Risk reporting is increasingly regarded by sophisticated investors as an important ingredient in their decision-making process, authors from EDHEC argue that the effective number of (uncorrelated) bets could be a useful risk indicator to be added to risk reports for equity and policy portfolios.
Risk reporting is increasingly regarded by sophisticated investors as an important ingredient in their decision-making process.
The most commonly used risk measures such as volatility (a measure of average risk), value-at-risk (a measure of extreme risk) or tracking error (a measure of relative risk), however, are typically backward-looking risk measures computed over one historical scenario.
As a result, they provide very little information, if any, regarding the possible causes of portfolio riskiness and the probability of a severe outcome in the future, and their usefulness in a decision-making context remains limited.
For example, an extremely risky portfolio such as a leveraged long position in far out-of-the-money put options may well appear extremely safe in terms of the historical values of these risk measures, that is until a severe market correction takes place.
This was pointed out by Andrew Ang, William Goetzmann, and Stephen Schaefer in their 2009 report to the Norwegian Ministry of Finance “Evaluation of Active Management of the Norwegian Government Pension Fund–Global”.
In this context, it is of critical importance for investors and asset managers to be able to rely on more forward-looking estimates of loss potential for their portfolios.
In recent research produced with the support of CACEIS as part of the research chair at EDHEC-Risk Institute on “New Frontiers in Risk Assessment and Performance Reporting,” we focused on analysing meaningful measures of how well, or poorly, diversified a portfolio is, exploring the implication in terms of advanced risk reporting techniques, and assessing whether a relationship exists between a suitable measure of the degree of diversification of a portfolio and its performance in various market conditions.
While the benefits of diversification are intuitively clear, the proverbial recommendation of “spreading eggs across many different baskets” is relatively vague, and what exactly a well-diversified portfolio is remains somewhat ambiguous in the absence of a formal quantitative framework for analysing such questions.
Fortunately, recent advances in financial engineering have paved the way for a better understanding of the true meaning of diversification.
In particular, academic research has highlighted that risk and allocation decisions could be best expressed in terms of rewarded risk factors, as opposed to standard asset class decompositions, which can be somewhat arbitrary.
For example, convertible bond returns are subject to equity risk, volatility risk, interest rate risk and credit risk. As a consequence, analysing the optimal allocation to such hybrid securities as part of a broad bond portfolio is not likely to lead to particularly useful insights.
Conversely, a seemingly well-diversified allocation to many asset classes that essentially load on the same risk factor (e.g., equity risk) can eventually generate a portfolio with very concentrated risk exposure.
More generally, given that security and asset class returns can be explained by their exposure to pervasive systematic risk factors, looking through the asset class decomposition level to focus on the underlying factor decomposition level appears to be a perfectly legitimate approach, which is also supported by standard asset pricing models such as the intertemporal CAPM or the arbitrage theory of capital asset pricing.
Two main benefits can be expected from shifting to a representation expressed in terms of risk factors, as opposed to asset classes.
On the one hand, allocating to risk factors may provide a cheaper, as well as more liquid and transparent, access to underlying sources of returns in markets where the value added by existing active investment vehicles has been put in question.
For example, the argument in favour of replicating mutual fund returns with suitably designed portfolios of factor exposures such as the value, small cap and momentum factors.
Similar arguments have been made for private equity and real estate funds, for example. On the other hand, allocating to risk factors should provide a better risk management mechanism, in that it allows investors to achieve an ex-ante control of the factor exposure of their portfolios, as opposed to merely relying on ex-post measures of such exposures.
In our research, we first review a number of weight-based measures of (naive) diversification as well as risk-based measures of (scientific) diversification that have been introduced in the academic and practitioner literature, and analyse the shortcomings associated with these measures.
We then argue that the effective number of (uncorrelated) bets (ENB), formally defined in Managing diversification as the dispersion of the factor exposure distribution, provides a more meaningful assessment of how well-balanced an investor’s dollar (egg) allocation to various baskets (factors) is.
We also provide an empirical illustration of the usefulness of this measure for intra-class and inter-class diversification. For intra-class diversification, we cast the empirical analysis in the context of various popular equity indices, with a particular emphasis on the S&P 500 index.
For interclass diversification, we analyse policy portfolios for two sets of pension funds, the first set being a large sample of the 1,000 largest US pension funds and the second set being a small sample of the world’s 10 largest pension funds.
In a first application to international equity indices, we use the minimal linear torsion approach to turn correlated constituents into uncorrelated factors, and find statistical evidence of a positive (negative) time-series and cross-sectional relationship between the ENB risk diversification measure and performance in bear (bull) markets.
We find a weaker relationship when using other diversification measures such as the effective number of constituents (ENC), thus confirming the relevance of the effective number of bets on uncorrelated risk factors as a meaningful measure of diversification.
Finally, we find the predictive power of the effective number of bets diversification measure for equity market performance to be statistically and economically significant, comparable to predictive power of the dividend yield for example, with an explanatory power that increases with the holding period.
In a second application to US pension fund policy portfolios, we find that better diversified policy portfolios, in the sense of a higher number of uncorrelated bets, tend to perform better on average in bear markets, even though top performers are, as expected, policy portfolios that are highly concentrated in the best performing asset class for the sample period under consideration.
Overall, our results suggest that the effective number of (uncorrelated) bets could be a useful risk indicator to be added to risk reports for equity and policy portfolios.
*Lionel Martellini is professor of finance at EDHEC Business School, and scientific director at EDHEC-Risk Institute
Romain Deguest, senior research engineer, EDHEC-Risk Institute
Tiffanie Carli, research Assistant, EDHEC-Risk Institute
The research from which this article was drawn was supported by CACEIS as part of the “New Frontiers in Risk Assessment and Performance Reporting” research chair at EDHEC-Risk Institute.
