[Returnanalytics-commits] r2140 - pkg/PortfolioAnalytics/sandbox/attribution/man
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Tue Jul 10 01:54:03 CEST 2012
Author: ababii
Date: 2012-07-10 01:54:02 +0200 (Tue, 10 Jul 2012)
New Revision: 2140
Modified:
pkg/PortfolioAnalytics/sandbox/attribution/man/Attribution.Rd
pkg/PortfolioAnalytics/sandbox/attribution/man/Attribution.geometric.Rd
pkg/PortfolioAnalytics/sandbox/attribution/man/Attribution.levels.Rd
pkg/PortfolioAnalytics/sandbox/attribution/man/AttributionFixedIncome.Rd
pkg/PortfolioAnalytics/sandbox/attribution/man/Carino.Rd
pkg/PortfolioAnalytics/sandbox/attribution/man/Conv.option.Rd
pkg/PortfolioAnalytics/sandbox/attribution/man/DaviesLaker.Rd
pkg/PortfolioAnalytics/sandbox/attribution/man/Frongello.Rd
pkg/PortfolioAnalytics/sandbox/attribution/man/Grap.Rd
pkg/PortfolioAnalytics/sandbox/attribution/man/Menchero.Rd
pkg/PortfolioAnalytics/sandbox/attribution/man/Return.annualized.excess.Rd
Log:
- update: corrected mistakes with pdf conversion
Modified: pkg/PortfolioAnalytics/sandbox/attribution/man/Attribution.Rd
===================================================================
--- pkg/PortfolioAnalytics/sandbox/attribution/man/Attribution.Rd 2012-07-09 17:44:19 UTC (rev 2139)
+++ pkg/PortfolioAnalytics/sandbox/attribution/man/Attribution.Rd 2012-07-09 23:54:02 UTC (rev 2140)
@@ -1,217 +1,207 @@
-\name{Attribution}
-\alias{Attribution}
-\title{performs arithmetic attribution}
-\usage{
- Attribution(Rp, wp, Rb, wb, wpf = NA, wbf = NA, S = NA,
- F = NA, Rpl = NA, Rbl = NA, Rbh = NA, bf = FALSE,
- method = c("none", "top.down", "bottom.up"),
- linking = c("carino", "menchero", "grap", "frongello", "davies.laker"),
- geometric = FALSE, adjusted = FALSE)
-}
-\arguments{
- \item{Rp}{T x n xts, data frame or matrix of portfolio
- returns}
-
- \item{wp}{vector, xts, data frame or matrix of portfolio
- weights}
-
- \item{Rb}{T x n xts, data frame or matrix of benchmark
- returns}
-
- \item{wb}{vector, xts, data frame or matrix of benchmark
- weights}
-
- \item{method}{Used to select the priority between
- allocation and selection effects in arithmetic
- attribution. May be any of: \itemize{ \item none -
- present allocation, selection and interaction effects
- independently, \item top.down - the priority is given to
- the sector allocation. Interaction term is combined with
- the security selection effect, \item bottom.up - the
- priority is given to the security selection. Interaction
- term is combined with the sector allocation effect}. By
- default "none" is selected}
-
- \item{wpf}{vector, xts, data frame or matrix with
- portfolio weights of currency forward contracts}
-
- \item{wbf}{vector, xts, data frame or matrix with
- benchmark weights of currency forward contracts}
-
- \item{S}{(T+1) x n xts, data frame or matrix with spot
- rates. The first date should coincide with the first date
- of portfolio returns}
-
- \item{F}{(T+1) x n xts, data frame or matrix with forward
- rates. The first date should coincide with the first date
- of portfolio returns}
-
- \item{Rpl}{xts, data frame or matrix of portfolio returns
- in local currency}
-
- \item{Rbl}{xts, data frame or matrix of benchmark returns
- in local currency}
-
- \item{Rbh}{xts, data frame or matrix of benchmark returns
- hedged into the base currency}
-
- \item{bf}{TRUE for Brinson and Fachler and FALSE for
- Brinson, Hood and Beebower arithmetic attribution}
-
- \item{linking}{Used to select the linking method to
- present the multi-period summary of arithmetic
- attribution effects. May be any of: \itemize{ \item
- carino - logarithmic linking coefficient method, \item
- menchero - Menchero's smoothing algorithm, \item grap -
- linking approach developed by GRAP, \item frongello -
- Frongello's linking method \item davies.laker - Davies
- and Laker's linking method By default Carino linking is
- selected}
-
- \item{geometric}{TRUE/FALSE, whether to use geometric or
- arithmetic excess returns for the attribution analysis}
-
- \item{adjusted}{TRUE/FALSE, whether to show original or
- smoothed attribution effects for each period}
-}
-\value{
- returns a list with the following components: excess
- returns with annualized excess returns over all periods,
- attribution effects (allocation, selection and
- interaction)
-}
-\description{
- Performance attribution analysis. Portfolio performance
- measured relative to a benchmark gives an indication of
- the value-added by the portfolio. Equipped with weights
- and returns of portfolio segments, we can dissect the
- value-added into useful components. This function is
- based on the sector-based approach to the attribution.
