Deflating without ratios
Finance & Accounting
|Speaker:||Paul Dunmore, Massey University, Wellington|
|Date:||Friday 12 March 2010|
This exploratory paper presents a new description of the relationship between pairs of firm-level accounting data, illustrated with the pair (liabilities, assets). A logarithmic polar-coordinate representation of the data allows all points to be viewed at once, reveals the structure of the data more clearly, respects the bookkeeping constraints on the variables, and ensures that similar firms are similarly described.
In this representation, the size of the firm (as related to the two variables being considered) is measured by the logarithm of the distance from the origin, and the relationship between the variables is represented by the compass “bearing”, the direction from the origin. Typically, the bearing is mean-reverting but the size is not. This property is exploited in a framework which represents the evolution of the relationship between variables over time in terms of a stochastic process for the bearing. The simple case of the Ornstein-Uhlenbeck process leads to an explicit formula for the cross-sectional distribution of the bearing; it is shown that this distribution is nearly normal, which is of benefit for empirical research.
As an application of this framework, the cross-sectional distributions of financial ratios are derived in terms of the underlying parameters of the time-series process. This yields explicit connections between the different distributions of the liabilities/assets, liabilities/equity, and net income/equity ratios. All of these ratios have infinite population moments, although the effects can perhaps be ignored for the liabilities/assets ratio.
As a further application and to illustrate the way in which the description reveals the structure of the data, the mean-reversion of profitability analyzed by Fama and French (2000) is re-examined.