Document Type masters report Author Name McArthur, Gregory D URN etd-050914-140237 Title Comparative Analysis of Ledoit's Covariance Matrix and Comparative Adjustment Liability Model (CALM) Within the Markowitz Framework Degree MS Department Mathematical Sciences Advisors Marcel Blais, Advisor Luca Capogna, Department Head Keywords covariance matrix estimation Ledoit's model shrink- Date of Presentation/Defense 2014-05-09 Availability unrestricted
Estimation of the covariance matrix of asset returns is a key com- ponent of portfolio optimization. Inherent in any estimation technique is the capacity to inaccurately re ect current market conditions. Typ- ical of Markowitz portfolio optimization theory, which we use as the basis for our analysis, is to assume that asset returns are stationary.
This assumption inevitably causes an optimized portfolio to fail during a market crash since estimates of covariance matrices of asset returns no longer re ect current conditions. We use the market crash of 2008 to exemplify this fact. A current industry-standard benchmark for estimation is the Ledoit covariance matrix, which attempts to adjust a portfolio's aggressiveness during varying market conditions. We test this technique against the CALM (Covariance Adjustment for Liabil- ity Management Method), which incorporates forward-looking signals for market volatility to reduce portfolio variance, and assess under certain criteria how well each model performs during recent market crash. We show that CALM should be preferred against the sample convariance matrix and Ledoit covariance matrix under some reason- able weight constraints.
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