View source: R/GRS.optimalweight.R
GRS.optimalweight | R Documentation |
The optimal level is calculated by minimizing expected loss from hypothesis testing.
The F-distributions are used to calculate the power, under the normality assumption
The power is calculated using a range of non-centrality parameters (lamdba), folloing a folded-normal distribution.
The weights are obtained from the density function of folded-normal distribution.
See, for details, Kim and Choi, 2017, Choosing the Level of Significance: A Decision-theoretic Approach.
GRS.optimalweight(T, N, K, theta, ratio, delta = 3, p = 0.5, k = 1, 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 |
delta |
the standard deviation of the folded-normal distribution, default is 3 |
p |
prior probability for H0, default is p = 0.5 |
k |
relative loss, k = L2/L1, default is k = 1 |
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 plot shows the folded-normal distribution.
opt.sig |
Optimal level of significance |
opt.crit |
Critical value 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, 2017, Empirical Validity of Asset-pricing Models: Application of Optimal Significance Level and Equal Probability Test
Kim and Choi, 2017, Choosing the Level of Significance: A Decision-theoretic Approach
GRS.optimalweight(T=90, N=25, K=3, theta=0.25, ratio=0.4)
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