[Returnanalytics-commits] r2249 - in pkg/PortfolioAnalytics/sandbox/attribution: R man
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Sun Aug 19 17:52:40 CEST 2012
Author: ababii
Date: 2012-08-19 17:52:39 +0200 (Sun, 19 Aug 2012)
New Revision: 2249
Modified:
pkg/PortfolioAnalytics/sandbox/attribution/R/AcctReturns.R
pkg/PortfolioAnalytics/sandbox/attribution/R/Attribution.geometric.R
pkg/PortfolioAnalytics/sandbox/attribution/R/Modigliani.R
pkg/PortfolioAnalytics/sandbox/attribution/R/Return.annualized.excess.R
pkg/PortfolioAnalytics/sandbox/attribution/R/attribution.R
pkg/PortfolioAnalytics/sandbox/attribution/R/attribution.levels.R
pkg/PortfolioAnalytics/sandbox/attribution/man/AcctReturns.Rd
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/Modigliani.Rd
pkg/PortfolioAnalytics/sandbox/attribution/man/Return.annualized.excess.Rd
Log:
- mistakes correction
- documentation update
Modified: pkg/PortfolioAnalytics/sandbox/attribution/R/AcctReturns.R
===================================================================
--- pkg/PortfolioAnalytics/sandbox/attribution/R/AcctReturns.R 2012-08-19 12:55:22 UTC (rev 2248)
+++ pkg/PortfolioAnalytics/sandbox/attribution/R/AcctReturns.R 2012-08-19 15:52:39 UTC (rev 2249)
@@ -1,24 +1,30 @@
#' Calculate account returns
#'
-#' Similar to the \code{PortfReturns}, but gives returns for the entire account
-#' and takes into account cashflows. Allows selecting between time-weighted
-#' returns and linked modified Dietz approach. If time-weighted method is
-#' selected, the returns are computed using: \deqn{r_{t}=\frac{V_{t}}{V_{t-1}+C_{t}}-1}
+#' Similar to the \code{PortfReturns} function, but gives returns for the
+#' entire account and takes into account external cashflows. External cashflows
+#' are defined as contributions to or withdrawals from the account. Allows
+#' selecting between time-weighted returns and linked modified Dietz approach.
+#' If time-weighted method is selected, returns at time \eqn{t} are computed
+#' using: \deqn{r_{t}=\frac{V_{t}}{V_{t-1}+C_{t}}-1}
#' where \eqn{V_{t}} - account value at time \eqn{t}, \eqn{C_{t}} - cashflow at
-#' time \eqn{t}.These returns then can be linked geometrically (for instance
-#' using \code{Return.cumulative} function from the \code{PerformanceAnalytics}
-#' package) to yield cumulative multiperiod returns:
+#' time \eqn{t}. The implicit assumption made here is that the cash flow is
+#' available for the portfolio manager to invest from the beginning of the day.
+#' These returns then can be chain linked with geometric compounding (for
+#' instance using \code{Return.cumulative} function from the
+#' \code{PerformanceAnalytics} package) to yield cumulative multi-period
+#' returns:
#' \deqn{1+r=\prod_{t=1}^{T}(1+r_{t})=\prod_{t=1}^{T}\frac{V_{t}}{V_{t-1}+C_{t}}}
-#' In case if there were no cashflows, the result reduces to simple one-period
-#' returns.
+#' In the case if there were no cashflows, the result reduces to simple
+#' one-period returns. Time-weighted returns has also an interpretation in
+#' terms of unit value pricing.
#' If Modified Dietz method is selected, monthly returns are computed taking
#' into account cashflows within each month:
#' \deqn{r = \frac{V_{t}-V_{t-1}-C}{V_{t-1}+\sum_{t}C_{t}\times W_{t}}}
#' where \eqn{C} - total external cash flows within a month,
-#' \eqn{C_{t}} - external cashflow on day \eqn{t},
-#' \eqn{W_{t}=\frac{TD-D_{t}}{TD}} - weighting ratio to be applied to external
+#' \eqn{C_{t}} - external cashflow at time \eqn{t},
+#' \deqn{W_{t}=\frac{TD-D_{t}}{TD}} - weighting ratio to be applied to external
#' cashflow on day \eqn{t},
-#' \eqn{TD} - total number of days wihting the month,
+#' \eqn{TD} - total number of days within the month,
#' \eqn{D_{t}} - number of days since the beginning of the month including
#' weekends and public holidays.
