GRS.optimal: Optimal Level of Significance for the GRS test: Normality...

Description Usage Arguments Details Value Note Author(s) References See Also Examples

View source: R/GRS.optimal.R

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

Usage

1
GRS.optimal(T, N, K, theta, ratio, 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

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 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).

Value

opt.sig

Optimal level of significance

opt.crit

Critical value corresponding to opt.sig

opt.beta

Type II error probability 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

1
GRS.optimal(T=90, N=25, K=3, theta=0.25, ratio=0.4) # Figure 3 of Kim and Shamsuddin (2017)

Example output

$opt.sig
[1] 0.11914

$opt.crit
[1] 1.451265

$opt.beta
[1] 0.1182896

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