- The workhorse is the Brinson model that explains the
- arithmetic difference between portfolio and benchmark
- returns. That is it breaks down the arithmetic excess
- returns at one level. If returns and weights are
- available at the lowest level (e.g. for individual
- instruments), the aggregation up to the chosen level from
- the hierarchy can be done using Return.level function.
- The attribution effects can be computed for several
- periods. The multi-period summary is obtained using one
- of linking methods: Carino, Menchero, GRAP, Frongello. It
- also allows to break down the geometric excess returns,
- which link naturally over time. Finally, it annualizes
- arithmetic and geometric excess returns similarly to the
- portfolio and/or benchmark returns annualization.
-}
-\details{
- The arithmetic excess returns are decomposed into the sum
- of allocation, selection and interaction effects across
- \deqn{n} sectors:
- \deqn{r-b=\overset{n}{\underset{i=1}{\sum}}\left(A_{i}+S_{i}+I_{i}\right)}
- The arithmetic attribution effects for the category
- \deqn{i} are computed as suggested in the Brinson, Hood
- and Beebower (1986): \deqn{A_{i}=(w_{pi}-w_{bi})\times
- R_{bi}} - allocation effect
- \deqn{S_{i}=w_{pi}\times(R_{pi}-R_{bi})} - selection
- effect \deqn{I_{i}=(w_{pi}-w_{bi})\times(r_{i}-b_{i})} -
- interaction effect \deqn{r} - total portfolio returns
- \deqn{b} - total benchmark returns \deqn{w_{pi}} -
- weights of the category \deqn{i} in the portfolio
- \deqn{w_{bi}} - weigths of the category \deqn{i} in the
- benchmark \deqn{R_{pi}} - returns of the portfolio
- category \deqn{i} \deqn{R_{bi}} - returns of the
- benchmark category \deqn{i} If Brinson and Fachler (1985)
- is selected the allocation effect differs:
- \deqn{A_{i}=(w_{pi}-w_{bi})\times (R_{bi} - b)} Depending
- on goals we can give priority to the allocation or to the
- selection effects. If the priority is given to the sector
- allocation the interaction term will be combined with the
- security selection effect (top-down approach). If the
- priority is given to the security selection, the
- interaction term will be combined with the
- asset-allocation effect (bottom-up approach). Usually we
- have more than one period. In that case individual
- arithmetic attribution effects should be adjusted using
- linking methods. Adjusted arithmetic attribution effects
- can be summed up over time to provide the multi-period
- summary:
- \deqn{r-b=\overset{T}{\underset{t=1}{\sum}}\left(A_{t}'+S_{t}'+I_{t}'\right)}
- , where \deqn{T} - number of periods; prime stands for
- the adjustment. The geometric attribution effects do not
- suffer from the linking problem. Moreover we don't have
- the interaction term. For more details about the
- geometric attribution see the documentation to
- \code{link{Attribution.geometric}} Finally, arithmetic
- annualized excess returns are computed as the arithmetic
- difference between annualised portfolio and benchmark
- returns: \deqn{AAER=r_{a}-b_{a}}; the geometric
- annualized excess returns are computed as the geometric
- difference between annualized portfolio and benchmark
- returns: \deqn{GAER=\frac{1+r_{a}}{1+b_{a}}-1} In the
- case of multi-currency portfolio, the currency return,
- currency surprise and forward premium should be
- specified. The multi-currency arithmetic attribution is
- handled following Ankrim and Hensel (1992). Currency
- returns are decomposed into the sum of the currency
- surprise and the forward premium: \deqn{R_{ci} = R_{cei}
- + R_{fpi}}, where \deqn{R_{cei} = \frac{S_{i}^{t+1} -
- F_{i}^{t+1}}{S_{i}^{t}} \deqn{R_{fpi} =
- \frac{F_{i}^{t+1}}{S_{i}^{t}} - 1} \deqn{S_{i}^{t}} -
- stop rate for asset i at time t \deqn{F_{i}^{t}} -
- forward rate for asset i at time t Excess returns are
- decomposed into the sum of allocation, selection and
- interaction effects as in the standard Brinson model:
- \deqn{r-b=\overset{n}{\underset{i=1}{\sum}}\left(A_{i}+S_{i}+I_{i}\right)}
- However the allocation effect is computed taking into
- account currency effects:
- \deqn{A_{i}=(w_{pi}-w_{bi})\times (R_{bi} - R_{ci} -
- R_{l})} - allocation \deqn{R_{l} =
- \overset{n}{\underset{i=1}{\sum}}w_{bi}\times(R_{bi}-R_{ci})}
- - benchmark return adjusted for currecy. The contribution
- from currency is analogous to asset allocation:
- \deqn{C_{i} = (w_{pi} - w_{bi}) \times (R_{cei} - e) +
- (w_{pfi} - w_{bfi}) \times (R_{fi} - e)} where \deqn{e =
- \overset{n}{\underset{i=1}{\sum}}w_{bi}\times R_{cei}}
- The final term, forward premium, is also analogous to the
- asset allocation: \deqn{R_{fi} = (w_{pi} - w_{bi}) \times
- (R_{fpi} - d)} where \deqn{d =
- \overset{n}{\underset{i=1}{\sum}}w_{bi}\times R_{fpi}}
- \deqn{R_{fpi}} - forward premium
-}
-\examples{
-data(attrib)
-Attribution(Rp, wp, Rb, wb, method = "top.down", linking = "carino")
-}
-\author{
- Andrii Babii
-}
-\references{
- Ankrim, E. and Hensel, C. \emph{Multi-currency
- performance attribution}.Russell Research Commentary.
