meanEstimation {RiskPortfolios}

Estimation of mean returns

Description

Function which is used to compute the estimation of the mean returns.

Usage

meanEstimation(rets, control = list())

Arguments

rets

a (T \times 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 estimate the mean returns, among 'naive', 'ewma', 'bs' and 'mart' where:

  'naive' is used to compute the arithmetic mean of the returns.

  'ewma' is used to compute the exponential weighted moving average mean of the returns. The data must be sorted from the oldest to the latest. See RiskMetrics (1996).

  'bs' is used to compute the Bayes-Stein estimation. See Jorion (1986).

  'mart' is used to compute the Martinelli (2008) implied returns.

  Default: type = 'naive'.

• lambda decay parameter. Default: lambda = 0.94.

Value

A (N \times 1) vector of expected returns.

Author(s)

David Ardia, Kris Boudt and Jean-Philippe Gagnon Fleury.

References

Jorion, P. (1986). Bayes-Stein estimation for portfolio analysis. Journal of Finance and Quantitative Analysis 21(3), pp.279-292.

Martellini, L. (2008). Towards the design of better equity benchmarks. Journal of Portfolio Management 34(4), Summer,pp.34-41.

RiskMetrics (1996) RiskMetrics Technical Document. J. P. Morgan/Reuters.

Examples

# Load returns of assets or portfolios
data("Industry_10")
rets = Industry_10

# Naive estimation of the mean
meanEstimation(rets)

# Naive estimation of the mean
meanEstimation(rets, control = list(type = 'naive'))

# Ewma estimation of the mean with default lambda = 0.94
meanEstimation(rets, control = list(type = 'ewma'))

# Ewma estimation of the mean with lambda = 0.9
meanEstimation(rets, control = list(type = 'ewma', lambda = 0.9))

# Martinelli's estimation of the mean
meanEstimation(rets, control = list(type = 'mart'))

# Bayes-Stein's estimation of the mean
meanEstimation(rets, control = list(type = 'bs'))