robustBayesianPortfolioOptimization: Construct a Bayesian mean-variance efficient frontier and...

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

Description

Construct a collection of portfolios along the Bayesian mean-variance efficient frontier where each portfolio is equally distanced in return space. The function also returns the most robust portfolio along the Bayesian efficient frontier

Usage

  robustBayesianPortfolioOptimization(mean_post, cov_post,
    nu_post, time_post, riskAversionMu = 0.1,
    riskAversionSigma = 0.1, discretizations = 10,
    longonly = FALSE, volatility)

Arguments

mean_post	the posterior vector of means (after blending prior and sample data)
cov_post	the posterior covariance matrix (after blending prior and sample data)
nu_post	a numeric with the relative confidence in the prior vs. the sample data. 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
time_post	a numeric
riskAversionMu	risk aversion coefficient for estimation of means.
riskAversionSigma	risk aversion coefficient for estimation of Sigma.
discretizations	an integer with the number of portfolios to generate along efficient frontier (equally distanced in return space). Parameter must be an integer greater or equal to 1.
longonly	a boolean for suggesting whether an asset in a portfolio can be shorted or not
volatility	a numeric with the volatility used to calculate gamma-m. gamma-m acts as a constraint on the maximum volatility of the robust portfolio. A higher volatility means a higher volatile robust portfolio may be identified.

Value

a list of portfolios along the frontier from least risky to most risky bayesianFrontier a list with portfolio along the Bayesian efficient frontier. Specifically: returns: the expected returns of each portfolio along the Bayesian efficient frontier volatility: the expected volatility of each portfolio along the Bayesian efficient frontier weights: the weights of each portfolio along the Bayesian efficient frontier robustPortfolio the most robust portfolio along the Bayesian efficient frontier. Specifically: returns: the expected returns of each portfolio along the Bayesian efficient frontier volatility: the expected volatility of each portfolio along the Bayesian efficient frontier weights: the weights of each portfolio along the Bayesian efficient frontier

w_{rB}^{(i)} = argmax_{w \in C, w' Σ_{1} w ≤q γ_{Σ}^{(i)} } \big\{w' μ^{1} - γ _{μ} √{w' Σ_{1} w} \big\}, γ_{μ} \equiv √{ \frac{q_{μ}^{2}}{T_{1}} \frac{v_{1}}{v_{1} - 2} } γ_{Σ}^{(i)} \equiv \frac{v^{(i)}}{ \frac{ ν_{1}}{ν_{1}+N+1} + √{ \frac{2ν_{1}^{2}q_{Σ}^{2}}{ (ν_{1}+N+1)^{3} } } }

Author(s)

Ram Ahluwalia [e-mail]

References

A. Meucci - Robust Bayesian Allocation - See formula (19) - (21) http://papers.ssrn.com/sol3/papers.cfm?abstract_id=681553

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