The constructed portfolios will be measured according to their risk-adjusted returns using common performance measurement tools. Following the methodology of other studies regarding SRI, this empirical study will apply the Sharpe ratio, Treynor ratio, and Jensen’s alpha to analyse the portfolios’ performances.
3.4.1 Sharpe Ratio
The Sharpe ratio is developed by, and named after, William Sharpe (1966) and is a common financial metric used to measure the performance of investment assets. The ratio was originally referred to as the reward-to-variability ratio, as it measures the average return achieved in excess of the risk-free rate per unit of volatility.
After getting considerable attention, Sharpe (1994) revised and renamed the ratio in his paper “The Sharpe
Ratio”. The measure is closely related to Markowitz’ (1952) MPT, as it argues that you should be compensated for enduring more risk. The mathematical expression for the Sharpe ratio is as follows:
𝑆ℎ𝑎𝑟𝑝𝑒 =𝑅.− 𝑟F 𝜎.
Where:
𝑟* is the risk-free rate 𝑅' is the portfolio return
𝜎' is the standard deviation of the portfolio
In theory, the risk-free rate is an investment return with zero risk. Thereby, the investor can isolate the return associated with undertaking risk and compare it to the level of risk endured. The Sharpe ratio can be used to find the most optimal portfolio on the efficient frontier, i.e. the one that yields the highest ratio and thereby the highest risk-adjusted return. The optimal portfolio should not be mistaken for the portfolio that provides the highest return. However, the investors can utilize the risk-free market to adopt the preferred risk-return trade-off and scale the investment up or down depending on risk aversion. Furthermore, the Sharpe ratio can both evaluate the portfolio’s past and expected performance, by using either historical or expected measures.
3.4.2 Treynor Ratio
The Treynor ratio is developed by Jack Treynor (1965) and is a performance measure similar to the Sharpe ratio (1994). The difference between the Treynor and Sharpe ratio is the risk measure. The Treynor ratio was originally called the reward-to-volatility ratio and measures the average return achieved in excess of the risk-free rate per unit of systematic risk, i.e. the portfolio beta. In other words, it measures the additional risk endured by holding the risky portfolio compared to holding the market portfolio. The relationship between the portfolio and the market is measured in beta, whereby the Treynor ratio can be written as:
𝑇𝑟𝑒𝑦𝑛𝑜𝑟 𝑟𝑎𝑡𝑖𝑜 =𝑅.− 𝑟F 𝛽.
Where:
Notion as above 𝛽' is the portfolio beta
Similar to the Sharpe ratio, a higher value indicates a better portfolio. The main difference between the two, is that the Sharpe ratio measures the performance compared to the risk-free market, whereas the Treynor ratio measures the performance compared to the market return. The Treynor ratio is also limited, as it is only applicable when measuring portfolio performance and not individual assets, whereas the Sharpe ratio is applicable for both. Another drawdown is that the Treynor ratio is a backward-looking method, where the accuracy of the beta estimate is highly dependent on the correct use of market benchmark. Therefore, the ratio should not be used as a standalone measure.
3.4.3 Jensen’s Alpha
Jensen’s alpha (henceforth alpha) is a risk-adjusted performance measure published by Michael Jensen (1968), and it constitutes a fundamental part of this thesis. Alpha compares the achieved portfolio return with the predicted return measured by any given performance benchmark model. In other words, the measure states whether you have been ‘correctly’ compensated for the risk you have endured by holding the risky portfolio.
The key feature of performance benchmark models is that they differentiate between two types of risk: 1) systematic risk and 2) non-systematic risk. The former is rewarded in terms of return, where an increase in systematic risk results in higher expected returns. The latter, on the other hand, is not compensated as it is assumed to be diversifiable and therefore has an expected return of zero. However, actual returns are rarely equal to expected returns and performance benchmarks are not perfect, which is where alpha becomes relevant.
Essentially, alpha is the intercept in the model. According to CAPM, alpha can be measured as follows:
𝛼 = 𝑅.− ,𝑟F+ 𝛽.∗ [𝑅G− 𝑟F]-
Where:
𝑟* is the risk-free rate
𝑅' is the realized return of the portfolio 𝛽' is the portfolio beta
𝑅+ is the realized return of the market portfolio
A positive alpha will conclude that the portfolio outperformed the market and generated higher returns than what was predicted by CAPM. Opposite, a negative value indicates that the portfolio has not generated the required return. If the securities in the portfolio are fairly priced, the portfolio return will be the same value as predicted by CAPM which will yield an alpha of zero. In this situation, the market is said to be efficient. The alpha measure can also be applied for multi-factor models where the equation above will be adjusted accordingly. Depending on which model is trusted to provide the best guess on the expected return, the alpha can be used to test whether the investor has been able to beat the market, by generating a positive alpha.
For the purpose of this thesis, alpha is used to assess the performance of the constructed portfolios according to the applied performance benchmark models, that is CAPM, Fama-French 3-, and 5-Factor models. More specifically, it is assessed whether alpha is significantly different looking across the high and low ESG-scoring portfolios.
Chapter 4
Data and Methodology
The purpose of the following chapter is to provide a clear depiction of the data and methodology that constitute the foundation of the subsequent analysis. The first section introduces the data that is used to conduct the analysis, which includes ESG scores and other relevant market data. The following section presents the methodology applied in this study to answer the formulated research question and subsequent hypotheses. The methodology is split into two sub sections, portfolio creation and portfolio testing. The last section includes an introduction of some important econometric considerations that needs to be accounted for when performing this type of quantitative study.