On volatile growth: Simple fitting of exponential functions taking into account values of every observation with any signs, applied to readily calculate a novel covariance-invariant CAGR

Abstract

The commonly used compound annual growth rate (Formula presented.) does not consider volatility, and its calculation fails for time series beginning or terminating with a zero or negative value, which may be the case for a company’s earnings history. Thus, a modification of the standard definition is proposed, derived from a covariance-invariant mapping of observations to a two-parameter exponential model. The novel growth rate is called “covariance-invariant (Formula presented.) “, which becomes (Formula presented.) for the special case of steady growth at a constant rate. It can be obtained using different options such as a chart, look-up table or formula. Further, the extension of the model by an additive constant may be used if negative values dominate. The approach is viewed as easy to apply as the log-linear model but with a superior performance. Compared to nonlinear least-squares regression, unique solutions can be obtained that allow a rather quick calculation.