An average annualized excess return is convenient for comparing excess returns.
Return.annualized.excess(Rp, Rb, scale = NA, geometric = TRUE)
| Rp | an xts, vector, matrix, data frame, timeSeries or zoo object of portfolio returns |
|---|---|
| Rb | an xts, vector, matrix, data frame, timeSeries or zoo object of benchmark returns |
| scale | number of periods in a year (daily scale = 252, monthly scale = 12, quarterly scale = 4) |
| geometric | generate geometric (TRUE) or simple (FALSE) excess returns, default TRUE |
Annualized returns are useful for comparing two assets. To do so, you must scale your observations to an annual scale by raising the compound return to the number of periods in a year, and taking the root to the number of total observations: $$prod(1+R_{a})^{\frac{scale}{n}}-1=\sqrt[n]{prod(1+R_{a})^{scale}}- 1$$
where scale is the number of periods in a year, and n is the total number of periods for which you have observations.
Finally having annualized returns for portfolio and benchmark we can compute annualized excess return as difference in the annualized portfolio and benchmark returns in the arithmetic case: $$er = R_{pa} - R_{ba}$$
and as a geometric difference in the geometric case: $$er = \frac{(1 + R_{pa})}{(1 + R_{ba})} - 1$$
Bacon, Carl. Practical Portfolio Performance Measurement and Attribution. Wiley. 2004. p. 206-207
data(managers) Return.annualized.excess(Rp = managers[,1], Rb = managers[,8])#> HAM1 #> Annualized Return 0.03718883