- November 2002
-
- Bacon, C. \emph{Practical Portfolio Performance
- Measurement and Attribution}. Wiley. 2004. Chapter 5, 6,
- 8
-
- Christopherson, Jon A., Carino, David R., Ferson, Wayne
- E. \emph{Portfolio Performance Measurement and
- Benchmarking}. McGraw-Hill. 2009. Chapter 18-19
-
- Brinson, G. and Fachler, N. (1985) \emph{Measuring non-US
- equity portfolio
-
- Gary P. Brinson, L. Randolph Hood, and Gilbert L.
- Beebower, \emph{Determinants of Portfolio Performance},
- Financial Analysts Journal,
-
- Karnosky, D. and Singer, B. \emph{Global asset management
- and performance attribution. The Research Foundation of
- the Institute of Chartered Financial Analysts}. February
- 1994.
-}
-\seealso{
- \code{\link{Attribution.levels}},
- \code{\link{Attribution.geometric}}
-}
-\keyword{attribution}
-
+\name{Attribution}
+\alias{Attribution}
+\title{performs arithmetic attribution}
+\usage{
+ Attribution(Rp, wp, Rb, wb, wpf = NA, wbf = NA, S = NA,
+ F = NA, Rpl = NA, Rbl = NA, Rbh = NA, bf = FALSE,
+ method = c("none", "top.down", "bottom.up"),
+ linking = c("carino", "menchero", "grap", "frongello", "davies.laker"),
+ geometric = FALSE, adjusted = FALSE)
+}
+\arguments{
+ \item{Rp}{T x n xts, data frame or matrix of portfolio
+ returns}
+
+ \item{wp}{vector, xts, data frame or matrix of portfolio
+ weights}
+
+ \item{Rb}{T x n xts, data frame or matrix of benchmark
+ returns}
+
+ \item{wb}{vector, xts, data frame or matrix of benchmark
+ weights}
+
+ \item{method}{Used to select the priority between
+ allocation and selection effects in arithmetic
+ attribution. May be any of: \itemize{ \item none -
+ present allocation, selection and interaction effects
+ independently, \item top.down - the priority is given to
+ the sector allocation. Interaction term is combined with
+ the security selection effect, \item bottom.up - the
+ priority is given to the security selection. Interaction
+ term is combined with the sector allocation effect}. By
+ default "none" is selected}
+
+ \item{wpf}{vector, xts, data frame or matrix with
+ portfolio weights of currency forward contracts}
+
+ \item{wbf}{vector, xts, data frame or matrix with
+ benchmark weights of currency forward contracts}
+
+ \item{S}{(T+1) x n xts, data frame or matrix with spot
+ rates. The first date should coincide with the first date
+ of portfolio returns}
+
+ \item{F}{(T+1) x n xts, data frame or matrix with forward
+ rates. The first date should coincide with the first date
+ of portfolio returns}
+
+ \item{Rpl}{xts, data frame or matrix of portfolio returns
+ in local currency}
+
+ \item{Rbl}{xts, data frame or matrix of benchmark returns
+ in local currency}
+
+ \item{Rbh}{xts, data frame or matrix of benchmark returns
+ hedged into the base currency}
+
+ \item{bf}{TRUE for Brinson and Fachler and FALSE for
+ Brinson, Hood and Beebower arithmetic attribution}
+
+ \item{linking}{Used to select the linking method to
+ present the multi-period summary of arithmetic
+ attribution effects. May be any of: \itemize{\item carino
+ - logarithmic linking coefficient method \item menchero -
+ Menchero's smoothing algorithm \item grap - linking
+ approach developed by GRAP \item frongello - Frongello's
+ linking method \item davies.laker - Davies and Laker's
+ linking method} By default Carino linking is selected}
+
+ \item{geometric}{TRUE/FALSE, whether to use geometric or
+ arithmetic excess returns for the attribution analysis}
+
+ \item{adjusted}{TRUE/FALSE, whether to show original or
+ smoothed attribution effects for each period}
+}
+\value{
+ returns a list with the following components: excess
+ returns with annualized excess returns over all periods,
+ attribution effects (allocation, selection and
+ interaction)
+}
+\description{
+ Performance attribution analysis. Portfolio performance
+ measured relative to a benchmark gives an indication of
+ the value-added by the portfolio. Equipped with weights
+ and returns of portfolio segments, we can dissect the
+ value-added into useful components. This function is
+ based on the sector-based approach to the attribution.
