# 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:

$$Product\text{}price=\frac{{\displaystyle \sum commissions}}{\left(\raisebox{1ex}{$\sum proceeds$}\!\left/ \!\raisebox{-1ex}{$CapEx\text{}IPI$}\right.\right)}$$

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,

$CapEx\text{}IPI$ is the implicit price index for Gross Fixed Capital Formation for the same year (currently 2012 = 100).

Dividing the nominal proceeds by the $CapEx\text{}IPI$ 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:

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

Basic formula for Paasche price index:

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

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

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

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