of the Edhec-Risk Institute charts how the main investment factors, such as value and momentum, have risen to prominence – aided by their relevance not just to US equities, but other markets too.
Asset-pricing theory postulates that multiple sources of systematic risk are priced in securities markets. The economic intuition for the existence of a reward for a given risk factor is that exposure to such a factor is undesirable for the average investor because it leads to losses in bad times.
For example, while investors may gain a payoff from exposure to illiquid securities as opposed to liquid ones, such illiquidity may lead to losses in times when liquidity dries up and a flight to quality occurs, such as during the 2008 financial crisis. In such conditions, hard-to-sell (illiquid securities) may post heavy losses.
While asset-pricing theory provides a sound rationale for the existence of multiple factors, theory provides little guidance on which factors should be rewarded.
Empirical research, however, has come up with a range of factors that have led to significant risk premia in typical samples of data from US and international equity markets. A key requirement for investors to accept factors as relevant in their investment process is related to the presence of a clear economic intuition as to why the exposure to this factor constitutes a systematic risk that requires a reward and is likely to continue producing a positive risk premium.
Edhec research in 2014 reviewed the empirical literature that has identified factors that impact the cross-section of expected stock returns and we count a total of 314 factors for which results have been published.
Several empirical studies have been carried out to identify the fundamental factors that explain average asset returns, as a complement to the market beta. They have highlighted two important factors that characterise a company’s risk: the book-to-market ratio and the company’s size measured by its market capitalisation.
EF Fama and KR French in 1996 analysed a range of cross-sectional return patterns such as the higher returns associated with contrarian stocks, stocks with low past sales growth, stocks with low price/earnings ratios and low debt-to-equity ratios. They concluded that their “three-factor model” appropriately captures such effects. It can be seen as a parsimonious way of capturing a range of seemingly different return patterns that have been highlighted in the empirical literature.
However, the three-factor model is not able to capture high returns to past short-term winner stock, so M Carhart extended Fama and French’s three-factor model where the additional factor is momentum, which enables the persistence of the returns to be measured.
Fama and French analysed how the “four-factor model” of Carhart performs in explaining the cross-section of stock returns in developed equity markets. They analysed stocks for four regions (North America, Europe, Japan and Asia Pacific excluding Japan) and found that both the value and the momentum effect are more pronounced in small-cap stocks, and especially micro-cap stocks, than in large-cap stocks.
In particular, neither the large-cap momentum factor nor the large-cap value factor have returns that are significantly different from zero at conventional levels of significance, and the difference of factor returns within small-cap stocks compared to within large-cap stocks is significant for both the value and momentum factor. Moreover, in order to explain return differences across portfolios within each of the four regions, local factors perform better than global factors, implying that factor pricing is not integrated across regions.
K Hou, GA Karolyi and BC Kho in 2011 compared the explanation power of traditional factor models – such as the capital asset pricing model (CAPM) or models using size and book-to-market factors – with a factor model including a value-based factor derived from cash flow-to-price instead of book-to-market. Using monthly returns for more than 27,000 stocks from 49 countries over the period from 1981 to 2003, they found that pricing errors for the latter model is lower than for traditional models and leads to fewer model rejections.
In addition, they found that including an additional factor based on stock price momentum usefully complements the explanatory power of the cash flow-to-price factor.
Fama and French (2014) proposed a five-factor model that includes two factors (profitability and investment) in addition to the initial three (market, size and book-to-market). They found it provides an acceptable description of average returns on portfolios formed on size and one or two of book-to-market, operating profitability and investment.
Investors who can identify rewarded risk factors and are able to accept the corresponding systematic risk exposures also have to come up with practical ways of implementing factor exposure. Therefore, implementation issues are of crucial importance. In particular, since most factors require frequent adjustments of positions, then transaction costs and tax effects may create a gap between the empirical evidence on factor portfolios and the payoffs attainable in practice.
While asset-pricing theory provides a sound rationale for the existence of multiple factors, theory provides little guidance on which factors should be expected to be rewarded. Empirical research, however, has come up with a range of factors that have led to significant risk premia in typical samples of data from US and international equity markets.
To accept factors as relevant in their investment process, investors need a clear economic intuition as to why the exposure to this factor constitutes a systematic risk that requires a reward and is likely to continue producing a positive risk premium. J Cochrane referred to the practice of identifying merely empirical factors as “factor fishing”. Research has identified factors that impact the cross-section of expected stock returns and count a total of 314 factors for which results have been published. There are seven main factors: value, momentum, low risk, size, liquidity, profitability and investment.
It is interesting to note that these factors have been found to explain expected returns across stocks not only in US markets, but also in international equity markets, and – in many cases – even in other asset classes including fixed income, currencies and commodities.
THE DEBATE CONTINUES
The debate about the existence of positive premia for these factors is far from closed. Therefore, what is important in addition to an empirical assessment of factor premia is to check whether there is any compelling economic rationale as to why a premium would persist. Such persistence can be expected notably if the premium is related to risk-taking. In an efficient market with rational investors, systematic differences in expected returns should be due to differences in risk.
This point is best illustrated by the example of the equity risk premium. Given the wide fluctuation of equity returns, the equity risk premium can be statistically indistinguishable from zero, even for relatively long sample periods. However, one may reasonably expect that stocks have higher reward than bonds because investors are reluctant to hold too much equity due to its risks.
For other equity risk factors, such as value, momentum, low risk and size, similar explanations that interpret the factor premia as compensation for risk have been put forward. It is worth noting that the existence of the factor premia could also be explained by investors making systematic errors due to behavioural biases, such as over-reaction or under-reaction to news on a stock. However, whether such behavioural biases can persistently affect asset prices in the presence of some smart investors who do not suffer from these biases is a point of contention.
For behavioural explanations to be relevant, it is necessary to assume that – in addition to biases – there are so-called “limits to arbitrage”, i.e. some market characteristics that prevent smart investors fully exploiting the resulting return patterns and thus making them disappear. Therefore, explanations of factor premia as compensation for risk are likely to provide the more compelling case for investment applications.
Felix Goltz is head of applied research at Edhec-Risk Institute
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