+ The workhorse is the Brinson model that explains the
+ arithmetic difference between portfolio and benchmark
+ returns. That is it breaks down the arithmetic excess
+ returns at one level. If returns and weights are
+ available at the lowest level (e.g. for individual
+ instruments), the aggregation up to the chosen level from
+ the hierarchy can be done using Return.level function.
+ The attribution effects can be computed for several
+ periods. The multi-period summary is obtained using one
+ of linking methods: Carino, Menchero, GRAP, Frongello. It
+ also allows to break down the geometric excess returns,
+ which link naturally over time. Finally, it annualizes
+ arithmetic and geometric excess returns similarly to the
+ portfolio and/or benchmark returns annualization.
+}
+\details{
+ The arithmetic excess returns are decomposed into the sum
+ of allocation, selection and interaction effects across n
+ sectors:
+ \deqn{R_{p}-R_{b}=\sum^{n}_{i=1}\left(A_{i}+S_{i}+I_{i}\right)}
+ The arithmetic attribution effects for the category i are
+ computed as suggested in the Brinson, Hood and Beebower
+ (1986): Allocation effect
+ \deqn{A_{i}=(w_{pi}-w_{bi})\times R_{bi}} Selection
+ effect \deqn{S_{i}=w_{pi}\times(R_{pi}-R_{bi})}
+ Interaction effect
+ \deqn{I_{i}=(w_{pi}-w_{bi})\times(R_{pi}-R_{bi})} r -
+ total portfolio returns, b - total benchmark returns,
+ w_pi - weights of the category i in the portfolio, w_bi -
+ weigths of the category i in the benchmark, R_pi -
+ returns of the portfolio category i, R_bi - returns of
+ the benchmark category i. If Brinson and Fachler (1985)
+ is selected the allocation effect differs:
+ \deqn{A_{i}=(w_{pi}-w_{bi})\times (R_{bi} - R_{b})}
+ Depending on goals we can give priority to the allocation
+ or to the selection effects. If the priority is given to
+ the sector allocation the interaction term will be
+ combined with the security selection effect (top-down
+ approach). If the priority is given to the security
+ selection, the interaction term will be combined with the
+ asset-allocation effect (bottom-up approach). Usually we
+ have more than one period. In that case individual
+ arithmetic attribution effects should be adjusted using
+ linking methods. Adjusted arithmetic attribution effects
+ can be summed up over time to provide the multi-period
+ summary:
+ \deqn{R_{p}-R_{b}=\sum^{T}_{t=1}\left(A_{t}'+S_{t}'+I_{t}'\right)}
+ where T is the number of periods and prime stands for the
+ adjustment. The geometric attribution effects do not
+ suffer from the linking problem. Moreover we don't have
+ the interaction term. For more details about the
+ geometric attribution see the documentation to
+ \code{Attribution.geometric} Finally, arithmetic
+ annualized excess returns are computed as the arithmetic
+ difference between annualised portfolio and benchmark
+ returns: \deqn{AAER=r_{a}-b_{a}} the geometric annualized
+ excess returns are computed as the geometric difference
+ between annualized portfolio and benchmark returns:
+ \deqn{GAER=\frac{1+r_{a}}{1+b_{a}}-1} In the case of
+ multi-currency portfolio, the currency return, currency
+ surprise and forward premium should be specified. The
+ multi-currency arithmetic attribution is handled
+ following Ankrim and Hensel (1992). Currency returns are
+ decomposed into the sum of the currency surprise and the
+ forward premium: \deqn{R_{ci} = R_{cei} + R_{fpi}} where
+ \deqn{R_{cei} = \frac{S_{i}^{t+1} -
+ F_{i}^{t+1}}{S_{i}^{t}}} \deqn{R_{fpi} =
+ \frac{F_{i}^{t+1}}{S_{i}^{t}} - 1} S^t_i - stop rate for
+ asset i at time t F^t_i - forward rate for asset i at
+ time t. Excess returns are decomposed into the sum of
+ allocation, selection and interaction effects as in the
+ standard Brinson model:
+ \deqn{R_{p}-R_{b}=\sum^{n}_{i=1}\left(A_{i}+S_{i}+I_{i}\right)}
+ However the allocation effect is computed taking into
+ account currency effects:
+ \deqn{A_{i}=(w_{pi}-w_{bi})\times (R_{bi} - R_{ci} -
+ R_{l})} Benchmark returns adjusted fo the currency:
+ \deqn{R_{l} = \sum^{n}_{i=1}w_{bi}\times(R_{bi}-R_{ci})}
+ The contribution from currency is analogous to asset
+ allocation: \deqn{C_{i} = (w_{pi} - w_{bi}) \times
+ (R_{cei} - e) + (w_{pfi} - w_{bfi}) \times (R_{fi} - e)}
+ where \deqn{e = \sum^{n}_{i=1}w_{bi}\times R_{cei}} The
+ final term, forward premium, is also analogous to the
+ asset allocation: \deqn{R_{fi} = (w_{pi} - w_{bi}) \times
+ (R_{fpi} - d)} where \deqn{d = \sum^{n}_{i=1}w_{bi}\times
+ R_{fpi}} and R_fpi - forward premium
+}
+\examples{
+data(attrib)
+Attribution(Rp, wp, Rb, wb, method = "top.down", linking = "carino")
+}
+\author{
+ Andrii Babii
+}
+\references{
+ Ankrim, E. and Hensel, C. \emph{Multi-currency
+ performance attribution}. Russell Research Commentary.