#' Finally monthly Modified Dietz returns can also be linked geometrically.
@@ -33,7 +39,7 @@
#' returns on, default NULL (all portfolios)
#' @param method Used to select between time-weighted and linked modified Dietz
#' returns. May be any of: \itemize{\item timeweighted \item dietz} By default
-#' time-weigthed is selected
+#' time-weighted is selected
#' @return returns xts with account returns
#' @author Brian Peterson, Andrii Babii
#' @seealso PortfReturns
@@ -47,8 +53,6 @@
#'
#' TODO explicitly handle portfolio weights
#'
-#' TODO provide additional methods of calculating returns
-#'
#' TODO support additions and withdrawals to available capital
#' @export
AcctReturns <-
@@ -122,4 +126,4 @@
}
}
return(returns)
-}
\ No newline at end of file
+}
Modified: pkg/PortfolioAnalytics/sandbox/attribution/R/Attribution.geometric.R
===================================================================
--- pkg/PortfolioAnalytics/sandbox/attribution/R/Attribution.geometric.R 2012-08-19 12:55:22 UTC (rev 2248)
+++ pkg/PortfolioAnalytics/sandbox/attribution/R/Attribution.geometric.R 2012-08-19 15:52:39 UTC (rev 2249)
@@ -1,9 +1,9 @@
-#' performs geometric attribution
+#' performs sector-based geometric attribution
#'
-#' Performance attribution of geometric excess returns. Calculates total
-#' geometric attribution effects over multiple periods. Used internally by the
-#' \code{\link{Attribution}} function. Geometric attribution effects in the
-#' contrast with arithmetic do naturally link over time multiplicatively:
+#' Performs sector-based geometric attribution of excess return. Calculates
+#' total geometric attribution effects over multiple periods. Used internally
+#' by the \code{\link{Attribution}} function. Geometric attribution effects in
+#' the contrast with arithmetic do naturally link over time multiplicatively:
#' \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 \eqn{t}:
@@ -173,4 +173,4 @@
}
return(result)
-}
\ No newline at end of file
+}
Modified: pkg/PortfolioAnalytics/sandbox/attribution/R/Modigliani.R
===================================================================
--- pkg/PortfolioAnalytics/sandbox/attribution/R/Modigliani.R 2012-08-19 12:55:22 UTC (rev 2248)
+++ pkg/PortfolioAnalytics/sandbox/attribution/R/Modigliani.R 2012-08-19 15:52:39 UTC (rev 2249)
@@ -1,17 +1,17 @@
#' Modigliani-Modigliani measure
#'
-#' The Modigliani-Modigliani measure is the portfolio return
-#' adjusted upward or downward to match the benchmark's standard
-#' deviation. This puts the portfolio return and the benchmark
-#' return on 'equal footing' from a standard deviation perspective.
+#' The Modigliani-Modigliani measure is the portfolio return adjusted upward
+#' or downward to match the benchmark's standard deviation. This puts the
+#' portfolio return and the benchmark return on 'equal footing' from a standard
+#' deviation perspective.
#' \deqn{MM_{p}=\frac{E[R_{p} - R_{f}]}{\sigma_{p}}=SR_{p} * \sigma_{b} +
#' E[R_{f}]}{MMp = SRp * sigmab + E[Rf]}
-#' where \eqn{SR_{p}}{SRp} - Sharpe ratio, \eqn{sigma_{b}}{sigmab} - benchmark
+#' where \eqn{SR_{p}}{SRp} - Sharpe ratio, \eqn{\sigma_{b}}{sigmab} - benchmark
#' standard deviation
#'
-#' This is also analogous to some approaches to 'risk parity'
-#' portfolios, which use (presumably costless) leverage
-#' to increase the portfolio standard deviation to some target.
