[Uwgarp-commits] r155 - in pkg/GARPFRM: R vignettes

[noreply at r-forge.r-project.org]

Author: tfillebeen
Date: 2014-03-31 02:55:39 +0200 (Mon, 31 Mar 2014)
New Revision: 155

Modified:
   pkg/GARPFRM/R/capm.R
   pkg/GARPFRM/vignettes/CAPM_TF.Rnw
   pkg/GARPFRM/vignettes/CAPM_TF.pdf
Log:
CAPM vignette update + minor code M

Modified: pkg/GARPFRM/R/capm.R
===================================================================
--- pkg/GARPFRM/R/capm.R	2014-03-31 00:21:40 UTC (rev 154)
+++ pkg/GARPFRM/R/capm.R	2014-03-31 00:55:39 UTC (rev 155)
@@ -2,25 +2,25 @@
 # Description for CAPM
 # @param r risk-free rate
 # @param mkrt market return
-# @return the function returns tstat upon default & pvalue when specified
+# @return the function returns tstat upon default & pvalue when spesignificanceLevelfied
 # @export
 # capm.tstats = function(r,mkrt,type = FALSE) {
-#   # Fiting CAPM and retrieve alpha specific tstats or pvalues
+#   # Fiting CAPM and retrieve alpha spesignificanceLevelfic tstats or pvalues
 #   capm.fit = lm(r~mkrt)    
 #   # Extract summary info
 #   capm.summary = summary(capm.fit) 
 #   if(is.null(type) | type=="pvalue"){
-#     # Retrieve p-value if specified
+#     # Retrieve p-value if spesignificanceLevelfied
 #     p.value = coef(capm.summary)[1,4]  
 #     p.value
 #   }else{
-#     # Otherwise retrieve t-stat if specified or on default
+#     # Otherwise retrieve t-stat if spesignificanceLevelfied or on default
 #     t.stat = coef(capm.summary)[1,3]  
 #     t.stat
 #   }
 # }
 
-#' Capital Asset Pricing Model
+#' Capital Asset PrisignificanceLevelng Model
 #' 
 #' TODO: Need a better description of the CAPM
 #' 
@@ -119,7 +119,7 @@
 #' Extract the standard error, t-values, and p-values from the CAPM object.
 #' 
 #' The t-statistic and corresponding two-sided p-value are calculated differently
-#' for the alpha and beta coefficients.
+#' for the alpha and beta coeffisignificanceLevelents.
 #' \itemize{
 #'   \item{alpha}{ the t-statistic and corresponding p-value are calculated to
 #'   test if alpha is significantly different from 0.
@@ -252,20 +252,20 @@
   # Plot Fitted SML
   plot(betas,mu.hat,main=main, ...=...)
   abline(sml.fit)
-  legend("topleft",1, "Estimated SML",1)                  
+  #legend("topleft",1, "Estimated SML",1)                  
 }
 
