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

ER_{t} = TR_{t} - R_{f,t} |

where:

ER_{t} denotes the excess return of the index at time *t*.

TR_{t} denotes the total return of the index at time *t*, described in Total Return Index Values

R_{f,t} 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:

ER_{local,t} = \sum_{i=1}^{n} (w_{i,t-1} \times ER_{i,t}) |

where:

ER_{local,t} denotes the local excess return of the index at time t*n* denotes the number of constituents in the index

w_{i,t-1} denotes the weight of constituent *i* at time *t-1*

ER_{i,t} 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.

ER_{j,t} = TR_{t} - R_{f\_j,t} |

where:

ER_{j,t} denotes the excess return of the index reported in currency *j* at time *t.*

TR_{t} denotes the total return of the index at time *t*, described in Total Investment Return.

R_{f\_j,t} 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

\bar{ER_{T}} = \frac{1}{T}\sum_{t=1}^{T} ER_{t} |

where:

\bar{ER_{T}} denotes the mean excess return of the index over the horizon.*t* denotes the number of periods in the time horizon.

ER_{t} denotes the excess return of the index at time *t.*