+ November 2002 \cr Bacon, C. \emph{Practical Portfolio
+ Performance Measurement and Attribution}. Wiley. 2004.
+ Chapter 5, 6, 8 \cr Christopherson, Jon A., Carino, David
+ R., Ferson, Wayne E. \emph{Portfolio Performance
+ Measurement and Benchmarking}. McGraw-Hill. 2009. Chapter
+ 18-19 \cr Brinson, G. and Fachler, N. (1985)
+ \emph{Measuring non-US equity portfolio performance}.
+ Journal of Portfolio Management. Spring. p. 73 -76. \cr
+ Gary P. Brinson, L. Randolph Hood, and Gilbert L.
+ Beebower, \emph{Determinants of Portfolio Performance}.
+ Financial Analysts Journal. vol. 42, no. 4, July/August
+ 1986, p. 39-44 \cr Karnosky, D. and Singer, B.
+ \emph{Global asset management and performance
+ attribution. The Research Foundation of the Institute of
+ Chartered Financial Analysts}. February 1994. \cr
+}
+\seealso{
+ \code{\link{Attribution.levels}},
+ \code{\link{Attribution.geometric}}
+}
+\keyword{attribution}
+
Modified: pkg/PortfolioAnalytics/sandbox/attribution/man/Attribution.geometric.Rd
===================================================================
--- pkg/PortfolioAnalytics/sandbox/attribution/man/Attribution.geometric.Rd 2012-07-09 17:44:19 UTC (rev 2139)
+++ pkg/PortfolioAnalytics/sandbox/attribution/man/Attribution.geometric.Rd 2012-07-09 23:54:02 UTC (rev 2140)
@@ -35,21 +35,14 @@
\code{\link{Attribution}} function. Geometric attribution
effects in the contrast with arithmetic do naturally link
over time multiplicatively:
- \deqn{\frac{(1+r)}{1+b}-1=\overset{n}{\underset{t=1}{\prod}}(1+A_{t}^{G})\times\overset{n}{\underset{t=1}{\prod}}(1+S{}_{t}^{G})-1}
+ \deqn{\frac{(1+R_{p})}{1+R_{b}}-1=\prod^{n}_{t=1}(1+A_{t}^{G})\times\prod^{n}_{t=1}(1+S{}_{t}^{G})-1}
+ Total allocation effect at time t:
+ \deqn{A_{t}^{G}=\frac{1+b_{S}}{1+R_{bt}}-1} Total
+ selection effect at time t:
+ \deqn{S_{t}^{G}=\frac{1+R_{pt}}{1+b_{S}}-1} Semi-notional
+ fund: \deqn{b_{S}=\sum^{n}_{i=1}w_{pi}\times R_{bi}}
}
\details{
- where \deqn{A_{t}^{G}} - total allocation effect at time
- t \deqn{S_{t}^{G}} - total selection effect at time t
- \deqn{A_{t}^{G}=\frac{1+b_{S}}{1+b_{t}}-1}
- \deqn{S_{t}^{G}=\frac{1+r_{t}}{1+b_{S}}-1}
- \deqn{b_{S}=\overset{n}{\underset{i=1}{\sum}}wp_{i}\times
- rb_{i}} \deqn{b_{S}} - semi-notional fund \deqn{w_{pt}} -
- portfolio weights at time t \deqn{w_{bt}} - benchmark
- weights at time t \deqn{r_{t}} - portfolio returns at
- time t \deqn{b_{t}} - benchmark returns at time t
- \deqn{r} - total portfolio returns \deqn{b} - total
- benchmark returns \deqn{n} - number of periods
-
The multi-currency geometric attribution is handled
following the Appendix A (Bacon, 2004).
