APPENDIX A

With the passage of the Investor and Capital Markets Relief Act, Congress has established a target amount of monies to be collected from fees charged to issuers based on the value of their registrations. This appendix provides the formula for determining such fees, which the Commission adjusts annually. Congress has mandated that the Commission determine these fees based on the "aggregate maximum offering prices," which measures the aggregate dollar amount of securities registered with the SEC over the course of the year. In order to maximize the likelihood that the amount of monies targeted by Congress will be collected, the fee rate must be set to reflect projected aggregate maximum offering prices. As a percentage, the fee rate equals the ratio of the target amounts of monies to the projected aggregate maximum offering prices.

For 2004, the Commission has estimated the aggregate maximum offering prices by projecting forward the trend established in the previous decade. More specifically, an ARIMA model was used to forecast the value of the aggregate maximum offering prices for months subsequent to March 2003, the last month for which the Commission has data on the aggregate maximum offering prices.

The following sections describe this process in detail.

A. Baseline estimate of the aggregate maximum offering prices for fiscal year 2004.

First, calculate the aggregate maximum offering prices (AMOP) for each month in the sample (March 1993 - March 2003). Next, calculate the percentage change in the AMOP from month-to-month.

Model the monthly percentage change in AMOP as a first order moving average process. The moving average approach allows one to model the effect that an exceptionally high (or low) observation of AMOP tends to be followed by a more "typical" value of AMOP.

Use the estimated moving average model to forecast the monthly percent change in AMOP. These percent changes can then be applied to obtain forecasts of the total dollar value of registrations. The following is a more formal (mathematical) description of the procedure:

1. Begin with the monthly data for AMOP. The sample spans ten years, from March 1993 to March 2003. There are 6 months in the sample for which the data are ommited because of the impact of extraordinary events (e.g., the 1995 government shutdown).

2. Divide each month's AMOP (column C) by the number of trading days in that month (column B) to obtain the average daily AMOP (AAMOP, column D).

3. For each month t, the natural logarithm of AAMOP is reported in column E.

4. Calculate the change in log(AAMOP) from the previous month as
   _t = log (AAMOP_t) - log(AAMOP_t-1). This approximates the percentage change.

5. Estimate the first order moving average model _t = + e_t-1 + e_t, where e_t denotes the forecast error for month t. The forecast error is simply the difference between the one-month ahead forecast and the actual realization of _t. The forecast error is expressed as e_t = _t - - e_t-1. The model can be estimated using standard commercially available software such as SAS or Eviews. Using least squares, the estimated parameter values are =0.01048 and =−0.76442.

6. For the month of April 2003, forecast _{t = 4/03} = + e_{t = 3/03}. For all subsequent months, forecast _t = .

7. Calculate forecasts of log(AAMOP). For example, the forecast of log(AAMOP) for June 2002 is given by FLAAMOP _{t = 6/02} = log(AAMOP _{t = 3/02}) + _{t = 4/02} + _{t = 5/02} + _{t = 6/02}.

8. Under the assumption that e_t is normally distributed, the n-step ahead forecast of AAMOP is given by exp(FLAAMOP_t + _n²/2), where _n denotes the standard error of the n-step ahead forecast.

9. For June 2003, this gives a forecast AAMOP of $12.8 Billion (Column I), and a forecast AMOP of $269.5 Billion (Column J).

10. Iterate this process through September 2004 to obtain a baseline estimate of the aggregate maximum offering prices for fiscal year 2004 of $3,684,909,630,358.

B. Using the forecasts from A to calculate the new fee rate.

1. Using the data from Table A, estimate the aggregate maximum offering prices between 10/1/03 and 9/30/04 to be $3,684,909,630,358.

2. The rate necessary to collect the target $467,000,000 in fee revenues set by Congress is then calculated as: $467,000,000 ÷ $3,684,909,630,358 = 0.00012670 (or $126.70 per million.).

Table B: Estimation of baseline of the aggregate maximum offering prices.

http://www.sec.gov/rules/other/33-8225a.htm