Estimation of the semideviation

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Description

Function which computes the semideviation

Usage

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semidevEstimation(rets, control = list())

Arguments

rets

a (T x N) matrix of past returns.

control

control parameters (see *Details*).

Details

The argument control is a list that can supply any of the following components:

type

method used to compute the semideviation vector, among 'naive' and 'ewma' where:

'naive' is used to compute the simple semideviation.

'ewma' is used to compute the exponential weighted moving average semideviation. The data must be sorted from the oldest to the latest.

The semideviation for one stock is computed as follows. First we select the returns which are smaller than the average of the past returns; we get a new vector of dimension K \times 1, K ≤ N. Then, the weight w_i for each observation at its corresponding time t is computed as w = λ^{t}. We obtain a Kx1 vector. The vector of weights is then normalized. Finally, the semideviation is obtained as the weighted standard deviation.

Default: type = 'naive'.

lambda

decay parameter. Default: lambda = 0.94.

Value

A (N x 1) vector of semideviations.

Author(s)

David Ardia <david.ardia@unifr.ch> and Jean-Philippe Gagnon Fleury.

Examples

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set.seed(3214)
T = 100
N = 25
rets = matrix(rnorm(T*N), nrow = T, ncol = N)

#Computes the naive semideviation estimation.
semidevEstimation(rets)

#Computes the naive estimation of the semideviation.
semidevEstimation(rets, control = list(type = "naive"))

#Computes the ewma estimation of the semideviation. Default lambda = 0.94.
semidevEstimation(rets, control = list(type = "ewma"))

#Computes the ewma estimation of the semideviation. Lambda = 0.9.
semidevEstimation(rets, control = list(type = "ewma", lambda = 0.9))