GRS.T: Sample Size Selection for the GRS test

In GRS.test: GRS Test for Portfolio Efficiency, Its Statistical Power Analysis, and Optimal Significance Level Calculation

Sample Size Selection for the GRS test

Description

Given the desired level of Type I and II error probabilities, the function returns the sample size required.

Usage

GRS.T(N, K, theta, ratio, alpha, beta, Tmax = 10000)

Arguments

N	the number of portfolio returns
K	the number of risk factors
theta	maximum Sharpe ratio of the K factor portfolios
ratio	theta/thetas, proportion of the potential efficiency
alpha	the desried level of significance, or Type I error probability
beta	the desried level of Type II error probability
Tmax	the maximum number of sample size, default is 10000

Details

the desired level of power = 1 - beta

Value

Required.T	required sample size
Critical.value	the corresponding critical value

Note

Critical.value is from the F-distribution with df1=N and df2=Required.T-N-K degrees of freedom, at the alpha level of significance.

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

Kim and Shamsuddin, 2017, Empirical Validity of Asset-pricing Models: Application of Optimal Significance Level and Equal Probability Test

Examples

GRS.T(N=25,K=3,theta=0.25,ratio=0.4,alpha=0.05, beta=0.05, Tmax=5000) 

GRS.test documentation built on July 2, 2022, 1:06 a.m.