# Quant analytics: Robust Bayesian Allocation question

(Last Updated On: January 7, 2012)

Quant analytics: Robust Bayesian Allocation question

How do I interpret the v_i — the numerator in formula (21) which calculates gamma_sigma — in the paper Robust Bayesian Allocation?

In the associated MATLAB code : http://www.mathworks.com/matlabcentral/fileexchange/31419, v_i seems to index the volatility of a particular portfolio along the efficient frontier identified by the sample covariance (ds_hat) and sample mu.

Below are the specific MATLAB code excerpts and my questions after the %:

PickVol = round( .8 * NumPortf ) % Why the arbitrary choice of .8?

v = ( ds_hat( PickVol ) ) ^ 2 % Why the use of ds_hat as opposed to use of Bayesian efficient frontier?

Robust Bayseian Allocation

Using the Bayesian posterior distribution of the market parameters we define self-adjusting uncertainty regions for the robust mean-variance problem. Under a…

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The efficient frontier (standard, Bayesian, or robust Bayesian) can be parametrized by the target volatility of the respective portfolio on the frontier, which is a free, positive parameter. That is the coefficient you see.
In the specific case, I am implementing the robust Bayesian formula (21) inhttp://www.symmys.com/node/102 but the same target appears in the standard formula (1) and in the robust formula (3) 