Optimal Level of Significance for the GRS test: Normality Assumption
The optimal level is calculated by minimizing expected loss from hypothesis testing
The F-distributions are used to calculate the power, under the normality assumption
GRS.optimal(T, N, K, theta, ratio, p = 0.5, k = 1, Graph = TRUE)
T: sample sizeN: the number of portfolio returnsK: the number of risk factorstheta: maximum Sharpe ratio of the K factor portfoliosratio: theta/thetas, proportion of the potential efficiencyp: prior probability for H0, default is p = 0.5k: relative loss, k = L2/L1, default is k = 1Graph: show graph if TRUE. No graph otherwiseBased on the power calculation of the GRS test, as in GRS (1989) DOI:10.2307/1913625.
The blue square in the plot is the point where the expected loss is mimimized.
The red horizontal line in the plot indicates the point of the covnentional level of significance (alpha = 0.05).
opt.sig: Optimal level of significance
opt.crit: Critical value corresponding to opt.sig
opt.beta: Type II error probability corresponding to opt.sig
Leamer, E. 1978, Specification Searches: Ad Hoc Inference with Nonexperimental Data, Wiley, New York.
Kim, JH and Ji, P. 2015, Significance Testing in Empirical Finance: A Critical Review and Assessment, Journal of Empirical Finance 34, 1-14. DOI:http://dx.doi.org/10.1016/j.jempfin.2015.08.006
Gibbons, Ross, Shanken, 1989. A test of the efficiency of a given portfolio, Econometrica, 57,1121-1152. DOI:10.2307/1913625
Kim and Shamsuddin, 2017, Empirical Validity of Asset-pricing Models: Application of Optimal Significance Level and Equal Probability Test
Jae H. Kim
ratio = theta/thetas
thetas = maximum Sharpe ratio of the K factor portfolios: GRS (1989) DOI:10.2307/1913625
Kim and Choi, 2017, Choosing the Level of Significance: A Decision-theoretic Approach
GRS.optimal(T=90, N=25, K=3, theta=0.25, ratio=0.4) # Figure 3 of Kim and Shamsuddin (2017)
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