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Building indices using risk components.
What Risk Types To Include: Expected Performance Assumptions
This conclusion leads us to the next issue: what risk types to consider. For example, for equity should we use a classic three-factor model (market, size and value, as described by Fama and French (1993)) or should we use an industry breakdown, or a combination of the two? For rates, should we use a principal-components breakdown (level, slope and convexity) or should we use a duration-based breakdown?
A well-designed risk-based benchmark contains all risks that the manager considers as part of the portfolio, but no others. The question then becomes what types of risk a manager would, or should, be given access to in order to construct the portfolio. Intuitively, a manager considers only those risk types for which he receives compensation in the form of a positive expected return, or those which reduce portfolio risk more than portfolio performance. This argument underscores a critical point: expected returns are always part of the benchmark construction, implicitly or explicitly.
It is generally believed that risk-based benchmarks do not rely on any performance forecast, but only on a risk forecast. However, creating a portfolio or a benchmark with the sole intention of minimising risk results in an all-cash portfolio or, if cash is not in the investable universe, the most cash-like instrument available to the manager, for example very low-duration bonds or very low-risk, low-beta equities. For example, in Figure 8 we compare three portfolios of equity and fixed income: one that aims to minimise risk, a second that aims to maximise the portfolio Sharpe ratio assuming both equity and rates have the same Sharpe ratio, and a third that is the "60/40". The results show that the first portfolio, which aims to minimise risk, is strongly correlated with fixed income (the lower-risk component of the portfolio) and has little relation to equities, while the "60/40" has the opposite behaviour. The second portfolio is equally correlated to rates and fixed income, a sensible outcome given the similar Sharpe ratio assumption, and arguably much more diversified than the other two portfolios.
Risk cannot be considered as a goal in itself. It must be combined with a performance goal, which requires assumptions about the future performance (i.e., the risk premium) of various risk types, that is the building blocks of the benchmark. This statement about risk premia assumptions being required for any benchmark design may seem strong, especially given that many risk-based portfolio construction methods6 claim not to rely on any performance information. For example, in a "risk-parity" portfolio, all components contribute equally to total portfolio risk. However, this design makes most financial sense when we assume the same premium (same Sharpe ratio) for each component. Thus, even these "performance-agnostic" methods embed some assumptions about the risk premium, albeit trivial ones.
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2011