+#' This is also analogous to some approaches to 'risk parity' portfolios, which
+#' use (presumably costless) leverage to increase the portfolio standard
+#' deviation to some target.
#'
#' @param Ra an xts, vector, matrix, data frame, timeSeries or zoo object of
#' asset returns
Modified: pkg/PortfolioAnalytics/sandbox/attribution/R/Return.annualized.excess.R
===================================================================
--- pkg/PortfolioAnalytics/sandbox/attribution/R/Return.annualized.excess.R 2012-08-19 12:55:22 UTC (rev 2248)
+++ pkg/PortfolioAnalytics/sandbox/attribution/R/Return.annualized.excess.R 2012-08-19 15:52:39 UTC (rev 2249)
@@ -20,7 +20,7 @@
#' \deqn{er = R_{pa} - R_{ba}}{er = Rpa - Rba}
#'
#' and as a geometric difference in the geometric case:
-#' \deqn{er = (1 + R_{pa}) / (1 + R_{ba}) - 1}{er = (1 + Rpa) / (1 + Rba) - 1}
+#' \deqn{er = \frac{(1 + R_{pa})}{(1 + R_{ba})} - 1}{er = (1 + Rpa) / (1 + Rba) - 1}
#'
#' @param Rp an xts, vector, matrix, data frame, timeSeries or zoo object of
#' portfolio returns
Modified: pkg/PortfolioAnalytics/sandbox/attribution/R/attribution.R
===================================================================
--- pkg/PortfolioAnalytics/sandbox/attribution/R/attribution.R 2012-08-19 12:55:22 UTC (rev 2248)
+++ pkg/PortfolioAnalytics/sandbox/attribution/R/attribution.R 2012-08-19 15:52:39 UTC (rev 2249)
@@ -1,21 +1,21 @@
-#' performs arithmetic attribution
+#' performs sector-based single-level attribution
#'
-#' 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 \code{\link{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 or Davies Laker. 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.
+#' Performs sector-based single-level 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
+#' \code{\link{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 or Davies Laker. 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.
#'
#' The arithmetic excess returns are decomposed into the sum of allocation,
#' selection and interaction effects across \eqn{n} sectors:
@@ -32,7 +32,7 @@
#' \eqn{R_{p}}{Rp} - total portfolio returns,
#' \eqn{R_{b}}{Rb} - total benchmark returns,
#' \eqn{w_{pi}}{wpi} - weights of the category \eqn{i} in the portfolio,
-#' \eqn{w_{bi}}{wbi} - weigths of the category \eqn{i} in the benchmark,
+#' \eqn{w_{bi}}{wbi} - weights of the category \eqn{i} in the benchmark,
#' \eqn{R_{pi}}{Rpi} - returns of the portfolio category \eqn{i},
#' \eqn{R_{bi}}{Rbi} - returns of the benchmark category \eqn{i}.
#' If Brinson and Fachler (1985) is selected the allocation effect differs:
@@ -77,7 +77,7 @@
#' effects:
#' \deqn{A_{i}=(w_{pi}-w_{bi})\times (R_{bi} - R_{ci} - R_{l})}{Ai =
#' (wpi - wbi) * (Rbi - Rci - Rl)}
-#' Benchmark returns adjusted fo the currency:
+#' Benchmark returns adjusted to the currency:
#' \deqn{R_{l} = \sum^{n}_{i=1}w_{bi}\times(R_{bi}-R_{ci})}
#' The contribution from the currency is analogous to asset allocation:
#' \deqn{C_{i} = (w_{pi} - w_{bi}) \times (R_{cei} - e) + (w_{pfi} - w_{bfi})
@@ -88,6 +88,10 @@
#' (Rfpi - d)}
#' where \deqn{d = \sum^{n}_{i=1}w_{bi}\times R_{fpi}}
#' and \eqn{R_{fpi}} - forward premium
+#' In general if the intent is to estimate statistical parameters, the
+#' arithmetic excess return is preferred. However, due to the linking
+#' challenges, it may be preferable to use geometric excess return if the
+#' intent is to link and annualize excess returns.
