Conventional Tracking Error

Investment risk is the unexpected future outcome of price changes in an investors' (stock) holdings (Welch, 2011). Variability of price changes is therefore regarded as a fundamental source of investment risk. Risk can be idiosyncratic (firm-specific) or systematic (market-wide) and absolute or relative (see Eling and Schuhmacher, 2007; Ross et al., 2008 for a comprehensive overview of risk measures). The simplest methods for assessing idiosyncratic investment risks are measures such as variance, standard deviations, semi- standard deviations, Sharpe ratios, which compare the variability within one investment. In contrast, popular methods to evaluate systematic investment risk are Beta (estimated using the capital asset pricing model), Treynor Ratio, and Lower Partial Moments (if the benchmark target return is a broad market return). Systematic risk measures compare return variability between two or more investments, generally in relation to a benchmark such as global or country stock indexes. Following my assessment of absolute risk properties between renewable and conventional energy equity indexes in Table 15, I continue my empirical risk analysis on relative risk measures, in particular, tracking error volatilities. The traditional tracking error is defined as the standard deviation of the time-series difference between a portfolio return and a selected benchmark portfolio return (Ammann and Zimmermann, 2001; Cremers and Petajisto, 2009). To give one example in how to interpret the tracking error in statistical terms, a tracking error of 5 percent, assuming a normal distribution 86 with mean 0 and standard deviation of 1, will have a 68 percent chance (one standard deviation) of losing or gaining up to 5 percent in excess of benchmark returns (Polakow, 2011). Tracking error volatility as a relative risk measure can be used for three purposes. First, it is used to determine the level of portfolio risk (Ammann and Zimmermann, 2001). Second, it is used to value active management. In other words, it describes to what extent a fund manager's portfolio deviates from a given benchmark portfolio. Third, it is an alternative risk-adjusted performance measure (Treynor and Black, 1973).87

86 _{Excess return data of my sample is leptokurtic rather than normally distributed. Assuming normally} distributed excess returns when they are leptokurtic could lead to an under-estimation of the tracking error (Huisman et al., 1998). However, a potential under-estimation of the tracking error would affect all sampled energy indexes to the same extent. For my sample this means that both, renewable and conventional energy indexes would be affected to the same degree.

87 _{Several studies discuss the "tracking-error problem" or "optimization problem", which aims to reduce tracking} error volatility when replicating a selected benchmark given security selection restrictions (see e.g. Jorion, 2003;

I will use tracking error volatility as my preferred risk measure for the following reasons: First, due to their simplicity and intuitive appeal, tracking errors are widely used risk measures in practice. It is "one of the main industry standards as a measure of relative risk" (Berkelaar et al., 2006:64). Furthermore, many institutional investors explicitly state a maximum acceptable tracking error in mandates to limit investment risks of their fund managers (Maspero and Saita, 2005). This allows us to draw practically relevant conclusions regarding the risk behaviour of renewable and conventional energy investments. Finally, studies show that tracking error volatility accurately predicts investment risks for both small and large portfolios in the short-term (Scowcroft and Sefton, 2001). Critics of the tracking error mainly argue against its ability to assess and compare the financial performance of competing actively managed funds (Cremers and Petajisto, 2009; Huij and Derwall, 2011; Israelsen and Cogswell, 2007). They feel it is not a sufficiently robust indicator for ranking and selecting superior investments. In particular, Huij & Derwall (2011), and Israelsen & Cogswell (2007) argue that tracking error should not be used as the only indicator for financial performance. These critiques are mainly targeted at the ability to compare financial performance across mutual funds. In my study, tracking error is expressed as the residual volatility of renewable energy index returns in excess of conventional energy index returns, which emphasise bets on systematic risks in the conventional energy industry.

Directly comparing renewable with conventional energy index returns is sensible from a research design and a practical perspective (see also Schröder, 2007). A direct comparison between the risks of renewable and conventional energy indexes is also intuitive from a practical perspective, because trustees of large institutional funds such as pension funds tend to have very specialised investment mandates with selected investment funds. The contracted mutual funds can have different investment styles (such as growth, emerging markets, long/short) that require specialised benchmarks, rather than a broad and general equity benchmark. Thus, the selection of appropriate benchmarks in itself requires some expertise (Ansell et al., 2003; Bailey, 1992). I choose to benchmark my sample of renewable energy indexes with conventional energy indexes to mimic a specialised energy mandate from investors. I obtain the tracking error by (i) regressing excess returns of renewable energy indexes on conventional energy indexes and (ii) computing the standard deviation of

the resulting regression residual. Thus, I compute the traditional regression-based tracking error88 (TE) as shown in Equation (15) and (16):

, , , , ,

,

( ) (15)

( ) (16)

clean t f t clean clean conventional t f t clean t

clean t R R R R TE            where, , , , , , Risk-Free Rate

Return on Clean Energy Index i

Return on Conventional Energy Index i Residual Clean Energy Index

( ) = Standard Deviation of Residual

f t clean t conventional t clean t clean t R R R       

I will estimate Equation (15) using ordinary least squares and Newey-West corrected standard errors, which are robust to heteroskedasticity and serial correlation. The interpretation of tracking error is straightforward. High (low) tracking errors indicate large (small) return deviations from a portfolio to its benchmark and vice versa. In the context of this chapter, high tracking errors increase relative return volatility of renewable energy firms compared to conventional energy firms, whereas a low tracking error results in a reduction of the relative return volatility of the firms in the renewable energy index.