# GRS.MLtest: GRS Test Statistic and p-value based on Maximum Likelihood... In GRS.test: GRS Test for Portfolio Efficiency, Its Statistical Power Analysis, and Optimal Significance Level Calculation

## Description

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

## Usage

 `1` ```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

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

 ```1 2 3 4``` ```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) ```

GRS.test documentation built on Dec. 4, 2017, 9:03 a.m.