The Macaulay Duration: A Key Indicator for the Risk-Adjustment in Fair Value

Abstract

International Financial Reporting Standards (IFRS) 13 Fair Value Measurement lays down two methods to adjust Expected Present Value (EPV) for risk. According to Method 1, expected cash inflows should be risk-adjusted by subtracting a risk-premium and discounted at the market risk-free rate, see (IFRS 13, B25). In contrast according to Method 2, expected cash inflows should be discounted at the risk-free rate augmented by a risk-premium addendum, see (IFRS 13, B26). Standard IFRS 13, B29 leaves the freedom to choose between the two methods. The aim of this note is to identify the relationship between the Risk-Adjusted EPVs rolled out from Method 1 and Method 2. First we introduce a theoretical solution to risk-adjustments compliant with the Standard IFRS 13, B29. Then, we set up a user-oriented proxy to connect the risk-premium present in Method 1 with the risk-adjusted rate present in Method 2. This proxy spots light on the key role played by the Macaulay Duration of expected inflows, rather than that of the lifetime of the project. As a consequence, projects expiring at the same redemption date and endowed with the same EPV and/or the same total inflow may differ considerably in risk-adjustments, due to different Macaulay Durations. A user-oriented method to properly to fast evaluate risk-adjustments for multi-cash inflow projects is provided. Sensitivity analysis of the impact of the Macaulay Duration on Risk-Adjusted EPV is also rolled out through numerical examples.