| Type: | Package |
| Title: | Covariance Matrix Estimation and Regularization for Finance |
| Version: | 1.1.0 |
| Description: | Estimation and regularization for covariance matrix of asset returns. For covariance matrix estimation, three major types of factor models are included: macroeconomic factor model, fundamental factor model and statistical factor model. For covariance matrix regularization, four regularized estimators are included: banding, tapering, hard-thresholding and soft- thresholding. The tuning parameters of these regularized estimators are selected via cross-validation. |
| URL: | http://github.com/yanyachen/FinCovRegularization |
| BugReports: | http://github.com/yanyachen/FinCovRegularization/issues |
| Depends: | R (≥ 2.10) |
| Imports: | stats, graphics, quadprog |
| License: | GPL-2 |
| LazyData: | true |
| RoxygenNote: | 5.0.1 |
| NeedsCompilation: | no |
| Packaged: | 2016-04-25 08:52:44 UTC; Administrator |
| Author: | YaChen Yan [aut, cre], FangZhu Lin [aut] |
| Maintainer: | YaChen Yan <yanyachen21@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2016-04-25 15:32:07 |
FinCovRegularization: Covariance Matrix Estimation and Regularization for Finance
Description
Estimation and regularization for covariance matrix of asset returns. For covariance matrix estimation, three major types of factor models are included: macroeconomic factor model, fundamental factor model and statistical factor model. For covariance matrix regularization, four regularized estimators are included: banding, tapering, hard-thresholding and soft-thresholding. The tuning parameters of these regularized estimators are selected via cross-validation.
The Squared Frobenius Norm
Description
Calculate the squared Frobenius norm of a matrix
Usage
F.norm2(matrix)
Arguments
matrix |
a matrix |
Value
a scalar of the squared Frobenius norm
Examples
data(m.excess.c10sp9003)
cov.SAM <- cov(m.excess.c10sp9003)
F.norm2(cov.SAM)
Covariance Matrix Estimation by Fundamental Factor Model
Description
Estimate covariance matrix by fitting a fundamental factor model using OLS or WLS regression
Usage
FundamentalFactor.Cov(assets, exposure, method = "WLS")
Arguments
assets |
a N*p matrix of asset returns, N indicates sample size and p indicates the dimension of asset returns |
exposure |
a p*q matrix of exposure indicator for the fundamental factor model, p corresponds to the dimension of asset returns, q indicates the number of fundamental industries |
method |
a character, indicating regression method: "OLS" or "WLS" |
Value
an estimated p*p covariance matrix
Examples
data(m.excess.c10sp9003)
assets <- m.excess.c10sp9003[,1:10]
Indicator <- matrix(0,10,3)
dimnames(Indicator) <- list(colnames(assets),c("Drug","Auto","Oil"))
Indicator[c("ABT","LLY","MRK","PFE"),"Drug"] <- 1
Indicator[c("F","GM"),"Auto"] <- 1
Indicator[c("BP","CVX","RD","XOM"),"Oil"] <- 1
FundamentalFactor.Cov(assets,exposure=Indicator,method="WLS")
Global Minimum Variance Portfolio
Description
Computing a global minimum variance portfolio weights from the estimated covariance matrix of return series.
Usage
GMVP(cov.mat, short = TRUE)
Arguments
cov.mat |
an estimated p*p covariance matrix |
short |
logical flag, indicating whether shortsales on the risky assets are allowed |
Value
a numerical vector containing the estimated portfolio weights
Examples
data(m.excess.c10sp9003)
assets <- m.excess.c10sp9003[,1:10]
GMVP(cov(assets), short=TRUE)
GMVP(cov(assets), short=FALSE)
Independence opreator on Covariance Matrix
Description
Apply independence model on a covariance matrix.
Usage
Ind.Cov(sigma)
Arguments
sigma |
a covariance matrix |
Value
a regularized covariance matrix after applying independence model
Examples
data(m.excess.c10sp9003)
cov.SAM <- cov(m.excess.c10sp9003)
Ind.Cov(cov.SAM)
Covariance Matrix Estimation by Macroeconomic Factor Model
Description
Estimate covariance matrix by fitting a macroeconomic factor model using time series regression
Usage
MacroFactor.Cov(assets, factor)
Arguments
assets |
a N*p matrix of asset returns, N indicates sample size and p indicates the dimension of asset returns |
factor |
a numerical vector of length N, or a N*q matrix of macroeconomic factor(s), q indicates the dimension of factors |
Value
an estimated p*p covariance matrix
Examples
data(m.excess.c10sp9003)
assets <- m.excess.c10sp9003[,1:10]
factor <- m.excess.c10sp9003[,11]
MacroFactor.Cov(assets, factor)
The Squared Operator Norm
Description
Calculate the squared Operator norm of a matrix
Usage
O.norm2(matrix)
Arguments
matrix |
a matrix |
Value
a scalar of the squared Operator norm
Examples
data(m.excess.c10sp9003)
cov.SAM <- cov(m.excess.c10sp9003)
O.norm2(cov.SAM)
Risk Parity Portfolio
Description
Computing a Risk Parity portfolio weights from the estimated covariance matrix of return series.
