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Author NameZhang, Yafei
Email Address yzhang7 at wpi.edu
TitleComparative Analysis of Ledoit's Covariance Matrix and Comparative Adjustment Liability Management (CALM) Model Within the Markowitz Framework
DepartmentMathematical Sciences
  • Marcel Y. Blais, Advisor
  • Keywords
  • covariance matrix estimation
  • Ledoit's model
  • shrinkage parameter
  • CALM
  • forward looking signal
  • Date of Presentation/Defense2014-05-08
    Availability unrestricted


    Estimation of the covariance matrix of asset returns is a key

    component of portfolio optimization. Inherent in any

    estimation technique is the capacity to inaccurately reflect

    current market conditions. Typical 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 Liability 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.

  • yzhang.pdf

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