Technical Note-Generalized Formula for the Periodic Linear Gradient Series Payment in a Skip Payment Loan with Arbitrary Skips

Formato derived a useful formula of the amount of periodic level (“equal”) payment in a skip payment loan with arbitrary skips using a second-order finite difference equation. Moon rederived Formato's formula using time value of money and also extended Formato's result to the case that periodic payments occur in a geometric-gradient series. We rederived equivalent of these formulas using time value of money. It is suggested that the obtained formulas and their derivations are simpler than previous results. We also extend Formato's result to the case that periodic payments occur in a linear-gradient series.     

Are Trade Size‐Based Inferences About Traders Reliable? Evidence from Institutional Earnings‐Related Trading

The use of observed transaction sizes to differentiate between “small” and “large” investor trading patterns is widespread. A significant concern in such studies is spurious effects attributable to misclassification of transactions, particularly those originating from large investors. Such effects can arise unintentionally, strategically, or endogenously. We examine comprehensive records of a sample of institutional investors (i.e., “large” traders), including their order sizes and overall position changes, to assess the degree to which such misclassifications give rise to spurious inferences about “small” and “large” investor trading activities. Our analysis shows that these institutions are heavily involved in small transaction activity. It also shows that they increase their order sizes substantially in announcement periods relative to nonannouncement periods, presumably as an endogenous response to earnings news. In the immediate earnings announcement period, transaction size‐based inferences about directional trading are quite misleading—producing spurious “small trader” effects and, more surprisingly, erroneous inferences about “large trader” activity.