Usage
RiskParity(cov.mat)
Arguments
cov.mat |
an estimated p*p covariance matrix |
Value
a numerical vector containing the estimated portfolio weights
Examples
data(m.excess.c10sp9003)
assets <- m.excess.c10sp9003[,1:10]
RiskParity(cov(assets))
Covariance Matrix Estimation by Statistical Factor Model
Description
Estimate covariance matrix by fitting a statistical factor model using principle components analysis
Usage
StatFactor.Cov(assets, k = 0)
Arguments
assets |
a matrix of asset returns |
k |
numbers of factors, if k = 0, automatically estimating by Kaiser method |
Value
an estimated p*p covariance matrix
Examples
data(m.excess.c10sp9003)
assets <- m.excess.c10sp9003[,1:10]
StatFactor.Cov(assets, 3)
Banding Opreator on Covariance Matrix
Description
Apply banding operator on a covariance matrix with a banding parameter.
Usage
banding(sigma, k = 0)
Arguments
sigma |
a p*p covariance matrix |
k |
banding parameter |
Value
a regularized covariance matrix after banding operation
References
"High-Dimensional Covariance Estimation" by Mohsen Pourahmadi
Examples
data(m.excess.c10sp9003)
cov.SAM <- cov(m.excess.c10sp9003)
banding(cov.SAM, 7)
Select Tuning Parameter for Banding Covariance Matrix by CV
Description
Apply K-fold cross-validation for selecting tuning parameters for banding covariance matrix using grid search strategy
Usage
banding.cv(matrix, n.cv = 10, norm = "F", seed = 142857)
Arguments
matrix |
a N*p matrix, N indicates sample size and p indicates the dimension |
n.cv |
times that cross-validation repeated, the default number is 10 |
norm |
the norms used to measure the cross-validation errors, which can be the Frobenius norm "F" or the operator norm "O" |
seed |
random seed, the default value is 142857 |
Details
For cross-validation, this function split the sample randomly into two pieces of size n1 = n-n/log(n) and n2 = n/log(n), and repeat this k times
Value
An object of class "CovCv" containing the cross-validation's result for covariance matrix regularization, including:
regularization |
regularization method, which is "Banding" |
parameter.opt |
selected optimal parameter by cross-validation |
cv.error |
the corresponding cross-validation errors |
n.cv |
times that cross-validation repeated |
norm |
the norm used to measure the cross-validation error |
seed |
random seed |
References
"High-Dimensional Covariance Estimation" by Mohsen Pourahmadi
Examples
data(m.excess.c10sp9003)
retcov.cv <- banding.cv(m.excess.c10sp9003, n.cv = 10,
norm = "F", seed = 142857)
summary(retcov.cv)
plot(retcov.cv)
# Low dimension
Hard-Thresholding Opreator on Covariance Matrix
Description
Apply hard-thresholding operator on a covariance matrix with a hard-thresholding parameter.
Usage
hard.thresholding(sigma, threshold = 0.5)
Arguments
sigma |
a p*p covariance matrix |
threshold |
hard-thresholding parameter |
Value
a regularized covariance matrix after hard-thresholding operation
References
"High-Dimensional Covariance Estimation" by Mohsen Pourahmadi
Examples
data(m.excess.c10sp9003)
cov.SAM <- cov(m.excess.c10sp9003)
hard.thresholding(cov.SAM, threshold = 0.001)
10 stock and S&P 500 excess returns
Description
A dataset containing monthly excess returns of 10 stocks and S$P 500 index return from January 1990 to December 2003
Usage
data(m.excess.c10sp9003)
Format
A matrix with 168 rows and 11 variables
plot CovCv object
Description
Visualizes the results of covariance matrix regularization parameter tuning
Usage
## S3 method for class 'CovCv'
plot(x, ...)
Arguments
x |
CovCv object to plot |
... |
other arguments ignored (for compatibility with generic) |
print CovCv object
Description
print selected optimal parameter
Usage
## S3 method for class 'CovCv'
print(x, ...)
Arguments
x |
CovCv object to plot |
... |
other arguments ignored (for compatibility with generic) |
Soft-Thresholding Opreator on Covariance Matrix
Description
Apply soft-thresholding operator on a covariance matrix with a soft-thresholding parameter.
