versus bottom decile portfolio amounts to 12% per annum for our universe of global large-cap stocks over the 1986-2006 period. Thirdly, we compare the volatility effect with the classic size, value and momentum strategies and control for these effects. In order to disentangle the volatility effect from those other effects we use global and local Fama and French regressions and apply a double sorting methodology. We find that the volatility effect is in fact a separate effect, and of comparable magnitude. Fourthly, we provide possible explanations for the success of the strategy which include leverage restrictions, inefficient industry practice or behavioral biases among private investors, which all flatten the risk-return relation. Finally, we argue that benefiting from the low volatility effect in reality is not easy, as long as institutional investors do not include low risk stocks as a separate asset class in their strategic asset allocation process.
The remainder of this paper is organized as follows. In the following section we first describe our data and methodology. Our primary focus is on a universe of global large-cap stocks. Subsequently, we present results for the US, European and Japanese markets in isolation. In the next section we control for other cross-sectional effects, again tested on global and regional markets separately. This is followed by a discussion of possible explanations for the superior Sharpe ratios of low risk portfolios. We end with our conclusions and implications for investors.
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