Building indices using risk components.

To determine what risk types to consider as a benchmark's building blocks, we should also ask what assumptions we are making about their premia. These assumptions, implicit or explicit in the chosen construction method, drive the risk types considered. Typically the assumptions are trivial, such as one that all risk premia are the same, because we do not want the benchmark to include information that the manager gets paid for. Although we want to attribute to the manager the entire portfolio return due to views on future performance, we need a base case to judge him against, a set of neutral views on performance, but views nonetheless. As a reference, Figure 9 shows the Sharpe ratio of major risk sources⁷, broken down by sub-periods. Notice the variability both across periods and across asset types, something to be expected given the notorious difficulty of forecasting them even over the long term.

What are the benefits of making these neutral views explicit? First, in doing so we understand better the source of any deviations from the benchmark, that is what the right or wrong calls made by a manager were and how are they reflected in deviations from the benchmark. We can do even more: we can modify those assumptions if we do not agree with them. For example, given the historically low levels of interest rates in 2011, we may not believe rates risk will carry the same premium (Sharpe ratio) as equity going forward, thus we will not allow them to contribute equally to our benchmark risk and tilt the benchmark more towards equities.

This discussion shows how we can select the building blocks of an index: select only those risk types that carry a risk premium. If we cannot distinguish among the magnitude of various risk premia, then we may choose to assume that all risk premia are the same.

Capacity And Market Weight Tilts
Intuitively, a benchmark that contains 50% Asset-Backed Securities (ABS) and 50% US Treasuries may seem inappropriate for a large fixed income manager, because there is not enough market capacity to invest 50% of the portfolio in ABS. Capacity must be considered even for a risk-based index design. However, capacity is investor-specific. The ABS and Treasuries benchmark above may suit a very small investor. Incorporating capacity in the index design tilts the risk weights towards market weights. The more importance capacity has, the more weights will be tilted towards market weights. At the extreme, for an investor the size of the entire market, the risk-weighted benchmark is the market-weighted one because of capacity. Therefore, capacity ties together risk-based and market value-based indices.

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