@@ -59,22 +52,20 @@
The individual allocation effects are computed using:
\deqn{(w_{pi}-w_{bi})\times\left(\frac{1+R_{bHi}}{1+b_{L}}-1\right)}
- where \deqn{b_{SH} = \underset{i}{\sum}((w_{pi} -
- w_{bi})R_{bHi} + w_{bi}R_{bLi})} - total semi-notional
- return hedged into the base currency
+ Where the total semi-notional returns hedged into the
+ base currency were used: \deqn{b_{SH} =
+ \sum_{i}w_{pi}\times R_{bi}((w_{pi} - w_{bi})R_{bHi} +
+ w_{bi}R_{bLi})} Total semi-notional returns in the local
+ currency: \deqn{b_{SL} = \sum_{i}w_{pi}R_{bLi}} Portfolio
+ returns in the local currency: \deqn{R_{pLi}} Benchmark
+ returns in the local currency: \deqn{R_{bLi}} Benchmark
+ returns hedged into the base currency: \deqn{R_{bHi}}
+ Total benchmark returns in the local currency:
+ \deqn{b_{L}} Total portfolio returns in the local
+ currency: \deqn{r_{L}} The total excess returns are
+ decomposed into:
+ \deqn{\frac{(1+R_{p})}{1+R_{b}}-1=\frac{1+r_{L}}{1+b_{SL}}\times\frac{1+b_{SH}}{1+b_{L}}\times\frac{1+b_{SL}}{1+b_{SH}}\times\frac{1+R_{p}}{1+r_{L}}\times\frac{1+b_{L}}{1+R_{b}}-1}
- \deqn{b_{SL} = \underset{i}{\sum}w_{pi}R_{bLi}} - total
- semi-notional return in the local currency \deqn{w_{pi}}
- - portfolio weights of asset i \deqn{w_{bi}} - benchmark
- weights of asset i \deqn{R_{pLi}} - portfolio returns in
- the local currency \deqn{R_{bLi}}} - benchmark returns in
- the local currency \deqn{R_{bHi}} - benchmark returns
- hedged into the base currency \deqn{b_{L}} - total
- benchmark returns in the local currency \deqn{r_{L}} -
- total portfolio returns in the local currency The total
- excess returns are decomposed into:
- \deqn{\frac{(1+r)}{1+b}-1=\frac{1+r_{L}}{1+b_{SL}}\times\frac{1+b_{SH}}{1+b_{L}}\times\frac{1+b_{SL}}{1+b_{SH}}\times\frac{1+r}{1+r_{L}}\times\frac{1+b_{L}}{1+b}-1}
-
where the first term corresponds to the selection, second
to the allocation, third to the hedging cost transferred
and the last two to the naive currency attribution
@@ -89,11 +80,10 @@
\references{
Christopherson, Jon A., Carino, David R., Ferson, Wayne
E. \emph{Portfolio Performance Measurement and
- Benchmarking}. McGraw-Hill. 2009. Chapter 18-19
-
+ Benchmarking}. McGraw-Hill. 2009. Chapter 18-19 \cr
Bacon, C. \emph{Practical Portfolio Performance
Measurement and Attribution}. Wiley. 2004. Chapter 5, 8,
- Appendix A
+ Appendix A \cr
}
\seealso{
\code{\link{Attribution}}
Modified: pkg/PortfolioAnalytics/sandbox/attribution/man/Attribution.levels.Rd
===================================================================
--- pkg/PortfolioAnalytics/sandbox/attribution/man/Attribution.levels.Rd 2012-07-09 17:44:19 UTC (rev 2139)
+++ pkg/PortfolioAnalytics/sandbox/attribution/man/Attribution.levels.Rd 2012-07-09 23:54:02 UTC (rev 2140)
@@ -21,8 +21,9 @@
style as buildHierarchy's output}
}
\value{
- returns the list with total attribution effects
- (allocation, selection and total) including total
+ returns the list with geometric excess returns including
+ annualized geometric excess returns, total attribution
+ effects (allocation, selection and total) including total
multi-period attribution effects, attribution effects at
each level and security selection
}
@@ -38,9 +39,10 @@
should be at the lowest level (e.g. individual
instruments). Benchmark should have the same number of
columns as portfolio. That is there should be a benchmark
- for each instrument in the portfolio. The contribution to
- the allocation in the ith category for the dth level is:
- \deqn{\left(^{d}wp_{i}-^{d}wb_{i}\right)\times\left(\frac{1+^{d}b_{i}}{1+^{d-1}b_{i}}-1\right)\times\frac{1+^{d-1}b_{i}}{1+bs^{d-1}}}
+ for each instrument in the portfolio (possibly 0). The
+ contribution to the allocation in the ith category for
+ the dth level is:
+ \deqn{\left(^{d}w_{pi}-^{d}w_{bi}\right)\times\left(\frac{1+^{d}R_{bi}}{1+^{d-1}R_{bi}}-1\right)\times\frac{1+^{d-1}R_{bi}}{1+bs^{d-1}}}
}
\details{
The total attribution for each asset allocation step in
@@ -48,7 +50,7 @@
\deqn{\frac{1+^{d}bs}{1+^{d-1}bs}-1}
The final step, stock selection, is measured by:
- \deqn{^{d}w_{i}\times\left(\frac{1+r_{i}}{1+^{d}b_{i}}-1\right)\times\frac{1+^{d}b_{i}}{1+^{d}bs}}
