# 2.6.3 Excess returns

Excess returns (ER) refer to the total investment return that exceeds the rate of return on a security perceived to be risk free.

where:

denotes the excess return of the index at time *t*.

denotes the total return of the index at time *t*.

denotes the short-term (three-month) risk-free rate at time *t*.

Since the choice of risk-free security impacts the excess return, *Scientific Infra & Private Assets* uses two different methods depending on the reporting currency of the index.

## Local currency indices

When indices are computed to report only local returns (ignoring the effect of foreign exchange movements on returns for a given investor), the excess return of the index consists of a weighted average of the individual constituents' excess returns, given the three-month risk-free rate in each country included in the index. Hence, the excess return is written as:

where:

denotes the local excess return of the index at time *t*.*n* denotes the number of constituents in the index.

denotes the weight of constituent *i* at time *t-1.*

denotes the excess return of constituent *i* at time *t.*

## Single currency indices

If the index is reported in currency *j (e.g. USD, CAD, GBP, JPY, EUR, or AUD) *then the reference three-month risk-free rate is that of the reporting currency.

where:

denotes the excess return of the index reported in currency *j* at time *t.*

denotes the total return of the index at time *t*.

denotes the risk-free rate in market *j* at time *t.*

## Mean excess return

The mean excess return is the average quarterly excess return of the index where:

denotes the mean excess return of the index over the horizon.*t* denotes the number of periods in the time horizon.

denotes the excess return of the index at time *t.*