GRS.Power {GRS.test}

Statistical Power of the GRS test

Description

Calculates the power of the GRS test with density functions under H0 and H1

Usage

GRS.Power(T, N, K, theta, ratio, alpha = 0.05, xmax = 10, 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

alpha

the level of significance, default is 0.05

xmax

the support of the desnity is from 0 to xmax, default is 10

Graph

show graph if TRUE. No graph otherwise

Details

Calculate the power following GRS (1989) <DOI:10.2307/1913625>

The distribution under H1 is based on the value of theta and ratio

Under H0: ratio = 1; under H1: ratio < 1

Value

Power

power of the test

Critical.value

critical value at alpha

Note

The graph option plots the density functions of the GRS test under H0 and H1.

The blue vertical line represents the critical value at alpha level of significance

The black density function is the one under H0, and the gray-shaded area is level of significance.

The red one is the one under H1, and the red-shaded area is the power.

Author(s)

Jae H. Kim

References

Gibbons, Ross, Shanken, 1989. A test of the efficiency of a given portfolio, Econometrica, 57,1121-1152. <DOI:10.2307/1913625>

See Also

GRS(1989) <DOI:10.2307/1913625>

Examples

GRS.Power(T=120, N=25, K=3, theta=0.3, ratio=0.5)  # Figure 1 of Kim and Shamsuddin (2016)