Disentangling Cognitive Bias in the Assessment of Investment Decisions: Derivation of Generalized Conditional Risk Attribution

Abstract

Conventional performance measurement methods concentrate on investment outcomes rather than the underlying investment process. This paper examines the effectiveness of the investment process by considering the essential part of any investment strategy: the investment decision.As recognized by Kahneman and Tversky [1979], the essential first step is to decompose returns into gains and losses. Using a fundamental investment decision matrix broadens the analysis beyond realized gains and losses to include an assessment of missed opportunities and losses avoided. This leads to an examination of investment strategies in terms of investment success versus error. We contrast these terms with traditional return and risk measures.The second step is to decompose investment decisions into the mutually exclusive categories of risk-taking and risk-reducing. Uncertainty observed in risk-taking activities is newly created at each manager's discretion, while the uncertainty in risk-reducing activities is already defined by an investor's portfolio. The conventional performance measurement approach fails to differentiate between these two types of decisions.The contrast between passive and active management styles of risk reduction becomes apparent from the perspective of investment success and error, particularly when using currency risk management as an illustration. Active information diagrams describe a geometric approach called conditional risk attribution. An active manager's skill lies in the ability to use information to maximize investment success and therefore minimize investment error. The choice of benchmark determines the degree of visibility of an investment exposure.We also address the problem of distinguishing between an active manager's skill and the uncontrollable impact of market movements. Having adjusted for the bias in an investment environment, it becomes possible, as a final step, to measure the information content of an active manager's strategy as the balance between investment success and error within a generalized conditional risk attribution framework.The unlimited nature of risk-taking decisions is evident when they are included in the framework. However, having defined an ex ante risk-taking limit, we can assess whether the choice of active manager has resulted in an enhancement of investment success over error. This allows investors to compare risk-taking managers with risk-reducing managers in the context of overall portfolio construction. The entire analysis is framed in terms of risk budgeting to demonstrate its general application to all asset classes and consequently to enhance total portfolio returns within the predetermined loss budget.