# 1.6.18 Factor Returns

JUNE 2024

In *Scientific Infra and Private Assets* asset pricing methodology, we decompose the excess expected return of an asset into multiple factors: size, leverage, profit, and investment. The exposures to each of those factors determine the returns that an asset can generate. By using long-short factor mimicking portfolios, we attribute the returns of infrastructure assets due to each of these factors.

Investors can use these factors for return attribution of their infrastructure portfolio, or in factor investing by selecting assets that have high/low exposures to each of these factors. The calculations of the individual factor returns are described below.

## Size Factor Return (SMB)

SMB_{(Leverage)} = 1/3 (Small Low Leverage + Small Medium Leverage + Small High Leverage) - 1/3 (Big Low Leverage + Big Medium Leverage + Big High Leverage)

SMB_{(}_{Profit}_{)} = 1/3 (Small Low Profit + Small Medium Profit + Small High Profit) - 1/3 (Big Low Profit + Big Medium Profit + Big High Profit)

SMB_{(Investment)} = 1/3 (Small Low Investment + Small Medium Investment + Small High Investment) - 1/3 (Big Low Investment + Big Medium Investment + Big High Investment)

SMB = 1/3 (SMB_{(Leverage) }+ SMB_{(Profitability) }+ _{ }SMB_{(Investment)})

where:

Small: Total Assets ≤ Median Total Assets

Big: Total assets > Median Total Assets

Low Leverage: Leverage

Medium Leverage: Median Leverage > Leverage ≤ 80^{th} Percentile Leverage

High Leverage: Leverage > 80^{th} Percentile Leverage

Low Profit: Profit ≤ 20^{th} Percentile Profit

Medium Profit: 20^{th} Percentile Profit > Profit ≤ 80^{th} Percentile Profit

High Profit: Profit > 20^{th} Percentile Profit

Low Investment: Investment ≤ Median Investment

Medium Investment: Median Investment > Investment ≤ 20^{th} Percentile Investment

High Investment: Investment > 80^{th} Percentile Profit

## Leverage Factor Return (HML_{(Leverage)})

HML_{(Leverage) }= 1/2 (Small High Leverage + Big High Leverage) - 1/2 (Small Low Leverage + Big Low Leverage)

where:

Small: Total Assets ≤ Median Total Assets

Big: Total assets > Median Total Assets

Low Leverage: Leverage ≤ Median Leverage

High Leverage: Leverage > Median Leverage

## Investment Factor Return (HML_{(Investment)})

HML_{(Investment) }= 1/2 (Small High Investment + Big High Investment) - 1/2 (Small Low Investment + Big Low Investment)

where:

Small: Total Assets ≤ Median Total Assets

Big: Total assets > Median Total Assets

Low Investment: Investment ≤ Median Investment

High Investment: Investment > Median Investment

## Profit Factor Return (HML_{(Profit)})

HML_{(Profit) }= 1/2 (Small High Profit + Big High Profit) - 1/2 (Small Low Profit + Big Low Profit)

where:

Small: Total Assets ≤ Median Total Assets

Big: Total assets > Median Total Assets

Low Profit: Profit ≤ Median Profit

High Profit: Profit > Median Profit

## Market Factor Return

Market Factor Return = Average return across all companies