Averaging Multiples: The Harmonic Mean

Analysts often use the harmonic mean and the weighted harmonic mean to average a group of multiples. The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals.

X = n/(Σ1/X_i)

If a set of weight w₁, w₂, ..., w_n is associated to the dataset x₁, x₂, ..., x_n, the weighted harmonic mean defined by:

The harmonic mean is the preferable method for averaging multiples, such as the price/earning ratio, in which price is in the numerator. If these ratios are averaged using an arithmetic mean (a common error), high data points are given greater weights than low data points. The harmonic mean, on the other hand, gives equal weight to each data point.

In general the harmonic mean is less than the arithmetic mean.

The Use of Stock Screens in Investment Management

Screening is the application of a set of criteria to reduce an investment universe to a smaller set of investments and is a part of many stock selection disciplines. In general, limitations of such screens include the lack of control in vendor-provided data of the calculation of important inputs (such as EPS) and the absence of qualitative factors.