 
 #' CAPM Hypothesis Test
 #' 
-#' Test the CAPM coefficients for significance.
+#' Test the CAPM coeffisignificanceLevelents for significance.
 #' 
 #' @details
-#' This function tests the significance of the coefficients (alpha and beta)
+#' This function tests the significance of the coeffisignificanceLevelents (alpha and beta)
 #' estimated by the CAPM.
 #' 
 #' #' The t-statistic and corresponding two-sided p-value are calculated differently
-#' for the alpha and beta coefficients.
+#' for the alpha and beta coeffisignificanceLevelents.
 #' \itemize{
 #'   \item{alpha}{ the t-statistic and corresponding p-value are calculated to
 #'   test if alpha is significantly different from 0.
@@ -281,44 +281,44 @@
 #'   }
 #' }
 #' 
-#' If the p-value is less than the specified confidence level, the null 
-#' hypothesis is rejected meaning that the coefficient is significant. If 
-#' the p-value is greater than the specified confidence level, the null 
+#' If the p-value is less than the spesignificanceLevelfied confidence level, the null 
+#' hypothesis is rejected meaning that the coeffisignificanceLevelent is significant. If 
+#' the p-value is greater than the spesignificanceLevelfied confidence level, the null 
 #' hypothesis cannot be rejected.
 #' 
 #' @param object a capm object created by \code{\link{CAPM}}
-#' @param CI confidence level
-#' @return TRUE if the null hypothesis is rejected (i.e. the estimated coefficient is significant)
-#' FALSE if the null hypothesis cannot be rejected (i.e. the estimated coefficient is not significant)
+#' @param significanceLevel confidence level
+#' @return TRUE if the null hypothesis is rejected (i.e. the estimated coeffisignificanceLevelent is significant)
+#' FALSE if the null hypothesis cannot be rejected (i.e. the estimated coeffisignificanceLevelent is not significant)
 #' @seealso \code{\link{getStatistics}}
 #' @author Thomas Fillebeen
 #' @export
-hypTest <- function(object,CI){
+hypTest <- function(object,significanceLevel){
   UseMethod("hypTest")
 }
 
 #' @method hypTest capm_uv
 #' @S3method hypTest capm_uv
-hypTest.capm_uv <- function(object, CI = 0.05){
+hypTest.capm_uv <- function(object, significanceLevel = 0.05){
   if(!inherits(object, "capm_uv")) stop("object must be of class capm_uv")
   tmp_sm = getStatistics(object)
-  # test for alpha p-value < CI
-  tmp_A = tmp_sm[1,4] < CI
-  # test for beta p-value < CI
-  tmp_B = tmp_sm[2,4] < CI
+  # test for alpha p-value < significanceLevel
+  tmp_A = tmp_sm[1,4] < significanceLevel
+  # test for beta p-value < significanceLevel
+  tmp_B = tmp_sm[2,4] < significanceLevel
   result = list(alpha = tmp_A, beta = tmp_B)
   return(result)
 }
 
 #' @method hypTest capm_mlm
 #' @S3method hypTest capm_mlm
-hypTest.capm_mlm <- function(object, CI = 0.05){
+hypTest.capm_mlm <- function(object, significanceLevel = 0.05){
   if(!inherits(object, "capm_mlm")) stop("object must be of class capm_mlm")
   tmp_sm = getStatistics(object)
-  # test for alpha p-value < CI
-  tmp_A = tmp_sm[seq(1,nrow(tmp_sm),2),4] < CI
-  # test for beta p-value < CI
-  tmp_B = tmp_sm[seq(2,nrow(tmp_sm),2),4] < CI
+  # test for alpha p-value < significanceLevel
+  tmp_A = tmp_sm[seq(1,nrow(tmp_sm),2),4] < significanceLevel
+  # test for beta p-value < significanceLevel
+  tmp_B = tmp_sm[seq(2,nrow(tmp_sm),2),4] < significanceLevel
   result = list(alpha = tmp_A, beta = tmp_B)  
   return(result)
 }

Modified: pkg/GARPFRM/vignettes/CAPM_TF.Rnw
===================================================================
--- pkg/GARPFRM/vignettes/CAPM_TF.Rnw	2014-03-31 00:21:40 UTC (rev 154)
+++ pkg/GARPFRM/vignettes/CAPM_TF.Rnw	2014-03-31 00:55:39 UTC (rev 155)
@@ -8,17 +8,12 @@
 \usepackage[round]{natbib}
 \usepackage{bm}
 \usepackage{verbatim}
+\usepackage[round]{natbib}
+\bibliographystyle{abbrvnat}
 \usepackage[latin1]{inputenc}
 \bibliographystyle{abbrvnat}
 
