# Technical supplement for the Investment Banking Services Price Index

Release date: July 8, 2019

## Overview

The annual Investment Banking Services Price Index (IBSPI) measures the change in prices for a portion of the activity of the Investment Banking Industry. Specifically, the index focuses on the underwriting of new issues of debt and equity which account for the bulk of industry output.Note 1 The primary purpose of the IBSPI is to deflate output in the Canadian System of Macroeconomic Accounts for underwriting activities by investment banks. The release of the 2018 IBSPI marks the implementation of methodological changes in the calculation of the index. This document describes the updated methodology.

## Data

The IBSPI is derived by combining data from two sources:

• FP Infomart©,Note 2 (underwriting transaction information with commissions through administrative data sources).
• The implicit price index for Gross Fixed Capital Formation, which is produced by the Macroeconomic Accounts Branch (MEAB), and is obtained from the Common Output Data Repository (CODR).Note 3

## Methodology

Transactions are placed into seven different groups (products) in order to maintain a certain level of homogeneity while still having enough observations to calculate unit prices for each product.Note 4 These seven products are: corporate ownership non-resource sector, corporate ownership resource sector, corporate income trusts, corporate structured funds, corporate debt, corporate preferred shares, and government debt. Government debt data is only available beginning in 2017, within which federal government debt securities (auctioned) and non-syndicated deals (based on reverse inquiries with very low commission) are excluded.

Furthermore, for the securities issued by corporate structured funds, only transactions of limited partnership units, trust units and capital shares are retained in this group. All other transactions (such as common shares and preferred shares) are placed into one of the other six securities groups as these transactions align better with these concepts.

The price for each product is defined as the following:

Where:

$\sum commissions$  is the sum of all commissions for the transactions in the sample within a given year,

$\sum proceeds$ Note 5 is the sum of all  proceeds for the transactions in the sample within a given year,

is the implicit price index for Gross Fixed Capital Formation for the same year (currently 2012 = 100).

Dividing the nominal proceeds by the in the same period holds the purchasing power of proceeds constant over time. Each product's commission revenue is used as weights to aggregate prices into an index. With the 2018 release, the index is calculated and published using three different index number formulas:

Basic formula for Laspeyres price index:

${I}_{Laspeyres}^{}=\frac{{\sum }_{i=0}^{n}{p}_{t}^{i}\ast {q}_{0}^{i}}{{\sum }_{i=0}^{n}{p}_{0}^{i}\ast {q}_{0}^{i}}$

Basic formula for Paasche price index:

${I}_{Paasche}^{}=\frac{{\sum }_{i=0}^{n}{p}_{t}^{i}\ast {q}_{t}^{i}}{{\sum }_{i=0}^{n}{p}_{0}^{i}\ast {q}_{t}^{i}}$

Basic formula for Fisher price index (Geometric average of Laspeyres and Paasche):

${I}_{Fisher}^{}=\sqrt{\frac{{\sum }_{i=0}^{n}{p}_{t}^{i}\ast {q}_{0}^{i}}{{\sum }_{i=0}^{n}{p}_{0}^{i}\ast {q}_{0}^{i}}\ast \frac{{\sum }_{i=0}^{n}{p}_{t}^{i}\ast {q}_{t}^{i}}{{\sum }_{i=0}^{n}{p}_{0}^{i}\ast {q}_{t}^{i}}}$

where: ${p}_{t}^{i}$ is the price for product $i$ in period $t\text{,}$ and ${q}_{t}^{i}$ is the quantity (proceeds adjusted by in period $t\text{)}$ for product $i$ in period $t\text{.}$

The Fisher index is an example of a superlative index and it is the preferred measure of price change when weights are volatile, as is the case with the IBSPI.

## Limitations of the IBSPI

One limitation of the Investment Banking Services Price Index is that it does not include corporate advisory services (mainly mergers and acquisitions, which is about one third of total output) since it is not required by regulation to disclose commission information for these types of transactions. If warranted, data from investment banks would need to be obtained, either by survey or other means in order to measure these activities in the future. One of the biggest challenges faced in the measurement of this sector, comes in the ability to distribute the underwriting deals into their correct product groupings. Deals for the same type of securities can vary period to period in terms of characteristics, and in the case where “sweeteners”Note 6 are added to attract underwriters and investors, it can be difficult to measure real prices and maintain a level of comparability over time. Therefore, research into the industry and analysis on the different types of transactions will continue and the methodology will be updated to reflect the evolution of investment banking sector.

## Notes

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