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# 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, described in Total Return Index Values.
$//$ denotes the short-term (three-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 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, described in Total Investment Return.
$//$ 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.

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