  The Hayashi-Yoshida (\HY)-estimator exhibits an intrinsic, telescoping
property that leads to an often overlooked computational bias, which we
denote,formulaic or intrinsic bias. This formulaic bias results in data loss by
cancelling out potentially relevant data points, the nonextant data points.
This paper attempts to formalize and quantify the data loss arising from this
bias. In particular, we highlight the existence of nonextant data points via a
concrete example, and prove necessary and sufficient conditions for the
telescoping property to induce this type of formulaic bias.Since this type of
bias is nonexistent when inputs, i.e., observation times, $\Pi^{(1)}
:=(t_i^{(1)})_{i=0,1,\ldots}$ and $\Pi^{(2)} :=(t_j^{(2)})_{j=0,1,\ldots}$, are
synchronous, we introduce the (a,b)-asynchronous adversary. This adversary
generates inputs $\Pi^{(1)}$ and $\Pi^{(2)}$ according to two independent
homogenous Poisson processes with rates a>0 and b>0, respectively. We address
the foundational questions regarding cumulative minimal (or least) average data
point loss, and determine the values for a and b. We prove that for equal rates
a=b, the minimal average cumulative data loss over both inputs is attained and
amounts to 25\%. We present an algorithm, which is based on our theorem, for
computing the exact number of nonextant data points given inputs $\Pi^{(1)}$
and $\Pi^{(2)}$, and suggest alternative methods. Finally, we use simulated
data to empirically compare the (cumulative) average data loss of the
(\HY)-estimator.