+ \deqn{^{d}w_{pi}\times\left(\frac{1+R_{pi}}{1+^{d}R_{bi}}-1\right)\times\frac{1+^{d}R_{bi}}{1+^{d}bs}}
}
\examples{
data(attrib)
Modified: pkg/PortfolioAnalytics/sandbox/attribution/man/AttributionFixedIncome.Rd
===================================================================
--- pkg/PortfolioAnalytics/sandbox/attribution/man/AttributionFixedIncome.Rd 2012-07-09 17:44:19 UTC (rev 2139)
+++ pkg/PortfolioAnalytics/sandbox/attribution/man/AttributionFixedIncome.Rd 2012-07-09 23:54:02 UTC (rev 2140)
@@ -1,109 +1,107 @@
-\name{AttributionFixedIncome}
-\alias{attribution}
-\alias{AttributionFixedIncome}
-\alias{fixed}
-\alias{income}
-\title{fixed income attribution}
-\usage{
- AttributionFixedIncome(Rp, wp, Rb, wb, Rf, Dp, Db, S,
- wbf, geometric = FALSE)
-}
-\arguments{
- \item{Rp}{T x n xts, data frame or matrix of portfolio
- returns}
-
- \item{wp}{vector, xts, data frame or matrix of portfolio
- weights}
-
- \item{Rb}{T x n xts, data frame or matrix of benchmark
- returns}
-
- \item{wb}{vector, xts, data frame or matrix of benchmark
- weights}
-
- \item{Rf}{T x n xts, data frame or matrix with risk free
- rates}
-
- \item{Dp}{T x n xts, data frame or matrix with portfolio
- modified duration}
-
- \item{Db}{T x n xts, data frame or matrix with benchmark
- modified duration}
-
- \item{wbf}{vector, xts, data frame or matrix with
- benchmark weights of currency forward contracts}
-
- \item{S}{(T + 1) x n xts, data frame or matrix with spot
- rates. The first date should coincide with the first date
- of portfolio returns}
-
- \item{geometric}{- TRUE/FALSE for geometric/arithmetic
- attribution}
-
- \item{wbf}{vector, xts, data frame or matrix with
- benchmark weights of currency forward contracts}
-}
-\value{
- list with total excess returns decomposed into
- allocation, selection (and currency effects)
-}
-\description{
- Performs fixed income attribution. The investment
- decision process for bond managers is very different from
- that of equity managers, therefore for most fixed income
- investment strategies the standard Brinson model is not
- suitable. Bonds are simply a series of defined future
- cash flows which are relatively easy to price. Fixed
- income performance is therefore driven by changes in the
- shape of the yield curve. Systematic risk in the form of
- duration is a key part of the investment process. Fixed
- income attribution is, in fact, a specialist form of
- risk-adjusted attribution. The arithmetic attribution is
- handled using weighted duration approach (Van Breukelen,
- 2000). The allocation, selection and currency allocation
- effects for category i are: \deqn{A_{i} = (D_{pi}\times
- w_{i}-D_{\beta}\times D_{bi}\times w_{pi})\times (-\Delta
- y_{bi} + \Delta y_{b})} \deqn{S_{i} = D_{i}\times
- w_{i}\times (-\Delta y_{ri} + \Delta y_{bi})} \deqn{C_{i}
- = (w_{pi} - w_{bi})\times (c_{i} + R_{fi} - c')} where
- \deqn{w_{pi}} - portfolio weights \deqn{w_{bi}} -
- benchmark weights \deqn{D_{i}} - modified duration in
- bond category i \deqn{D_{\beta}=\frac{D_{r}}{D_{b}}} -
- duration beta \deqn{D_{r}} - portfolio duration
- \deqn{D_{b}} - benchmark duration \deqn{D_{bi}} -
- benchmark duration for category i \deqn{D_{pi}} -
- portfolio duration for category i \deqn{\Delta y_{ri}} -
- change in portfolio yield for category i \deqn{\Delta
- y_{bi}} - change in benchmark yield for category i
- \deqn{\Delta y_{b}} - change in benchmark yield
- \deqn{R_{ci} - currency returns for category i
- \deqn{R_{fi}} - risk-free rate in currency of asset i
- \deqn{c'= \underset{i}{\sum}w_{bi}\times(R_{ci}+R_{fi})}
- The geometric attribution is adapted using Van Breukelen
- (2000) approach for the arithmetic attribution. The
- individual allocation and selection effects are computed
- as follows:
- \deqn{A_{i}=D_{i}w_{pi}-D_{\beta}D_{bi}w_{bi}}
- \deqn{S_{i}=\frac{D_{pi}}{D_{bi}}\times (R_{bi} - R_{fi})
- + R_{fi}}
-}
-\examples{
-data(attrib)
-AttributionFixedIncome(Rp, wp, Rb, wb, Rf, Dp, Db, S, wbf, geometric = FALSE)
-}
-\author{
- Andrii Babii
-}
-\references{
- Bacon, C. \emph{Practical Portfolio Performance
- Measurement and Attribution}. Wiley. 2004. Chapter 7
-
- Van Breukelen, G. \emph{Fixed income attribution}.
