[BETA] Fortnightly

Financial experts often depart from standard financial principles and practices in recommending the appropriate rate of return for public utilities. But ratemaking draws from many fields, not just finance; there may be good reasons for some alterations. In other cases, however, analysts are unaware of violating principles. This article discusses the tendency of some analysts to use historic averages of certain financial variables, as opposed to current spot values, in

return-on-equity (ROE) analyses. More specifically, the question centers on the choice of dividend and bond yields in cost-of-equity models.

The discounted cash flow (DCF) model follows this general form:

Required Return = DIVIDEND YIELD + Expected Dividend Growth

To estimate the required ROE with this model, the analyst must select a dividend yield as well as a growth rate.

Similarly, the risk premium model involves selecting a bond yield and an expected risk premium estimate:

Required Return = BOND YIELD + Expected Risk Premium

Ideally, when using either model, it would be helpful to know what the dividend or bond yield will be in the near future, since regulators are setting rates that will be in effect for the indefinite future. Unfortunately, professional forecasts of financial variables are notoriously unreliable and appear to be getting worse, not better, over time.1 In keeping with these financial research findings, I develop yield estimates based on actual rather than forecasted data.

There are two basic choices for the yield: 1) averages of historic yields (such as a 12-month average), and 2) the current or spot yield (such as today's dividend yield).

Statistical Characteristics of Dividend and Bond Yields

Financial economists determined long ago that forecasts based on spot data were in many cases better predictors of future financial variables than forecasts based on any average of historic yields. As time went on, researchers further noted that certain financial data are generated by what are known as nonstationary processes: A nonstationary series does not tend to revert to a fixed mean or average over time. In their pioneering work on time series analysis in the late 60's and early 70's, Box and Jenkins noted that the data used in business applications is especially likely to exhibit this tendency:

"[F]orecasting has been of particular importance in industry, business, and economics, where many time series are often better represented as nonstationary, and in particular, as having no natural mean."2

The absence of any natural mean for the nonstationary series used in many business applications proves that historic averages provide no useful information about future values of dividends.

Just to be clear, while many data series used in business applications are nonstationary, one should not assume that all data series exhibit this characteristic. Many do not. For example, to estimate the likely dividend payout ratios for utilities, averages of past ratios may be very helpful in predicting future values.3

The "random walk" model (a nonstationary, non-mean-reverting process) is often used to approximate the behavior of bond yields and dividend yields:4

Yieldt+1 = Yieldt + et+1

Elegant in its simplicity, the model indicates that the forecast of tomorrow's yield is