Efficiency of Asset Valuation Rules under Price Movement and Measurement Errors - Lim, Suk S.; Sunder, Shyam (The Accounting Review, 1991)
[Errors arise in measuring changes in prices of assets due to imperfection and incompleteness of asset markets. Furthermore, the rates of price-change, and the magnitudes of errors of measurement vary and are often correlated across assets. Suppose we characterize an economy by means and variances of price changes for individual goods and of measurement errors in these changes as well as by the degree of diversification in the asset portfolios held by individual firms. In such an economy, the linear valuation rule that yields the most efficient estimate of change in the economic value of these asset portfolios is the one that minimizes the mean squared error (MSE). This paper presents a linear aggregation model of valuation to help understand how the minimum MSE valuation rule is affected by various parameters that characterize the economy, and the circumstances under which historical-cost valuation rule yields a (statistically) more precise estimate of the unobserved economic value of firms' assets than the current valuation rule. The analytical findings of the paper are consistent with the reluctance of accountants to depart from historical cost in spite of the existence of low inflation, and in spite of scholarly critiques of this valuation rule by Chambers (1966), Edwards and Bell (1961), Sterling (1970) and others. They are also consistent with the use of specific price indexes by most firms to prepare SFAS 33 disclosures. Several testable implicatons of the results are provided. A direct comparison of the characteristics of valuation rules is complicated by the heterogeneity of the decision contexts in which accounting numbers are used. We use the mean squared error (MSE) between the principal value and its various estimators to rank the latter. Using this criterion, previous simpler models that ignore the presence of measurement errors in price changes have shown that the use of increasingly detailed price indexes yields more precise valuation; current valuation is the most precise valuation rule because it uses the most detailed set of indexes (Sunder 1978). We show that this basic result does not hold when the measurement of price changes is subject to errors. As the magnitude of these measurement errors increases relative to the magnitude of price changes, the most accurate valuation rule requires a less detailed set of price indexes. A key implication of this result is that the existence of inflation or deflation is not sufficient for general-price-level valuation, specific-price-index valuation, or current valuation to dominate historical-cost valuation as an estimator of the economic value of firms' assets. Historical-cost valuation is dominated by others only when the magnitude of price changes are large relative to the errors of measurement in price changes.]