The {BLCOP} package is an implementation of the Black-Litterman and copula opinion pooling frameworks. The Black-Litterman model was devised in 1992 by Fisher Black and Robert Litterman. Their goal was to create a systematic method of specifying and then incorporating analyst/portfolio manager views into the estimation of market parameters.
BLViews() and COPViews() construct views objectsaddBLViews() and addCOPViews() allow more views to be added to existing objectsdistribution() and mvdistribution() create distribution and mvdistribution objectsBLPosterior() calculates the posterior distribution using the Black-Litterman modelCOPPosterior() calculates the posterior distribution using copula opinion poolingYou can install the released version of BLCOP from CRAN with:
And the development version from GitHub with:
library(BLCOP)
# For a matrix of monthly returns for 6 assets
head(monthlyReturns)
#> IBM MS DELL C JPM BAC
#> 1998-02-02 0.057620253 0.19578623 0.40667739 0.1224778047 0.157384084 0.143954576
#> 1998-03-02 -0.005457679 0.04383326 -0.51565628 0.0785547367 0.087215863 0.064817518
#> 1998-04-01 0.115529027 0.08233841 0.19188192 0.0198333333 0.027283511 0.041952290
#> 1998-05-01 0.014067489 -0.01027006 0.02055728 0.0009805524 -0.018908776 -0.006578947
#> 1998-06-01 -0.022893617 0.17050986 0.12619828 -0.0101224490 -0.444607915 0.015761589
#> 1998-07-01 0.154080655 -0.04717084 0.17002478 0.1091868712 0.001589404 0.039900900
# Define a pick matrix (a vector of confidences)
pickMatrix <- matrix(c(1/2, -1, 1/2, 0, 0, 0),
nrow = 1,
ncol = 6)
# Create a views object
views <- BLViews(P = pickMatrix,
q = 0.06,
confidences = 100,
assetNames = colnames(monthlyReturns))
# Determine the posterior distribution of these assets
BLPosterior(monthlyReturns, views, tau = 1/2, marketIndex = sp500Returns)
#> Prior means:
#> IBM MS DELL C JPM BAC
#> 0.002269870 0.005799591 -0.001161339 0.001718354 -0.009042287 0.005472691
#> Posterior means:
#> IBM MS DELL C JPM BAC
#> 0.009795730 -0.016744179 0.014453759 -0.004741680 -0.015465517 0.001505639
#> Posterior covariance:
#> IBM MS DELL C JPM BAC
#> IBM 0.022113337 0.011762652 0.013388809 0.009418743 0.01189892 0.006017050
#> MS 0.011762652 0.033040555 0.018441735 0.014076656 0.01650328 0.009143918
#> DELL 0.013388809 0.018441735 0.048344919 0.008453909 0.01088555 0.005957519
#> C 0.009418743 0.014076656 0.008453909 0.017307957 0.01246270 0.007215142
#> JPM 0.011898924 0.016503281 0.010885549 0.012462701 0.03032755 0.012937189
#> BAC 0.006017050 0.009143918 0.005957519 0.007215142 0.01293719 0.011893184