#'
#' @aliases Attribution
#' @param Rp T x n xts, data frame or matrix of portfolio returns
@@ -365,4 +369,4 @@
c("Currency management", "Forward Premium")
}
return(result)
-}
\ No newline at end of file
+}
Modified: pkg/PortfolioAnalytics/sandbox/attribution/R/attribution.levels.R
===================================================================
--- pkg/PortfolioAnalytics/sandbox/attribution/R/attribution.levels.R 2012-08-19 12:55:22 UTC (rev 2248)
+++ pkg/PortfolioAnalytics/sandbox/attribution/R/attribution.levels.R 2012-08-19 15:52:39 UTC (rev 2249)
@@ -1,6 +1,6 @@
-#' provides multi-level geometric performance attribution
+#' provides multi-level sector-based geometric attribution
#'
-#' Provides multi-level geometric performance attribution. The Brinson model
+#' Provides multi-level sector-based geometric attribution. The Brinson model
#' attributes excess returns at one level. This function works with more
#' complex decision processes. For instance, the 3-level decision process
#' may have the following levels: type of asset - country - sector. The
Modified: pkg/PortfolioAnalytics/sandbox/attribution/man/AcctReturns.Rd
===================================================================
--- pkg/PortfolioAnalytics/sandbox/attribution/man/AcctReturns.Rd 2012-08-19 12:55:22 UTC (rev 2248)
+++ pkg/PortfolioAnalytics/sandbox/attribution/man/AcctReturns.Rd 2012-08-19 15:52:39 UTC (rev 2249)
@@ -22,35 +22,41 @@
\item{method}{Used to select between time-weighted and
linked modified Dietz returns. May be any of:
\itemize{\item timeweighted \item dietz} By default
- time-weigthed is selected}
+ time-weighted is selected}
}
\value{
returns xts with account returns
}
\description{
- Similar to the \code{PortfReturns}, but gives returns for
- the entire account and takes into account cashflows.
- Allows selecting between time-weighted returns and linked
+ Similar to the \code{PortfReturns} function, but gives
+ returns for the entire account and takes into account
+ external cashflows. External cashflows are defined as
+ contributions to or withdrawals from the account. Allows
+ selecting between time-weighted returns and linked
modified Dietz approach. If time-weighted method is
- selected, the returns are computed using:
+ selected, returns at time \eqn{t} are computed using:
\deqn{r_{t}=\frac{V_{t}}{V_{t-1}+C_{t}}-1} where
\eqn{V_{t}} - account value at time \eqn{t}, \eqn{C_{t}}
- - cashflow at time \eqn{t}.These returns then can be
- linked geometrically (for instance using
- \code{Return.cumulative} function from the
- \code{PerformanceAnalytics} package) to yield cumulative
- multiperiod returns:
+ - cashflow at time \eqn{t}. The implicit assumption made
+ here is that the cash flow is available for the portfolio
+ manager to invest from the beginning of the day. These
+ returns then can be chain linked with geometric
+ compounding (for instance using \code{Return.cumulative}
+ function from the \code{PerformanceAnalytics} package) to
+ yield cumulative multi-period returns:
\deqn{1+r=\prod_{t=1}^{T}(1+r_{t})=\prod_{t=1}^{T}\frac{V_{t}}{V_{t-1}+C_{t}}}
- In case if there were no cashflows, the result reduces to
- simple one-period returns. If Modified Dietz method is
- selected, monthly returns are computed taking into
- account cashflows within each month: \deqn{r =
+ In the case if there were no cashflows, the result
+ reduces to simple one-period returns. Time-weighted
+ returns has also an interpretation in terms of unit value
+ pricing. If Modified Dietz method is selected, monthly
+ returns are computed taking into account cashflows within
+ each month: \deqn{r =
\frac{V_{t}-V_{t-1}-C}{V_{t-1}+\sum_{t}C_{t}\times
W_{t}}} where \eqn{C} - total external cash flows within
- a month, \eqn{C_{t}} - external cashflow on day \eqn{t},
- \eqn{W_{t}=\frac{TD-D_{t}}{TD}} - weighting ratio to be
+ a month, \eqn{C_{t}} - external cashflow at time \eqn{t},
+ \deqn{W_{t}=\frac{TD-D_{t}}{TD}} - weighting ratio to be
applied to external cashflow on day \eqn{t}, \eqn{TD} -
- total number of days wihting the month, \eqn{D_{t}} -
+ total number of days within the month, \eqn{D_{t}} -
number of days since the beginning of the month including
weekends and public holidays. Finally monthly Modified
Dietz returns can also be linked geometrically.
