GRS Test Statistic and p-value based on Maximum Likelihood Estimator for Covariance matrix

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Description

W statistic given in (7) of GRS (1989) <DOI:10.2307/1913625>

Usage

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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

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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)