- Journal of Performance
-}
-\seealso{
- \code{\link{Attribution.levels}},
- \code{\link{Attribution.geometric}}
-}
-\keyword{attribution}
-
+\name{AttributionFixedIncome}
+\alias{attribution}
+\alias{AttributionFixedIncome}
+\alias{fixed}
+\alias{income}
+\title{fixed income attribution}
+\usage{
+ AttributionFixedIncome(Rp, wp, Rb, wb, Rf, Dp, Db, S,
+ wbf, geometric = FALSE)
+}
+\arguments{
+ \item{Rp}{T x n xts, data frame or matrix of portfolio
+ returns}
+
+ \item{wp}{vector, xts, data frame or matrix of portfolio
+ weights}
+
+ \item{Rb}{T x n xts, data frame or matrix of benchmark
+ returns}
+
+ \item{wb}{vector, xts, data frame or matrix of benchmark
+ weights}
+
+ \item{Rf}{T x n xts, data frame or matrix with risk free
+ rates}
+
+ \item{Dp}{T x n xts, data frame or matrix with portfolio
+ modified duration}
+
+ \item{Db}{T x n xts, data frame or matrix with benchmark
+ modified duration}
+
+ \item{wbf}{vector, xts, data frame or matrix with
+ benchmark weights of currency forward contracts}
+
+ \item{S}{(T + 1) x n xts, data frame or matrix with spot
+ rates. The first date should coincide with the first date
+ of portfolio returns}
+
+ \item{geometric}{- TRUE/FALSE for geometric/arithmetic
+ attribution}
+
+ \item{wbf}{vector, xts, data frame or matrix with
+ benchmark weights of currency forward contracts}
+}
+\value{
+ list with total excess returns decomposed into
+ allocation, selection (and currency effects)
+}
+\description{
+ Performs fixed income attribution. The investment
+ decision process for bond managers is very different from
+ that of equity managers, therefore for most fixed income
+ investment strategies the standard Brinson model is not
+ suitable. Bonds are simply a series of defined future
+ cash flows which are relatively easy to price. Fixed
+ income performance is therefore driven by changes in the
+ shape of the yield curve. Systematic risk in the form of
+ duration is a key part of the investment process. Fixed
+ income attribution is, in fact, a specialist form of
+ risk-adjusted attribution. The arithmetic attribution is
+ handled using weighted duration approach (Van Breukelen,
+ 2000). The allocation, selection and currency allocation
+ effects for category i are: \deqn{A_{i} = (D_{pi}\times
+ w_{pi}-D_{\beta}\times D_{bi}\times w_{pi})\times
+ (-\Delta y_{bi} + \Delta y_{b})} \deqn{S_{i} =
+ D_{i}\times w_{pi}\times (-\Delta y_{ri} + \Delta
+ y_{bi})} \deqn{C_{i} = (w_{pi} - w_{bi})\times (c_{i} +
+ R_{fi} - c')} where w_pi - portfolio weights, w_bi -
+ benchmark weights, D_i - modified duration in bond
+ category i. Duration beta:
+ \deqn{D_{\beta}=\frac{D_{r}}{D_{b}}} D_r - portfolio
+ duration, D_b - benchmark duration, D_bi - benchmark
+ duration for category i, D_pi - portfolio duration for
+ category i, Delta y_ri - change in portfolio yield for
+ category i, Delta y_bi - change in benchmark yield for
+ category i, Delta y_b - change in benchmark yield, R_ci-
+ currency returns for category i, R_fi - risk-free rate in
+ currency of asset i, \deqn{c'=
+ \sum_{i}w_{bi}\times(R_{ci}+R_{fi})} The geometric
+ attribution is adapted using Van Breukelen (2000)
+ approach for the arithmetic attribution. The individual
+ allocation and selection effects are computed as follows:
+ \deqn{A_{i}=D_{i}w_{pi}-D_{\beta}D_{bi}w_{bi}}
+ \deqn{S_{i}=\frac{D_{pi}}{D_{bi}}\times (R_{bi} - R_{fi})
+ + R_{fi}}
+}
+\examples{
+data(attrib)
+AttributionFixedIncome(Rp, wp, Rb, wb, Rf, Dp, Db, S, wbf, geometric = FALSE)
+}
+\author{
+ Andrii Babii
+}
+\references{
+ Bacon, C. \emph{Practical Portfolio Performance
+ Measurement and Attribution}. Wiley. 2004. Chapter 7 \cr
+ Van Breukelen, G. \emph{Fixed income attribution}.
+ Journal of Performance Measurement. Sumer. p. 61-68. 2000
+ \cr
+}
+\seealso{
+ \code{\link{Attribution.levels}},
+ \code{\link{Attribution.geometric}}
+}
+\keyword{attribution}
+
Modified: pkg/PortfolioAnalytics/sandbox/attribution/man/Carino.Rd
===================================================================
--- pkg/PortfolioAnalytics/sandbox/attribution/man/Carino.Rd 2012-07-09 17:44:19 UTC (rev 2139)
+++ pkg/PortfolioAnalytics/sandbox/attribution/man/Carino.Rd 2012-07-09 23:54:02 UTC (rev 2140)
@@ -1,78 +1,72 @@
-\name{Carino}
-\alias{Carino}
[TRUNCATED]
To get the complete diff run:
svnlook diff /svnroot/returnanalytics -r 2140
More information about the Returnanalytics-commits
mailing list