1 / 16

Covariance Estimation For Markowitz Portfolio Optimization

Explore efficient portfolio selection using covariance estimation methods. Compare results through resampling. Discuss future work on robust allocation strategies.

avick
Download Presentation

Covariance Estimation For Markowitz Portfolio Optimization

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Covariance Estimation For Markowitz Portfolio Optimization Ka Ki Ng Nathan Mullen PriyankaAgarwal Dzung Du RezwanuzzamanChowdhury

  2. Outline • Work Done Last Week • Some Results • Conclusion and Future Work

  3. Portfolio Selection Problem • Given N stocks with mean return μ and covariance matrix Σ • Markowitz’s portfolio selection framework: where q is the expected return level (constrain). • Closed form solution:

  4. Work done • Implement PCA estimator • Run constrained portfolio selection for all our covariance matrix estimators. • Resampling (Bootstrapping) Approach

  5. PCA Estimator

  6. Backtesting • Time window: same as Ledoit and Wolf’s paper • Use NYSE and AMEX stocks from August 1962 to July 1995 • For each year t from 1972 to 1994 • In-sample period: August of year t-10 to July of year t for estimation • Out-of-sample period : August of year t to July of year t+1

  7. Horse Race

  8. Horse Race (PCA) 3/10/2010 8

  9. More Horse Race Mean return of non-constrained portfolio: 0.7% – 1.2%

  10. More Horse Race

  11. Another Approach ??? • Main disadvantage of the classical MV-portfolio optimization: extremely sensitive to the [unknown] input estimates of mean and covariance matrix. • Small change in mean or covariance estimates lead to significant change in weights.

  12. Michaud’s Resampling (Bootstrapping) • Estimate (μ, Σ) from the observed data • Propose the distribution for the observed data, e.g., L ~ N(μ, Σ) • Resample n (large) of Monte Carlo scenarios • Solve the optimization problem for each MC scenario • Resampling allocation computed as the average of all obtained allocations

  13. Resampling (Bootstrapping)

  14. Future Work • Implement remaining estimators • Check the constrained portfolio problem, compare to similar results from literature • Clean up MATLAB codes

  15. Robust Allocation 3/10/2010 15

  16. THANK YOU!

More Related