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Asset allocation (Principles of Asset allocation (MVO maximize the Exp…

- - - - :red_cross: based on estimates and outputs are sensitive to small changes to inputs (esp in expected returns)
        :red_cross: AA tend to be highly concentrated
        
        Fixes:
        
        Reverse Optimization: start with an assumed set of optimal weights + covariances + risk aversion coefficient and solve for expected returns
        
        Black-Litterman Model: allows for investors own distinctive view from those produced by reverse optmization (absolute return forecast or return differentials - asset class A outperform B by X bps)
        
        Resampled MVO: use monte carlo to estimate a large number of market assumptions
        
        Adding constraints beyond budget constraints (specific set allocation or range)
      - :red_cross: Investors are concerned about more than mean & variance of returns
        
        Fix:
        
        mean-variance optimizations tools
      - :red_cross:AA may appear diversified but source of risk isnt
        
        use factor
      - :red_cross: Many portfolios exist to pay for liability, MVO are not connected of what influences liabilities
        
        Use liability-relative or goals based AA
      - :red_cross:MVO is a single framework and does not take trading and taxes
        
        Use simulation
    - - Solutions
        
        exclude less liquid assets in optimization process (only optimize 90% then 10% into illiquid assets)
        
        include but try to model specific risk (factor-based allocation)
        
        attempt to model (use better estimates)
    - - Marginal contribution to total risk MCTR= Beta x sd
        
        rate of risk would change with small change in weights
      - Absolute contribution to risk ACTR = weight x MCTR
        
        how much the asset class contributes to SD
        
        sum of ACTR = SD of portfolio
      - An allocation is optimal when E(Ri) - Rf / MCTR is the same for all asets and matches Sharpe ratio of portfolio
- - - - SAA
    - - SAA