Tracking error decision rules and accumulated wealth

Nathan Berg and Donald Lien

Applied Mathematical Finance, 2003, vol. 10, issue 2, 91-119

Abstract: There is compelling evidence that typical decision-makers, including individual investors and even professional money managers, care about the difference between their portfolio returns and a reference point, or benchmark return. In the context of financial markets, likely benchmarks against which investors compare their own returns include easy-to-focus-on numbers such as one's own past payoffs, historical average payoffs, and the payoffs of competitors. Referring to the gap between one's current portfolio return and the benchmark return as 'tracking error', this paper develops a simple model to study the consequences and possible origins of investors who use expected tracking error to guide their portfolio decisions, referred to as 'tracking error types'. In particular, this paper analyses the level of risk-taking and accumulated wealth of tracking error types using standard mean-variance investors as a comparison group. The behaviour of these two types are studied first in isolation, and then in an equilibrium model. Simple analytic results together with statistics summarizing simulated wealth accumulations point to the conclusion that tracking error—whether it is interpreted as reflecting inertia, habituation, or a propensity to make social comparisons in evaluating one's own performance—leads to greater risk-taking and greater shares of accumulated wealth. This result holds even though the two types are calibrated to be identically risk-averse when expected tracking error equals zero. In the equilibrium model, increased aggregate levels of risk-taking reduce the returns on risk. Therefore, the net social effect of tracking-error-induced risk-taking is potentially ambiguous. This paper shows, however, that tracking error promotes a pattern of specialization that helps the economy move towards the path of maximum accumulated wealth.

Date: 2003
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DOI: 10.1080/1350486032000088912

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