A Note on Statistics to Determine Asset Value from Multiple Methods

The article investigates three ways of forming a final estimate using two different estimators with different variances and possibly also biases: (1) taking the estimate produced by the better estimator, (2) taking their simple average, (3) taking their weighted average. It is shown that if there is no serious positive correlation, using both estimators is always preferable. Simple average is justified if both estimators exhibit similar variances or when variances are unknown. Weighted average is optimal in all other cases. In valuation, the findings are, however, useful only in limited number of situations. Combining unbiased estimates obtained from the same relatively large and well composed sample of comparison companies is the most common possible application. The optimal weight rule in that case is based on variances, not on standard deviations or coefficients of variation. The approach is also useful for cross-checking expert weight assignment.