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

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

Description

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

Under the assumption of equal prior and identical losses from Type I and II errors

Usage

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

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 is the point where the expected loss is mimimized.

The red horizontal line indicate 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, 2016, Reapparaising Empirical Validity of Asset-Pricing Models with consideration of Statistical Power. Working Paper

See Also

Kim and Ji (2015)

Examples

1
GRS.optimal(T=90, N=25, K=3, theta=0.25, ratio=0.4) # Figure 3 of Kim and Shamsuddin (2016)


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