GRS.MLtest {GRS.test} | R Documentation |
GRS Test Statistic and p-value based on Maximum Likelihood Estimator for Covariance matrix
Description
W statistic given in (7) of GRS (1989) <DOI:10.2307/1913625>
Usage
GRS.MLtest(ret.mat, factor.mat)
Arguments
ret.mat |
portfolio return matrix, T by N |
factor.mat |
matrix of risk factors, T by K |
Details
T: sample size, N: number of portfolio returns, K: number of risk factors
Value
GRS.stat |
GRS test statistic |
GRS.pval |
its p-value |
theta |
maximum Sharpe ratio of the K factor portfolios |
thetas |
slope of the efficient frontier based on all assets |
ratio |
theta/thetas, proportion of the potential efficiency |
Note
Applicable to CAPM as well as a multi-factor model
Author(s)
Jae H. Kim
References
Gibbons, Ross, Shanken, 1989. A test of the efficiency of a given portfolio, Econometrica, 57,1121-1152. <DOI:10.2307/1913625>
See Also
Fama and French, 1993, Common risk factors in the returns on stocks and bonds, Journal of Financial Economics, 33, 3-56. <DOI:10.1016/0304-405X(93)90023-5>
Fama and French, 2015, A five-factor asset-pricing model, Journal of Financial Economics, 116-1-22. <DOI:http://dx.doi.org/10.1016/j.jfineco.2014.10.010>
Examples
data(data)
factor.mat = data[1:342,2:4] # Fama-French 3-factor model
ret.mat = data[1:342,8:ncol(data)] # 25 size-BM portfolio returns
GRS.MLtest(ret.mat,factor.mat) # See column (iv), Table 9C of Fama-French (1993)