\HeaderA{Return.annualized}{calculate an annualized return for comparing instruments with different length history}{Return.annualized}
\keyword{ts}{Return.annualized}
\keyword{multivariate}{Return.annualized}
\keyword{distribution}{Return.annualized}
\keyword{models}{Return.annualized}
\begin{Description}\relax
An average annualized return is convenient for comparing returns.
\end{Description}
\begin{Usage}
\begin{verbatim}
Return.annualized(R, scale = NA, geometric = TRUE)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{R}] an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns 
\item[\code{scale}] number of periods in a year (daily scale = 252, monthly scale = 12, quarterly scale = 4) 
\item[\code{geometric}] generate geometric (TRUE) or simple (FALSE) returns, default TRUE 
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
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:
\deqn{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:

\deqn{\overline{R_{a}} \cdot scale}{}
\end{Details}
\begin{Value}
annualized return
\end{Value}
\begin{Author}\relax
Peter Carl
\end{Author}
\begin{References}\relax
Bacon, Carl. \emph{Practical Portfolio Performance Measurement and Attribution}. Wiley. 2004. p. 6
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{Return.cumulative}{Return.cumulative}},
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
data(managers)
Return.annualized(managers[,1,drop=FALSE])
Return.annualized(managers[,1:8])
Return.annualized(managers[,1:8],geometric=FALSE)
\end{ExampleCode}
\end{Examples}

