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

Spawns an object of class `del_sropt`

.

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

`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 |

`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, |

`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 |

`epoch` |
the string representation of the 'epoch', defaulting to 'yr'. |

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.

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.

**WARNING:** This function is not well tested, may contain errors, may change in the
next package update. Take caution.

2FIX: allow rownames?

Steven E. Pav [email protected]

Other del_sropt: `as.del_sropt`

,
`is.del_sropt`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
# 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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