 \let\proglang=\textsf
-%\newcommand{\pkg}[1]{{\fontseries{b}\selectfont #1}}
-%\newcommand{\R}[1]{{\fontseries{b}\selectfont #1}}
-%\newcommand{\email}[1]{\href{mailto:#1}{\normalfont\texttt{#1}}}
-%\newcommand{\E}{\mathsf{E}}
-%\newcommand{\VAR}{\mathsf{VAR}}
-%\newcommand{\COV}{\mathsf{COV}}
-%\newcommand{\Prob}{\mathsf{P}}
 
 \renewcommand{\topfraction}{0.85}
 \renewcommand{\textfraction}{0.1}
@@ -26,12 +21,9 @@
 \setlength{\textwidth}{15cm} \setlength{\textheight}{22cm} \topmargin-1cm \evensidemargin0.5cm \oddsidemargin0.5cm
 
 \usepackage[latin1]{inputenc}
-% or whatever
 
 \usepackage{lmodern}
 \usepackage[T1]{fontenc}
-% Or whatever. Note that the encoding and the font should match. If T1
-% does not look nice, try deleting the line with the fontenc.
 
 \begin{document}
 
@@ -41,7 +33,7 @@
 \maketitle
 
 \begin{abstract}
-Standard Capital Asset Pricing Model (CAPM) fitting and testing using Quandl data.
+Standard Capital Asset PrisignificanceLevelng Model (CAPM) fitting and testing using CRSP data.
 
 CAPM Assumptions
 1. Identical investors who are price takers;
@@ -51,7 +43,7 @@
 5. Investors only care about portfolio expected return and variance;
 6. Market consists of all publicly traded assets.
 
-The Consumption-Oriented CAPM is analogous to the simple form of the CAPM. Except that the growth rate of per capita consumption has replaced the rate of return on the market porfolio as the influence effecting returns.
+The Consumption-Oriented CAPM (CCAPM) is analogous to the simple form of the CAPM. Except that the growth rate of per capita consumption has replaced the rate of return on the market porfolio as the influence effecting returns.
 \end{abstract}
 
 \tableofcontents
@@ -73,7 +65,7 @@
 @
 
 
-Summarize the start and end dates corresponding to the first 4 large cap returns.
+In order to get a quick look at the structure of the data inputted into the CAPM model summarize the start and end dates corresponding to the first 4 large cap returns.
 <<ex2>>=
 # Illustrate the type of data being analzyed: start-end dates.
 start(stock.df[,1:4])
@@ -83,7 +75,7 @@
 @
 
 \subsection{Estimate Excess Returns}
-Estimate excess returns: subtracting off risk-free rate.
+Estimate excess returns: subtracting off risk-free rate. The risk-free rate of return used for determining the risk premium is usually the historical arithmetic average risk free rates, as opposed to the current risk free rate.
 <<ex3>>=
 # Excess Returns initialized before utilizing in CAPM
 exReturns <- Return.excess(stock.df, rfr)
@@ -91,7 +83,21 @@
 @
 
 \subsection{Fitting CAPM Model: Univariate}
-Run CAPM regression for AMAT and estimate CAPM with $\alpha=0$ \& $\beta=1$ for asset.
+The CAPM formula: for individual security apply the security market line (SML) and its relation to expected return and sytematic risk ($\beta$) in order to illustrate how the market prices individual secruities in relation to their security risk asset class. Run test for the following CAPM estimate: 
+\begin{equation}
+R_{i,t} - R_f = \alpha_i + \beta_i (R_{M,t} - R_f) + \epsilon_{i,t}
+\end{equation}
+Test:
+\begin{equation}
+H_0: \alpha = 0 ;
+H_1: \alpha \neq 0
+\end{equation}
+\begin{equation}
+H_0: \beta = 1 ;
+H_1: \beta \neq 1
+\end{equation}
+
+That is run CAPM regression for AMAT and estimate CAPM with $\alpha=0$ \& $\beta=1$ for asset. The getStatistics method will reflect these alternative hypothesis tests. Finally, when plotting the asset the legend shows the coefficient values and their standard error.
 <<ex4>>=
 # Univariate CAPM
 uv <- CAPM(exReturns[,1], mrkt)
@@ -102,7 +108,7 @@
 @
 
