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Very interesting research, James. Here are some possible ways to measure hype that would work with negative values:

Nomenclature:

prediction = predicted EPS

actual = actual EPS

abs = absolute value

**Hype as the log of absolute value of the prediction error**

hype = log( abs( prediction – actual) )

**Same thing, but as a fraction of the absolute value of the actual EPS**

hype = log( abs( prediction – actual) / abs(actual ) )

With these definitions, ‘hype’ becomes a general measure of prediction error, which is not necessarily what you want. But as Scott notes, prior to taking the absolute values, you could record the sign of (prediction – actual), and then add it back after taking the log. That way, you distinguish between pessimism and hype and also constrain the spread in the measurement.