An average annualized return is convenient for comparing returns.
Return.annualized(R, scale = NA, geometric = TRUE)
| R | an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns |
|---|---|
| scale | number of periods in a year (daily scale = 252, monthly scale = 12, quarterly scale = 4) |
| geometric | utilize geometric chaining (TRUE) or simple/arithmetic chaining (FALSE) to aggregate 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.
For simple returns (geometric=FALSE), the formula is: $$\overline{R_{a}} \cdot scale$$
Bacon, Carl. Practical Portfolio Performance Measurement and Attribution. Wiley. 2004. p. 6
data(managers) Return.annualized(managers[,1,drop=FALSE])#> HAM1 #> Annualized Return 0.137532Return.annualized(managers[,1:8])#> HAM1 HAM2 HAM3 HAM4 HAM5 HAM6 #> Annualized Return 0.137532 0.1746569 0.1512147 0.1214798 0.03731645 0.1372755 #> EDHEC LS EQ SP500 TR #> Annualized Return 0.1180134 0.09674533Return.annualized(managers[,1:8],geometric=FALSE)#> HAM1 HAM2 HAM3 HAM4 HAM5 HAM6 #> Annualized Return 0.1334727 0.1697184 0.1493636 0.1322 0.04905974 0.1326563 #> EDHEC LS EQ SP500 TR #> Annualized Return 0.11454 0.1039841