del_sropt: Create an 'del_sropt' object.

Description

Spawns an object of class del_sropt.

Usage

del_sropt(z.s, z.sub, df1, df2, df1.sub, drag = 0, ope = 1, epoch = "yr")

Value

a list cast to class del_sropt, with attributes

sropt: the optimal Sharpe statistic.
sropt.sub: the optimal Sharpe statistic on the subspace.
df1: the number of assets.
df2: the number of observed vectors.
df1.sub: the input df1.sub term.
drag: the input drag term.
ope: the input ope term.
T2: the Hotelling \(T^2\) statistic.
T2.sub: the Hotelling \(T^2\) statistic on the subspace.

Arguments

z.s: an optimum Sharpe ratio statistic, on some set of assets.
z.sub: an optimum Sharpe ratio statistic, on a linear subspace of the assets. If larger than z.s an error is thrown.
df1: the number of assets in the portfolio.
df2: the number of observations.
df1.sub: the rank of the linear subspace of the hedge constraint. by restricting attention to the subspace.
drag: the 'drag' term, \(c_0/R\). defaults to 0. It is assumed that drag has been annualized, i.e. has been multiplied by \(\sqrt{ope}\). This is in contrast to the c0 term given to sr.
ope: the number of observations per 'epoch'. For convenience of interpretation, The Sharpe ratio is typically quoted in 'annualized' units for some epoch, that is, 'per square root epoch', though returns are observed at a frequency of ope per epoch. The default value is 1, meaning the code will not attempt to guess what the observation frequency is, and no annualization adjustments will be made.
epoch: the string representation of the 'epoch', defaulting to 'yr'.

Author

Steven E. Pav shabbychef@gmail.com

Details

The del_sropt class contains information about the difference between two rescaled T^2-statistics, useful for spanning tests, and inference on hedged portfolios. The following are list attributes of the object:

sropt: The (optimal) Sharpe ratio statistic of the 'full' set of assets.
sropt_sub: The (optimal) Sharpe ratio statistic on some subset, or linear subspace, of the assets.
df1: The number of assets.
df2: The number of observations.
df1.sub: The number of degrees of freedom in the hedge constraint.
drag: The drag term, which is the 'risk free rate' divided by the maximum risk.
ope: The 'observations per epoch'.
epoch: The string name of the 'epoch'.

For the most part, this constructor should not be called directly, rather as.del_sropt should be called instead to compute the needed statistics.

Examples

Run this code

# roll your own.
ope <- 253

set.seed(as.integer(charToRaw("be determinstic")))
n.stock <- 10
X <- matrix(rnorm(1000*n.stock),nrow=1000)
Sigma <- cov(X)
mu <- colMeans(X)
w <- solve(Sigma,mu)
z <- t(mu) %*% w
n.sub <- 6
w.sub <- solve(Sigma[1:n.sub,1:n.sub],mu[1:n.sub])
z.sub <- t(mu[1:n.sub]) %*% w.sub
df1.sub <- n.stock - n.sub

roll.own <- del_sropt(z.s=z,z.sub=z.sub,df1=10,df2=1000,
 df1.sub=df1.sub,ope=ope)
print(roll.own)

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