GRS.Powerfunc {GRS.test}

Power functions for the GRS test

Description

The function plots the power functions for a range of sample size (T), given the other parameter values

Usage

GRS.Powerfunc(Tvec, N, K, theta, alpha = 0.05)

Arguments

Tvec

a vector of sample sizes

N

the number of portfolio returns

K

the number of risk factors

theta

maximum Sharpe ratio of the K factor portfolios

alpha

the level of significance, default is 0.05

Details

The power is plotted against the ratio=theta/thetas, the proprotion of potential efficiency

Value

Power: Matrix of power values plotted

Note

Under H0: ratio = 1, so the power = alpha when ratio = 1.

The power increases as the ratio declines from 1.

The power increases with sample size, so the upper power function is associated with larger sample size.

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.Powerfunc(Tvec=c(60,120),N=25, K=3,theta=0.3)  # Figure 2 of Kim and Shamsuddin (2016)