GRS.optimalboot function

Optimal Level of Significance for the GRS test: Bootstrapping

The optimal level is calculated by minimizing expected loss from hypothesis testing

The bootstrap is used to calculate the power.

The power is calculated at the estimated values (unrestricted) of parameters under H1.

GRS.optimalboot(ret.mat,factor.mat,p=0.5,k=1,nboot=3000,wild=FALSE,Graph=TRUE)

Arguments

• ret.mat: portfolio return matrix, T by N
• factor.mat: matrix of risk factors, T by K
• p: prior probability for H0, default is p = 0.5
• k: relative loss, k = L2/L1, default is k = 1
• nboot: the number of bootstrap iterations, the default is 3000
• wild: if TRUE, wild bootsrap is conducted; if FALSE (default), bootstrap is based on iid residual resampling
• Graph: show graph if TRUE (default). No graph otherwise

Details

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).

The function also returns the density functions under H0 and H1 (black and red curves, with vertical line the critical value at the optimal level).

Returns

• opt.sig: Optimal level of significance

• opt.crit: Critical value corresponding to opt.sig

• opt.beta: Type II error probability corresponding to opt.sig

References

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

Author(s)

Jae H. Kim

Note

The example below sets nboot=500 for faster execution, but a higher number is recommended.

See Also

Kim and Choi, 2017, Choosing the Level of Significance: A Decision-theoretic Approach

Examples

data(data)
n=60; m1=nrow(data)-n+1; m2=nrow(data)  # Choose the last n observations from the data set
factor.mat = data[m1:m2,2:6]            # Fama-French 5-factors
ret.mat = data[m1:m2,8:ncol(data)]      # 25 size-BM portfolio returns
GRS.optimalboot(ret.mat,factor.mat,p=0.5,k=1,nboot=500,wild=TRUE,Graph=TRUE)