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Unformatted text preview: ected returns and covariance matrix are
given. Obviously, in practice this is not the case and these need to be
o How do we estimate these?
o Can we use the historical sample returns to calculate the past average
returns and covariance matrix? What complicates the matter is that M-V optimization is sensitive to the
o That is, small changes in the expected returns and covariance matrix
may result in large changes in the resulting portfolio weights
o Any estimate is subject to estimation error (sampling error). If the
average estimation error is large the output from M-V could be garbage
at best In this handout we will talk about how to estimate the expected returns
using the Black-Litterman model; we also briefly discuss robust optimization RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 11/11/2012. © P. KOLM. 5 Impact of Estimation Error in M-V Optimization Simple portfolio rules (e.g. equal weighting) often outperforms M-V (Jobson
and Korkie (1981), Jorion (1985)) Portfolio optimizers are often “error maximizers” (Michaud (1998)) Optimal portfolios are not necessarily well diversified and result in “corner
solutions”(Green and Hollifield (1992)) Estimation errors in returns are one order of magnitude more important
than the estimation errors in the covariance matrix (Kallberg and Ziemba
(1984), Best and Grauer (1991; (1991), Chopra and Ziemba (1993)) RIS...
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- Fall '14