 \subsection{CAPM Model: Multiple Asset Analysis}
-Run CAPM regression
+The CAPM function can handle multiple assets at once, and will cycle through each asset one at a time and output the results. When plotting the asset the legend shows the coefficient values and their standard error. Run CAPM regression:
 <<ex5>>=
 # MLM CAPM for AMAT, AMGN, and CAT
 mlm <- CAPM(exReturns[,1:3], mrkt)
@@ -113,22 +119,30 @@
 @
 
 \section{Testing CAPM}
-\subsection{Retrieve $\alpha$ \& $\beta$ and Estimate Result Significance}
-Retrieve $\alpha$ \& $\beta$ from CAPM object for one or multiple assets and run hypothesis test.
+\subsection{Retrieve $\alpha$ \& $\beta$ and Run a Hypothesis Test to Estimate Result Significance}
+Retrieve $\alpha$ \& $\beta$ from CAPM object for one or multiple assets and run hypothesis test. Then specify a significance level to test using the hypTest method:
+\begin{equation}
+H_0: \alpha = 0 ;
+H_1: \alpha \neq 0
+\end{equation}
+\begin{equation}
+H_0: \beta = 1 ;
+H_1: \beta \neq 1
+\end{equation}
 <<ex6>>=
 # For uv
 getBetas(uv)
 getAlphas(uv)
-hypTest(uv, CI=0.05)
+hypTest(uv, significanceLevel=0.05)
 # For mlm
 getBetas(mlm)
 getAlphas(mlm)
-hypTest(mlm, CI=0.05)
+hypTest(mlm, significanceLevel=0.05)
 @
 
 \subsection{Estimate Expected Returns and Plot}
-Plot expected return versus beta.
-Estimate expected returns
+Security Market Line (SML) of the CAPM. The SML is a represesentation of the CAPM. It illustrates the expected rate of return of an individual security as a function of systematic, non-diversified risk (known as $\beta$).
+Plot expected return versus $\beta$.
 <<ex7>>=
 # MLM CAPM
 mlm <- CAPM(exReturns[,], mrkt)
@@ -138,9 +152,9 @@
 @
 
 \section{Consumption-Oriented CAPM}
-\subsection{Fitting C-CAPM}
-
-Run C-CAPM regression for CONS (Consumption).
+\subsection{Fitting CCAPM}
+To illustate the power of the CAPM model test its relationship with explanatory variable consumption. Running consumption alone results in a model that is underspecified. But once savings, and income are added the explanatory power of the model is enhanced but that is beyond the illustrative purpose of this vignette.
+Run CCAPM regression for CONS (Consumption).
 <<ex8>>=
 # Load FED consumption data: CONS
 data(consumption)
@@ -157,5 +171,5 @@
 plot(capm.cons)
 @
 
-NOTE: Specific problems with C-CAPM is that it suffers from two puzzles: the equity premium puzzle (EPP) and the risk-free rate puzzle (RFRP). EPP implies that investors are extremely risk averse to explain the existence of a market risk premium. While RFRP stipulates that investors save in TBills despite the low rate of return.
+NOTE: Particular problems with C-CAPM is that it suffers from two puzzles: the equity premium puzzle (EPP) and the risk-free rate puzzle (RFRP). EPP implies that investors are extremely risk averse to explain the existence of a market risk premium. While RFRP stipulates that investors save in TBills despite the low rate of return.
 \end{document}

Modified: pkg/GARPFRM/vignettes/CAPM_TF.pdf
===================================================================
--- pkg/GARPFRM/vignettes/CAPM_TF.pdf	2014-03-31 00:21:40 UTC (rev 154)
+++ pkg/GARPFRM/vignettes/CAPM_TF.pdf	2014-03-31 00:55:39 UTC (rev 155)
@@ -1,49 +1,48 @@
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To get the complete diff run:
    svnlook diff /svnroot/uwgarp -r 155