@@ -61,8 +67,6 @@
TODO explicitly handle portfolio weights
- TODO provide additional methods of calculating returns
-
TODO support additions and withdrawals to available
capital
}
Modified: pkg/PortfolioAnalytics/sandbox/attribution/man/Attribution.Rd
===================================================================
--- pkg/PortfolioAnalytics/sandbox/attribution/man/Attribution.Rd 2012-08-19 12:55:22 UTC (rev 2248)
+++ pkg/PortfolioAnalytics/sandbox/attribution/man/Attribution.Rd 2012-08-19 15:52:39 UTC (rev 2249)
@@ -1,6 +1,6 @@
\name{Attribution}
\alias{Attribution}
-\title{performs arithmetic attribution}
+\title{performs sector-based single-level attribution}
\usage{
Attribution(Rp, wp, Rb, wb, wpf = NA, wbf = NA, S = NA,
F = NA, Rpl = NA, Rbl = NA, Rbh = NA, bf = FALSE,
@@ -84,16 +84,16 @@
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
+ Performs sector-based single-level 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
@@ -123,7 +123,7 @@
\eqn{R_{p}}{Rp} - total portfolio returns,
\eqn{R_{b}}{Rb} - total benchmark returns,
\eqn{w_{pi}}{wpi} - weights of the category \eqn{i} in
- the portfolio, \eqn{w_{bi}}{wbi} - weigths of the
+ the portfolio, \eqn{w_{bi}}{wbi} - weights of the
category \eqn{i} in the benchmark, \eqn{R_{pi}}{Rpi} -
returns of the portfolio category \eqn{i},
\eqn{R_{bi}}{Rbi} - returns of the benchmark category
@@ -176,7 +176,7 @@
account currency effects:
\deqn{A_{i}=(w_{pi}-w_{bi})\times (R_{bi} - R_{ci} -
R_{l})}{Ai = (wpi - wbi) * (Rbi - Rci - Rl)} Benchmark
- returns adjusted fo the currency: \deqn{R_{l} =
+ returns adjusted to the currency: \deqn{R_{l} =
\sum^{n}_{i=1}w_{bi}\times(R_{bi}-R_{ci})} The
contribution from the currency is analogous to asset
allocation: \deqn{C_{i} = (w_{pi} - w_{bi}) \times
@@ -186,7 +186,12 @@
asset allocation: \deqn{R_{fi} = (w_{pi} - w_{bi}) \times
(R_{fpi} - d)}{Rfi = (wpi - wbi) * (Rfpi - d)} where
\deqn{d = \sum^{n}_{i=1}w_{bi}\times R_{fpi}} and
- \eqn{R_{fpi}} - forward premium
+ \eqn{R_{fpi}} - forward premium In general if the intent
+ is to estimate statistical parameters, the arithmetic
+ excess return is preferred. However, due to the linking
+ challenges, it may be preferable to use geometric excess
+ return if the intent is to link and annualize excess
+ returns.
