GRS.optimalweight {GRS.test}

Weighted Optimal Level of Significance for the GRS test: Normality Assumption

Description

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

The power is calculated using a range of non-centrality parameters (lamdba), folloing a folded-normal distribution.

The weights are obtained from the density function of folded-normal distribution.

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

Usage

GRS.optimalweight(T, N, K, theta, ratio, delta = 3, p = 0.5, k = 1, Graph = TRUE)

Arguments

T

sample size

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

delta

the standard deviation of the folded-normal distribution, default is 3

p

prior probability for H0, default is p = 0.5

k

relative loss, k = L2/L1, default is k = 1

Graph

show graph if TRUE. No graph otherwise

Details

Based on the power calculation of the GRS test, as in GRS (1989) <DOI:10.2307/1913625>.

The plot shows the folded-normal distribution.

Value

opt.sig

Optimal level of significance

opt.crit

Critical value corresponding to opt.sig

Note

ratio = theta/thetas

thetas = maximum Sharpe ratio of the K factor portfolios: GRS (1989) <DOI:10.2307/1913625>

Author(s)

Jae H. Kim

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

See Also

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

Examples

GRS.optimalweight(T=90, N=25, K=3, theta=0.25, ratio=0.4)