5. Theoretical framework
5.2 Performance measures and systematic risk factors
Source: MSCI (2018)
From the figure above, it is apparent how the low-end ESG quintile is more exposed to idiosyncratic risk incidents (fraud, corruption, litigation etc.). An idiosyncratic risk incident is in this case defined as drawdown of >95% or bankruptcy. The incident-corresponding ESG-rating is defined as the ESG-rating before the drawdown period begun. This can be explained by an existing positive relationship between ESG characteristics and risk control (Giese et al, 2017).
With better standards for risk control, high ESG-rated companies experience a lower
frequency of serious firm-specific incidents. A consistent pattern of high ESG scores and low idiosyncratic risk is emerging through academic work (f.ex. Bauer et al 2009; Oikonomou et al, 2011; Lee and Faff, 2009) and seems to extend to most markets. Furthermore, higher rated companies are found to carry lower cost of capital (Bauer et al, 2009; Fulten et al, 2012;
Oikonomou et al, 2011), which can factor into long-term company-specific sustainability.
Ultimately ESG considerations are found to act like an insurance from idiosyncratic downside risk.
Economic theory tells us that an investor is not compensated for taking on increased
idiosyncratic (or diversifiable) risk. Can ESG create increased risk-adjusted returns by taking advantage of the markets underestimation of idiosyncratic risk connected to ESG-factors?
5.2 Performance measures and systematic risk factors
Measuring financial performance, one is interested in more than the expected return of the investment. Investing money in mutual funds comes with inherent risk. In a theoretical world with risk-neutral investors or infinite money, the level of exposure to systematic risk would not play a role in performance measures. However, according to behavioral finance, the average investor is risk averse (and does not possess infinite capital). Risk aversion insinuates that if returns are equal, investors will choose the option with lower associated risk. In some
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cases (typically more extreme cases), investors are also willing to sacrifice expected returns to align with their utility regarding loss-aversion. Thus, performance is measured by analyzing the relationship between expected return and associated risk.
But what risk? As mentioned above, an investor is not compensated for taking on
idiosyncratic risk, also known as unsystematic, firm-specific or diversifiable risk. The latter synonym, “diversifiable risk” indicates that such risk can be removed through sufficient diversification. Imagine two investors, one diversified, the other not. When investing in the same asset, the first investor does only have to worry about the systematic risk factors, as when this particular asset performs poorly, he is compensated in other aspects of his portfolio.
The second investor is subjected to a larger portion of total risk and therefore should require a lower price. However, as there are enough diversified investors in the market, an asset is priced in accordance with its associated systematic risk factors. Systematic risk factors can be avoided by an individual, but someone must always undertake them and is therefore
compensated.
The capital asset pricing model (CAPM) (Sharpe, 1964; Lintner, 1965) is the cornerstone of empirical analysis. The model was built on the seminal work of Markowitz (1952) on diversification, and describes the relationship between an investment’s expected return in relation to its associated market risk:
𝐸(𝑟𝑖) − 𝑟𝑓= 𝛽𝑖∗ (𝐸(𝑟𝑚) − 𝑟𝑓)
Where
𝐸(𝑟𝑝) is the expected return of the investment, 𝑟𝑓 is the risk-free investment option,
𝛽𝑖 is the sensitivity of investment returns with respect to market returns, calculated as the covariance between the investment and the market divided by the market variance, and 𝐸(𝑟𝑚) is the expected market return.
Fama and French (1993) expand on CAPM, as they find that univariate market-based models do not adequately embody common risk factors in the stock market. In their paper, Fama and French introduce two new explanatory variables of expected stock returns, namely the SMB and the HML-factors. The first factor, SMB, or small minus big relates to company size. The
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factor encompasses the historical excess (average) returns of small-cap companies over large-cap companies. The factor is purely based on the relationship between returns and
capitalization and is included in the model on the rationale that small-cap stocks tend to provide higher returns than large-cap counterparts. HML, or high minus low refers to a company’s book-to-market ratio. The rationale behind this factor is that high book-to-market companies, or “value stocks” on average give higher returns than low book-to-market equites, or “growth stocks”.
Combining the two above-mentioned risk factors with the market factor, this model is known as the Fama-French Three-Factor Model, formulated as:
𝐸(𝑟𝑖) − 𝑟𝑓 = 𝛽1(𝐸(𝑟𝑚) − 𝑟𝑓) + 𝛽2𝑆𝑀𝐵 + 𝛽3𝐻𝑀𝐿
In the multi-factor model, the 𝛽𝑖 are factor coefficients that explain how the asset or portfolio is affected by market risk (𝛽1), capitalization (𝛽2) and book-to-market ratio (𝛽3). Recall from the literature review that sustainable funds have historically invested in large-cap stocks (Van Beurden and Gössling (2008); Johnsen and Gjølberg, (2008) Dolvin et al (2017); Auran and Kristiansen (2016)).
With the theoretical model established, we can employ historical data to estimate variables and create the following, practicable model:
𝑟𝑖− 𝑟𝑓 = 𝛼𝑖 + 𝛽1(𝑟𝑚−𝑟𝑓) + 𝛽2𝑆𝑀𝐵 + 𝛽3𝐻𝑀𝐿 + 𝜀𝑖
Where
𝑟𝑖 is the estimated expected investment returns, 𝑟𝑓 is a measure for risk-free rate,
𝑟𝑚 is the estimated expected market return, and 𝜀𝑖 is the error term, or residuals from the regression.
The 𝛼, often referred to as “Jensen’s Alpha” (Jensen, 1967) is a measure of abnormal
performance, i.e. performance not explained by the factor model. In this paper, I use Jensen’s three-factor alpha as well as the Sharpe ratio (Sharpe, 1966) to measure risk-adjusted
performance. The Sharpe ratio is defined as the expected return in excess of the risk-free rate relative to acquired risk. In practice, it is the earned excess return divided by the historical standard deviation. The multivariate regression is performed in Microsoft Excel, using
36 ordinary least squares (OLS).