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:

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.