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
Details
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:
$$\overline{R_{a}} \cdot scale$$
References
Bacon, Carl. Practical Portfolio Performance
Measurement and Attribution. Wiley. 2004. p. 6