# Tag Info

10

Short of having a 'reasonable' predictive model for expected returns and the covariance matrix, there are a couple lines of attack. Shrinkage estimators (via Bayesian inference or Stein-class of estimators) Robust portfolio optimization Michaud's Resampled Efficient Frontier Imposing norm constraints on portfolio weights Naively, shrinkage methods ...

8

Both answers from Shane and Vishal Belsare make sense and detail different models. In my experience, I have never been satisfied by a unique model since the majority of papers out there can be split in two categories: Those that predict the mean component of the problem. Those that predict the variance component of the problem. The ideal (to read ...

7

Hey, it's early days yet. After all it is still called MODERN portfolio theory. I think there are two main issues and they are both really cultural: 1) specifying alphas 2) wild results Alphas I agree with Gappy that alphas are the key thing you need to have effectiveness (unless you are doing minimum variance). Having a vector of expected returns is ...

6

I believe there are several ways you can tackle your problems. First, you mentioned that your perform several optimizations. One solution that comes to mind instead of speeding up the optimization itself is to perform the optimizations in parallel, so you could look at Mathwork's Parallel Computing Toolbox. Second, providing the optimizer with a good ...

6

You raise a very important point, which unfortunately doesn't have a simple answer. Black-Litterman addresses the allocation problem by allowing you to provide a prior within a bayesian framework. It doesn't really tell you how to produce the prior itself. But more importantly, it doesn't address the fundamental problem: it's difficult to accurately ...

5

Bernd Scherer has done exactly this test in his text "Portfolio Construction and Risk Budgeting 4th Edition". There is an SSRN paper by Scherer called "Resampled Efficiency and Portfolio Choice (2004)" you can take a look at as well. I would suggest you skip re-sampling (especially if you have a long-only portfolio) and take a look at Meucci's Robot ...

3

I think the original reference of mean-variance portfolios being “error maximizing portfolios” is: Michaud, R. (1989). “The Markowitz Optimization Enigma: Is Optimization Optimal?” Financial Analysts Journal 45(1), 31–42. The reason is that even small changes in the estimated means can result in huge changes in the whole portfolio structure. Have a ...

3

In addition to the points above, I'd say that asset managers also have to bear two things in mind that limit their ability to "properly" optimise their portfolios: 1) general restrictions on asset allocation (regulatory, contractual, common-sense) 2) transaction cost In my experience, asset managers do use a variety of optimisation techniques occasionally ...

3

In robust optimization, the true return is not known, we just have a prior $\alpha$ and you have to take into account a possible misestimate which can lower the true return. This is done under the assumption that the posterior return will be within the prior return $\alpha$ plus minus the error being in some $\sigma$-interval. Now a try for a more formal ...

3

The biggest problem with mean-variance optimization is that the sensitivity of the estimated covariance matrix. Mean variance optimization assumes that one "knows" the covariance of each asset with every other asset, or that the covariance matrix is constant. Without this assumption the MVO framework is not tractable. Axioma and others do a lot more than ...

2

Assuming those are arithmetic returns and covariances at the horizon, calculate a $9\times1$ vector containing the betas with respect to the world index using the covariance matrix, call it $\beta$. The covariance resulting from the world index can be described as $\beta\sigma_{world}^{2}\beta'$. The matrix ...

2

One of the most salient empirical examples of "error maximization" is provided by Chopra and Ziemba (1993): Chopra, Vijay K., and William T. Ziemba. 1993. “The Effect of Errors in Means, Variances, and Covariances on Optimal Portfolio Choice.” Journal of Portfolio Management, vol. 19, no. 2 (Winter):6–11. The authors compare the performance of ...

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There is a great deal of misinformation and out-of-date information on this site. Many of the references in this discussion and elsewhere have serious research flaws. The Michaud efficient frontier was invented and patented by Robert Michaud and Richard Michaud, U.S. patent # 6,003,018. The alternatives discussed here are not patented nor in many cases ...

1

Before answering your questions directly i would like to briefly restate the idea of the resampled efficent frontier: One of the problem with classical mean variance optimization is (even if the multivariate normal assumption holds) that you cant estimate $\mu$ and $\Omega$ (which is usually denoted as $\Sigma$) exactly. Thats why you incur estimation ...

1

Let $\mu$ and $\Sigma$ be the expected mean and covariance matrices for a mean-variance optimization. For a standard, unconstrained, utility-based optimization, it can be shown that the optimal weights will equal $$w=\frac{1}{\lambda}\Sigma^{-1}\mu$$ where $\lambda$ is an arbitrary risk aversion coefficient. In order to measure the sensitivity of the ...

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