Calculates the returns of an asset in excess of the given "risk free rate" for the period.
Return.excess(R, Rf = 0)
| R | an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns |
|---|---|
| Rf | risk free rate, in same period as your returns, or as a single digit average |
Ideally, your risk free rate will be for each period you have returns observations, but a single average return for the period will work too.
Mean of the period return minus the period risk free rate $$\overline{(R_{a}-R_{f})}$$
OR
mean of the period returns minus a single numeric risk free rate $$\overline{R_{a}}-R_{f}$$
Note that while we have, in keeping with common academic usage, assumed that the second parameter will be a risk free rate, you may also use any other timeseries as the second argument. A common alteration would be to use a benchmark to produce excess returns over a specific benchmark, as demonstrated in the examples below.
Bacon, Carl. Practical Portfolio Performance Measurement and Attribution. Wiley. 2004. p. 47-52
data(managers) head(Return.excess(managers[,1,drop=FALSE], managers[,10,drop=FALSE]))#> HAM1 > US 3m TR #> 1996-01-31 0.00284 #> 1996-02-29 0.01532 #> 1996-03-31 0.01179 #> 1996-04-30 -0.01338 #> 1996-05-31 0.00317 #> 1996-06-30 -0.00802head(Return.excess(managers[,1,drop=FALSE], .04/12))#> HAM1 > Rf #> 1996-01-31 0.004066667 #> 1996-02-29 0.015966667 #> 1996-03-31 0.012166667 #> 1996-04-30 -0.012433333 #> 1996-05-31 0.004266667 #> 1996-06-30 -0.007233333head(Return.excess(managers[,1:6], managers[,10,drop=FALSE]))#> HAM1 > US 3m TR HAM2 > US 3m TR HAM3 > US 3m TR HAM4 > US 3m TR #> 1996-01-31 0.00284 NA 0.03034 0.01764 #> 1996-02-29 0.01532 NA 0.03112 0.01552 #> 1996-03-31 0.01179 NA 0.02209 -0.01351 #> 1996-04-30 -0.01338 NA 0.04062 0.01932 #> 1996-05-31 0.00317 NA 0.03087 -0.00163 #> 1996-06-30 -0.00802 NA -0.03442 -0.00602 #> HAM5 > US 3m TR HAM6 > US 3m TR #> 1996-01-31 NA NA #> 1996-02-29 NA NA #> 1996-03-31 NA NA #> 1996-04-30 NA NA #> 1996-05-31 NA NA #> 1996-06-30 NA NAhead(Return.excess(managers[,1,drop=FALSE], managers[,8,drop=FALSE]))#> HAM1 > SP500 TR #> 1996-01-31 -0.0266 #> 1996-02-29 0.0100 #> 1996-03-31 0.0059 #> 1996-04-30 -0.0238 #> 1996-05-31 -0.0182 #> 1996-06-30 -0.0077