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

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

1 | ```
GRS.optimal(T, N, K, theta, ratio, Graph = "TRUE")
``` |

`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 |

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).

`opt.sig ` |
Optimal level of significance |

`opt.crit ` |
Critical value corresponding to opt.sig |

`opt.beta ` |
Type II error probability corresponding to opt.sig |

ratio = theta/thetas

thetas = maximum Sharpe ratio of the K factor portfolios: GRS (1989) <DOI:10.2307/1913625>

Jae H. Kim

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

Kim and Ji (2015)

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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