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Risk-Weighted Indexing
By Radu Gabudean | 26 October, 2011   

Building indices using risk components.


Risk-Weighted Indexing

In the expanding index universe, new categories of risk-weighted and fundamental indices are garnering interest alongside well-established market-weighted indices. As their distinguishing feature, risk-weighted indices employ quantitative forecasts of risk to achieve better diversification. In contrast, fundamental indices focus on future expected performance to achieve diversification. Market-weighted indices do not directly employ any forecasts and rely on current valuations as the metric that summarises all forecasting information.

The theoretical foundation for risk-weighted indexing can be traced back to Markowitz's mean-variance efficiency. More recently, in the equity asset class there have been several commercial implementations that rely on modified versions of the mean-variance optimisation1. In fixed income, some incipient efforts have been made to mirror the approach used for equities, but the only full-fledged implementations simply link weights with key characteristics that drive risk, such as duration or/and spread2. Across asset classes, risk-based methods are used mainly for portfolio construction, such as the "risk-parity" approach, and index implementations are missing, even though the same methodologies that are applied to portfolio construction could be applied to index construction as well.

WHY RISK-WEIGHTED INDICES?

Risk-based indices are typically useful for asset owners and managers who incorporate quantitative measures of risk in their portfolio construction. Such asset owners may employ risk-based methods to allocate assets across various managers and to create benchmarks for judging the managers' performance. Portfolio managers, whether they are asset allocators or product specialists, may use these benchmarks as a starting point for portfolio construction.

Risk-based portfolios give more weight to assets that either reduce the overall portfolio risk or increase it by less, aiming to maximise diversification benefits. If asset owners leave risk weightings out of the benchmark's construction methodology, they implicitly allow managers to reap the benefits of diversification and claim them as managerial skill, an undesirable outcome.

An appropriate benchmark should also match the investment philosophy of the associated portfolio. A benchmark must incorporate all relevant public information, while being careful to be agnostic about information that is the purview of the portfolio manager. Therefore, when well-known risk metrics, such as volatility, are part of the investment process, asset owners may prefer to use a risk-based index as a benchmark.

Let's consider the example of a manager who allocates to equity and fixed income. The goal is for each allocation to contribute to portfolio risk proportionally to its risk-adjusted performance. For clarity, let's take the Sharpe ratio as the metric for risk-adjusted performance and let's define risk as volatility. As a benchmark, the asset owner may use a base case when both assets are expected to have the same Sharpe ratio. Therefore, fixed income and equity must contribute equally to the total benchmark risk. These conditions meet the asset owner's requirements for a good benchmark, since it includes public information that is used in the portfolio construction process but which is not part of the manager's performance assessment. Furthermore, it avoids information that the owner considers to be the purview of the portfolio manager, such as the relative performance of equity and fixed income. Any deviation of the portfolio from the benchmark will reflect directly the manager's skill at forecasting that relative performance.

In our example, the risk-based benchmark is composed of 25% equity and 75% fixed income3. This benchmark differs from a typical market-weighted combination of equity and fixed income (60% equity and 40% fixed income, or "60/40") because the equity part drives most of the "60/40" portfolio while the fixed income part has little influence. The last point is illustrated in Figure 1, which shows the properties of the 60/40 portfolio and its two components. The portfolio volatility is very similar to the volatility of the equity allocation alone—and much higher than the volatility of the fixed income part. Moreover, equity has an almost perfect correlation with the portfolio, while fixed income has a correlation of less than 50%. The equity dominance over the 60/40 portfolio showcases its lack of diversification.

The 60/40 Portfolio And Its Components




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