Performance Measurement Theory
1. Introduction
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1.1 The main purpose of investment performance
measurement and attribution is to determine in a quantitative sense how well a
portfolio has performed and where that performance has come from.
Mathematically, performance measurement is relatively straightforward compared
with risk measurement, although careful attention to accounting detail is
required. Different audiences may want to see attribution subdivisions in
different ways. Because results are often highly sensitive to the accuracy of
input data, it can also provide a useful check of the accuracy of the
underlying accounting process. Performance attribution involves calculating the
total returns for both fund and benchmark (for the relevant period), creating
suitably accurate models of how these total returns can be built up from the
various constituent parts, and then decomposing the differences in ways that
are illuminating to the various audiences. For a hedge fund or a trading
account, there might be no explicit benchmark as such, so performance
attribution might instead concentrate on a cash benchmark.
1.2 The modelling process will subdivide time into
various periods. Returns do not compound additively over time, but
geometrically. The root time period can be as short as a single day, although
such a short period can create extra work without necessarily offering any
material improvement in accuracy. Even over very short periods it may be
necessary to make assumptions or approximations, or equivalently you may have
to accept that there will be residuals that need explaining or quantifying.
1.3 Ideally any performance attribution should
start with the contributions to performance arising from each individual line
of stock for both the fund and the benchmark. These would then be grouped
together in some suitable fashion, e.g. a country/sector
classification/portfolio design structure (for equity and managed funds) and/or
using factor exposures such as duration (for bond funds). This may
involve a hierarchical structure, drilling down potentially several levels.
Sometimes cash is kept separate, and sometimes aggregated with the rest of the
portfolio. Security classifications need to be maintained (including relevant
factor exposures). The classification of a given security and its factor
exposures may change over time. If the portfolio contains derivatives or
similar instruments their values may need to be divided between two or more characteristics/factors
simultaneously, often positive to one characteristic/factor and negative to
another, see e.g. Kemp (1997), LIFFE (1992a)
or LIFFE
(1992b). Carrying out the same calculations for large numbers of funds
simultaneously is facilitated by giving careful consideration to how to store
all of this data in a suitable fashion, and how to process it efficiently. Many
of the same data management issues also arise in practical risk management
systems.
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