The author analyzes return variations linked to market factor anomalies or dimensional beta using the Fama–French three-factor; Carhart four-factor; Fama–French five-factor; and Asness, Frazzini, and Pedersen (AFP) five- and six-factor models. These models test systematic risk by using the CAPM.

The author finds significant variations in explaining sources of risk across 22 developed and 21 emerging markets. Each market is considered unique in terms of factor risk characteristics, and in many emerging markets, risk as explained by the CAPM is not the true risk measure.

Contrary to the well-known risk–return efficiency framework, the author finds that over the time period studied, lower market risk results in higher excess return in 19 of 22 developed markets, which represents a major anomaly and is supported by prior research. Although the AFP models result in reducing market risk in 15 developed markets and enhancing alpha in 11 markets, the author notes that the CAPM generates excess returns in 8 developed markets.

The results in the emerging markets are quite different. Emerging markets are seen to be less mature and remain exposed to factor risk.

When world equity markets are considered as a whole, all the models generate similar alpha and market risk. It would seem that large companies are actually overvalued. The author finds, moreover, that each market is unique, and thus a one-size-fits-all approach in asset allocation cannot be adopted across all markets.

Portfolio managers and investors in general will find the conclusions of this research useful, particularly in helping them to differentiate among the 43 equity markets studied and to devise strategies to enhance risk-adjusted returns based on the dimensional and time-varying return anomalies identified within the models. Caution is nonetheless required, given the uniqueness of each market.

The author uses MSCI Global Equity Markets Standard Price Monthly Index data from January 1991 to December 2016 for developed markets. The exception is Israel, for which data are available starting in January 1993. In the case of emerging markets, the majority have data available from January 1991; in six markets, data are gathered from January 1993, and in four, from January 1995. The analysis and results reflect the construction methodology adopted by MSCI.

The author subsequently conducts a regression analysis of the CAPM and the five other market factor models to assess the impact of the factors on market risks and characteristics and to evaluate their efficacy. The factors include size, value, momentum, profitability, investment, quality, and low beta. The author presents contributions to improve alpha in different markets.

In the developed world, the CAPM has the lowest market risk in five markets and the highest alpha in eight markets. The eight markets, which might represent the most efficient markets, include Australia, Austria, Belgium, Ireland, New Zealand, Portugal, Switzerland, and the United Kingdom. In the United States, the Carhart four-factor model results in the highest alpha. The author also finds that lower market risk translates into higher excess return in 19 of the 22 developed markets.

In the case of emerging markets, most are not risk or return efficient, and the CAPM beta thus cannot be regarded as a true measure of market risk. Columbia, Hungary, Malaysia, Peru, and South Africa seem to be the most efficient markets in the emerging world. Investing in high credit quality companies can also improve alpha in emerging markets.

When world equity markets are considered in aggregate, all the models generate similar alpha and market risk.

According to the risk–return efficiency framework, higher market risk should translate into higher excess return, but this is not always the case, partly because of dimensional and time-varying return anomalies in different markets.

Despite its various questionable assumptions, the CAPM is still seen to be quite effective in explaining alpha in developed markets. Investors may be tempted to use such research findings to differentiate among equity markets around the world and devise a profitable investment strategy. Believers in the efficient market hypothesis could also pay attention to Australia, Austria, Belgium, Ireland, New Zealand, Portugal, Switzerland, and the United Kingdom—perhaps the most efficient markets.

I do have concerns that the data used in the analysis cover a fairly short period (beginning in 1991). Furthermore, the impact of transaction and friction costs, dividends, taxes, inflation, limitations on the repatriation of investment income, and exchange rate volatility do not seem to have been considered across the different markets, and using a generalized approach to devise an investment strategy for each market is not recommended. Further research is warranted, but the author’s findings remain relevant. I note that the CAPM can still be used to generate alpha, especially in the developed world. Large companies seem overvalued, and investors paying attention to the value premium might benefit from superior returns.