# GRS.Power: Statistical Power of the GRS test In GRS.test: GRS Test for Portfolio Efficiency, Its Statistical Power Analysis, and Optimal Significance Level Calculation

## Description

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

## Usage

 1 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.

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>

GRS(1989) <DOI:10.2307/1913625>

## Examples

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

### Example output

$Power [1] 0.8389462$Critical.value
[1] 1.625954


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