PartialConfidencePosterior: Constructs the partial confidence posterior based on a prior,...

In R-Finance/Meucci: Collection of functionality ported from the MATLAB code of Attilio Meucci.

Description

Constructs the partial confidence posterior based on prior (mean vector and covariance matrix) and a posterior with a relative confidence in the prior vs. the sample data

Usage

  PartialConfidencePosterior(mean_sample, cov_sample,
    mean_prior, cov_prior, relativeConfidenceInMeanPrior,
    relativeConfidenceInCovPrior, sampleSize)

Arguments

mean_sample	the mean of the sample returns
cov_sample	the sample covariance matrix
mean_prior	the prior for the mean returns
cov_prior	the covariance matrix prior
relativeConfidenceInMeanPrior	a numeric with the relative confidence in the mean prior vs. the sample mean. A value of 2 indicates twice as much weight to assign to the prior vs. the sample data. Must be greater than or equal to zero
relativeConfidenceInCovPrior	a numeric with the relative confidence in the covariance prior vs. the sample covariance. A value of 2 indicates twice as much weight to assign to the prior vs. the sample data. Must be greater than or equal to zero
sampleSize	a numeric with the number of rows in the sample data used to estimate mean_sample and cov_sample

Details

T_{1} \equiv T_{0} + T \\ μ_{1} \equiv \frac{1}{ T_{1} } \big( T_{0} μ_{0} + T \hat{ μ } \big) \\ ν_{1} \equiv ν_{0} + T \\ Σ_{1} \equiv \big( ν_{0} Σ_{0} + T \hat{ Σ } + \frac{ \big(μ_{0} - \hat{μ} \big) \big(μ_{0} - \hat{μ} \big)' }{ \big( \frac{1}{T} + \frac{1}{T_{0} } \big) }

Value

mean_post a vector with the confidence weighted posterior mean vector of asset returns blended from the prior and sample mean vector

cov_post a covariance matrix the confidence weighted posterior covariance matrix of asset returns blended from the prior and sample covariance matrix

time_post a numeric

nu_pst a numeric

Author(s)

Ram Ahluwalia [e-mail]

References

A. Meucci - Robust Bayesian Allocation - See formula (11) - (14) http://papers.ssrn.com/sol3/papers.cfm?abstract_id=681553

R-Finance/Meucci documentation built on May 8, 2019, 3:52 a.m.