My random thoughts/questions about portfolio optimization , some of which got answered based on the work I had been doing in the last 2-3 weeks. Some remain unanswered!.

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  1. Is efficient allocation a myth ? Abnormal Returns
  2. If multivariate gaussian is a theoretical approximation in the classic mv optimization, will a multivariate t suffice ? what multivariate distribution should one assume in computing portfolio risk and return ?
  3. To what extent robust estimators (mcd, shrink estimators) are useful in minimizing time varying nature of efficient frontier?
  4. Is Michaud’s efficient frontier , a parametric approach to investing or non-parametric ? Resampled frontier takes a parametric approach, while rebalancing the portfolio takes a non-parametric approach?
  5. Should one use a shrinkage estimator and then generate a resampled frontier instead of relying on sample mean and covariance for resampling?
  6. What is the effect of bootstrapping from historical returns and then drawing a million frontiers? Will it be appropriate way to do things when compared to sampling from a known distribution ?
  7. How do you illustrate the risk return surface ? a contour, persp plot or a lattice plot ?
  8. What can one infer from the implied returns ?
  9. How do you select the time period that you need to include to calculate risk return estimates ? 2 years / 3 years / 4 years / 6 years ?
  10. Should you give importance to robust covariance estimation or robust mean estimation ?
  11. Is shrinkage estimator better than mcd estimator for asset allocation with about 5 assets ?
  12. Should one use non-parametric bootstrapping OR follow montecarlo based on some known multivariate distribution?
  13. Which estimation error effect is greater in the context of efficient frontier - estimation error in mean or estimation error in covariance ?
  14. When do you rebalance a portfolio?
  15. Is a quant based trigger not useful in a scenario where you sell a product to a lot of retail investors and quant based rebalancing is an implementation nightmare ?
  16. Should I take monthly returns or daily returns or weekly returns for portfolio optimization?
  17. If I am using a shrinkage estimator for parameter estimation, should I use the same shrinkage estimator for the resampled portfolio? Since I am anyway using shrinkage for the initial historical data ,why should I use shrinkage again for the multivariate sample generated?
  18. Is it better to pitch a product saying, “Here is the expected return and here is the range of volatilities that can hit you " OR “Here is the expected risk and here is the range of returns that this portfolio can give you " …. Statistically , they are 2 different types of information as each a slice in one of the directions of risk return surface. However from a Behavioral economics perspective, what needs to be done ?
  19. How does one implement MCD estimator ? How does one implement shrinkage estimator ?
  20. What is the different between mcd in MASS and MCD in robustbase package , in terms of implementation ?
  21. Sortino ratio / Sharpe ratio — Which one makes sense to report and pitch to clients ?
  22. If I have n historical time series points, what number of points should i take in order to define it as a bootstrapped sample ? Does sample have any meaning at all, when talking in terms of financial time series which are stochastic ?
  23. Am I living in a fancy world where I am sampling mean and cov for a set of assets when I know that they are not capturing the time variant nature of the series ?
  24. Comparison of all the robust estimators on the same historical data
  25. Who generates views in Black-Litterman model ? If one looks at the credit crisis and most of the wall street analysts failure in predicting the same, does black-litterman work in the real world ?