GRS.Powerfunc function

Power functions for the GRS test

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

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

Returns

Power:Matrix of power values plotted

References

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

Author(s)

Jae H. Kim

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.

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)