}
\examples{
data(attrib)
Modified: pkg/PortfolioAnalytics/sandbox/attribution/man/Attribution.geometric.Rd
===================================================================
--- pkg/PortfolioAnalytics/sandbox/attribution/man/Attribution.geometric.Rd 2012-08-19 12:55:22 UTC (rev 2248)
+++ pkg/PortfolioAnalytics/sandbox/attribution/man/Attribution.geometric.Rd 2012-08-19 15:52:39 UTC (rev 2249)
@@ -1,6 +1,6 @@
\name{Attribution.geometric}
\alias{Attribution.geometric}
-\title{performs geometric attribution}
+\title{performs sector-based geometric attribution}
\usage{
Attribution.geometric(Rp, wp, Rb, wb, Rpl = NA, Rbl = NA,
Rbh = NA)
@@ -29,9 +29,9 @@
multi-period attribution effects
}
\description{
- Performance attribution of geometric excess returns.
- Calculates total geometric attribution effects over
- multiple periods. Used internally by the
+ Performs sector-based geometric attribution of excess
+ return. Calculates total geometric attribution effects
+ over multiple periods. Used internally by the
\code{\link{Attribution}} function. Geometric attribution
effects in the contrast with arithmetic do naturally link
over time multiplicatively:
Modified: pkg/PortfolioAnalytics/sandbox/attribution/man/Attribution.levels.Rd
===================================================================
--- pkg/PortfolioAnalytics/sandbox/attribution/man/Attribution.levels.Rd 2012-08-19 12:55:22 UTC (rev 2248)
+++ pkg/PortfolioAnalytics/sandbox/attribution/man/Attribution.levels.Rd 2012-08-19 15:52:39 UTC (rev 2249)
@@ -1,6 +1,6 @@
\name{Attribution.levels}
\alias{Attribution.levels}
-\title{provides multi-level geometric performance attribution}
+\title{provides multi-level sector-based geometric attribution}
\usage{
Attribution.levels(Rp, wp, Rb, wb, h, ...)
}
@@ -29,7 +29,7 @@
each level and security selection
}
\description{
- Provides multi-level geometric performance attribution.
+ Provides multi-level sector-based geometric attribution.
The Brinson model attributes excess returns at one level.
This function works with more complex decision processes.
For instance, the 3-level decision process may have the
Modified: pkg/PortfolioAnalytics/sandbox/attribution/man/Modigliani.Rd
===================================================================
--- pkg/PortfolioAnalytics/sandbox/attribution/man/Modigliani.Rd 2012-08-19 12:55:22 UTC (rev 2248)
+++ pkg/PortfolioAnalytics/sandbox/attribution/man/Modigliani.Rd 2012-08-19 15:52:39 UTC (rev 2249)
@@ -17,12 +17,12 @@
\description{
The Modigliani-Modigliani measure is the portfolio return
adjusted upward or downward to match the benchmark's
- standard deviation. This puts the portfolio return and
+ standard deviation. This puts the portfolio return and
the benchmark return on 'equal footing' from a standard
deviation perspective. \deqn{MM_{p}=\frac{E[R_{p} -
R_{f}]}{\sigma_{p}}=SR_{p} * \sigma_{b} + E[R_{f}]}{MMp =
SRp * sigmab + E[Rf]} where \eqn{SR_{p}}{SRp} - Sharpe
- ratio, \eqn{sigma_{b}}{sigmab} - benchmark standard
+ ratio, \eqn{\sigma_{b}}{sigmab} - benchmark standard
deviation
}
\details{
Modified: pkg/PortfolioAnalytics/sandbox/attribution/man/Return.annualized.excess.Rd
===================================================================
--- pkg/PortfolioAnalytics/sandbox/attribution/man/Return.annualized.excess.Rd 2012-08-19 12:55:22 UTC (rev 2248)
+++ pkg/PortfolioAnalytics/sandbox/attribution/man/Return.annualized.excess.Rd 2012-08-19 15:52:39 UTC (rev 2249)
@@ -43,8 +43,8 @@
R_{ba}}{er = Rpa - Rba}
and as a geometric difference in the geometric case:
- \deqn{er = (1 + R_{pa}) / (1 + R_{ba}) - 1}{er = (1 +
- Rpa) / (1 + Rba) - 1}
+ \deqn{er = \frac{(1 + R_{pa})}{(1 + R_{ba})} - 1}{er = (1
+ + Rpa) / (1 + Rba) - 1}
}
\examples{
data(attrib)
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