1.6.3 Excess Returns

Excess returns (ER) refers to total investment return that exceeds the rate of return on a security that is 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, described in Total Return Index Values
 denotes the short-term (3-month) risk-free rate at time t.

Since the choice of risk-free security impacts the excess return, EDHECinfra 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 3-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 3-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, described in 1.5.2 Total Investment Return.
 denotes the risk-free rate in market j at time t. 

Mean excess return

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.