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On the Choice of Asset Price Indices: Performance Measurement versus Asset Class Analysis Authors: Liang Peng Source: Working Paper, SSRN Date: November 2003 |
Abstract
Indices have two main uses in asset management. They serve to analyze the risk and returns of asset classes and to measure portfolio performance. The development of an index involves two aspects. The first aspect concerns the choice of the index that will be suited to the relevant needs and the second aspect relates to the estimation of the index chosen. Depending on market conditions, the difficulties encountered will not be the same. The construction of an index is easier in liquid markets, where individual asset values are consistently observed, than in real estate and venture capital markets, where observations are sparse. Numerous articles have considered the problem of index estimators, while the interest in index selection is more recent. Peng underlined the fact that different indices are required depending on their dedicated use. On the subject of index choice, Peng mentions the study by Geltner and Ling (2000), in which they propose to distinguish between asset class research indices and evaluation benchmark indices, in order to meet different research needs, but they present few practical index selection criteria.
In the present article, Peng goes further and studies how to choose indices to suit performance analysis and asset class attributes. He thus describes two different criteria to select indices, whether these indices are intended to evaluate performance or to analyze asset class attributes. He relies on the fact that indices can be interpreted in two different ways: an index can be interpreted as a portfolio, therefore it can serve as a benchmark for portfolio performance measurement; an index can also be interpreted as a representative asset, and thus helps to investigate asset class attributes. Using statistical models, the author first shows that an index that captures the characteristics of the representative asset well does not necessarily track a desired portfolio well. On the other hand, indices that closely track portfolio performance over time may misrepresent the risk and return characteristics of the representative assets. Therefore, there may not be a single index that is appropriate for both research needs. He then uses simulations to evaluate the magnitude of quantitative differences between different indices. In particular, he studies the two types of widely-used indices: equal-weighted and value-weighted indices.
The selection of indices to measure portfolio performance uses what the author calls the moment-matching criterion: the index intended to measure the performance of a portfolio shall be estimated on the basis of the moment condition that defines the return of the portfolio. The selection of indices to study the risk and returns of the representative asset uses what the author calls the process-matching criterion. An index tracking the representative asset should be estimated using a model that correctly specifies the actual data generating process. This criterion is consistent with the conventional definition of econometric model specification.
This paper demonstrates that the choice of indices can have substantial economic consequences because the magnitude of the distinctions between indices can be significant. The paper uses simulations to show that the average appreciation rate and the time series variance of an equal-weighted and a value-weighted index can differ dramatically if the idiosyncratic appreciation components are auto-correlated and have large variance. Furthermore, the magnitude of the difference increases with the auto-correlation and the variance. Therefore, in markets with heterogeneous sub-markets, the choice of index is particularly important.
The author concludes by noting that he does not propose any econometric method here to estimate indices when observations are sparse, but that this would be a challenging research question for future investigation.
References
Geltner D., Ling D., “Benchmarks & Index Needs in the U.S. Private Real Estate Investment Industry: Trying to Close the Gap”, A RERI Study for the Pension Real Estate Association, 2000.
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