Usage
soft.thresholding(sigma, threshold = 0.5)
Arguments
sigma |
a covariance matrix |
threshold |
soft-thresholding parameter |
Value
a regularized covariance matrix after soft-thresholding operation
References
"High-Dimensional Covariance Estimation" by Mohsen Pourahmadi
Examples
data(m.excess.c10sp9003)
cov.SAM <- cov(m.excess.c10sp9003)
soft.thresholding(cov.SAM, threshold = 0.001)
Display a useful description of a CovCv object
Description
Display a useful description of a CovCv object
Usage
## S3 method for class 'CovCv'
summary(object, ...)
Arguments
object |
CovCv object to summarise |
... |
other arguments ignored (for compatibility with generic) |
Tapering Opreator on Covariance Matrix
Description
Apply tapering operator on a covariance matrix with tapering parameters.
Usage
tapering(sigma, l, h = 1/2)
Arguments
sigma |
a p*p covariance matrix |
l |
tapering parameter |
h |
the ratio between taper l_h and parameter l |
Value
a regularized covariance matrix after tapering operation
References
"High-Dimensional Covariance Estimation" by Mohsen Pourahmadi
Examples
data(m.excess.c10sp9003)
cov.SAM <- cov(m.excess.c10sp9003)
tapering(cov.SAM, l=7, h = 1/2)
Select Tuning Parameter for Tapering Covariance Matrix by CV
Description
Apply K-fold cross-validation for selecting tuning parameters for tapering covariance matrix using grid search strategy
Usage
tapering.cv(matrix, h = 1/2, n.cv = 10, norm = "F", seed = 142857)
Arguments
matrix |
a N*p matrix, N indicates sample size and p indicates the dimension |
h |
the ratio between taper l_h and parameter l |
n.cv |
times that cross-validation repeated, the default number is 10 |
norm |
the norms used to measure the cross-validation errors, which can be the Frobenius norm "F" or the operator norm "O" |
seed |
random seed, the default value is 142857 |
Details
For cross-validation, this function split the sample randomly into two pieces of size n1 = n-n/log(n) and n2 = n/log(n), and repeat this k times
Value
An object of class "CovCv" containing the cross-validation's result for covariance matrix regularization, including:
regularization |
regularization method, which is "Tapering" |
parameter.opt |
selected optimal parameter by cross-validation |
cv.error |
the corresponding cross-validation errors |
n.cv |
times that cross-validation repeated |
norm |
the norm used to measure the cross-validation error |
seed |
random seed |
References
"High-Dimensional Covariance Estimation" by Mohsen Pourahmadi
Examples
data(m.excess.c10sp9003)
retcov.cv <- tapering.cv(m.excess.c10sp9003, n.cv = 10,
norm = "F", seed = 142857)
summary(retcov.cv)
plot(retcov.cv)
# Low dimension
Select Tuning Parameter for Thresholding Covariance Matrix by CV
Description
Apply K-fold cross-validation for selecting tuning parameters for thresholding covariance matrix using grid search strategy
Usage
threshold.cv(matrix, method = "hard", thresh.len = 20, n.cv = 10,
norm = "F", seed = 142857)
Arguments
matrix |
a N*p matrix, N indicates sample size and p indicates the dimension |
method |
thresholding method, "hard" or "soft" |
thresh.len |
the number of thresholding values tested in
cross-validation, the thresholding values will be a sequence of
|
n.cv |
times that cross-validation repeated, the default number is 10 |
norm |
the norms used to measure the cross-validation errors, which can be the Frobenius norm "F" or the operator norm "O" |
seed |
random seed, the default value is 142857 |
Details
For cross-validation, this function split the sample randomly into two pieces of size n1 = n-n/log(n) and n2 = n/log(n), and repeat this k times
Value
An object of class "CovCv" containing the cross-validation's result for covariance matrix regularization, including:
regularization |
regularization method, which is "Hard Thresholding" or "Soft Thresholding" |
parameter.opt |
selected optimal parameter by cross-validation |
cv.error |
the corresponding cross-validation errors |
n.cv |
times that cross-validation repeated |
norm |
the norm used to measure the cross-validation error |
seed |
random seed |
threshold.grid |
thresholding values tested in cross-validation |
References
"High-Dimensional Covariance Estimation" by Mohsen Pourahmadi
Examples
data(m.excess.c10sp9003)
retcov.cv <- threshold.cv(m.excess.c10sp9003, method = "hard",
thresh.len = 20, n.cv = 10, norm = "F", seed = 142857)
summary(retcov.cv)
plot(retcov.cv)
# Low dimension
Minimum threshold constant
Description
This function is for determining the minimum constant in the threshold that guarantees the positive definiteness of the estimator.
Usage
threshold.min(sigma, method = "hard")
Arguments
sigma |
a covariance matrix |
method |
a character, indicating thresholding method: "soft" or "hard" |
Value
minimum constant for thresholding
References
"High-Dimensional Covariance Estimation" by Mohsen Pourahmadi