A Technical Note on ROE Value Added

In chapter 3, the residual earnings model is written as:

That is correct. But, with the ROE version there is a point to note:

For years after the first year ahead (year 1), ROE is strictly

which is not equal to Expected ROE_t. You might be familiar with this from a statistics course: The expectation of a product (multiplication) of two numbers is not the same as the product of their expectations.

This is just a technical point. We always forecast expected earnings and book value, as in the first residual earnings equation: What will be the book value in years ahead and what will be the earnings that the book value (assets -liabilities) will yield?