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READING 29: ACTIVE EQUITY INVESTING: portFolio cONSTRUCTIONn :building…

- - - - Active equity portfolios aim to outperform a benchmark after all costs
        
        The excess return above a benchmark (= active return)
        
        achieved by over-weighting the outperformers :muscle:
        
        R (A) = Sum of Active Weight (i) x R(i)
        Active Weight (i)= the difference between portfolio and benchmark weight for security i
    - - The level of strategic long-term exposures to rewarded factors
        
        Rewarded factors are risks that are widely accepted as offering long-term positive risk premiums [market risk (beta), size, value, liquidity, etc.]
      - Tactical exposures to mispriced investment that generate alpha :star:
        
        Relation
      - Idiosyncratic risk (from concentrated active positions) that generates returns related to luck (in the sense that it is not due to market risk exposure or value-added alpha)
        
        Relation
      - Decomposition of realized (ex post) active return
        (https://bit.ly/2RKY8xk)
  - - - Overweight/Underweight Rewarded Factors :gift:
      - :man-swimming::skin-tone-6:: taking exposures to (long term) rewarded risks that differ from those of the benchmark (i.e. active return due to differences in beta)
      - beta refers to sensitivity to a rewarded risk factor
        such as the market risk of CAPM, or the market,
        size, and value factors of the Fama and French model
    - - via factor timing :timer_clock: identifying when a factor might outperform/underperform its average return
      - identifying mispricings :telescope:
      - Apply to both:
        
        rewarded (ex. value :diamonds: vs. growth :deciduous_tree:)
        
        unrewarded (ex. geo- :globe_with_meridians:, :desert_island: thematic exposures ) factors
      - Alpha skills are excess returns related to the unique skills and strategies of the manager
    - - to balance managers' confidence in their alpha and factor insights while mitigating idiosyncratic risks coming from concentrated positions.
      - GENERAL RULE: :sparkler: smaller positions in a greater number of securities will diversify away idiosyncratic risk and lead to lower portfolio volatility
      - Will affect all 3 source of active return, but the most dramatic impact will be on indiosyncratic risk
    - - fundamental law of active management :champagne:
        
        E(A)= Info coefficient IC x BR^(1/2) x Active risk x transfer coefficient TC
        [ ]https://bit.ly/394vDAB
        
        shows that there is a direct link between breadth and
        expected outperformance - a larger number of independent decisions (higher breadth) should lead to higher active return
  - - - Portfolio construction can be viewed as an optimization problem with a goal (the objective function) and a set of constraints.
    - - Specifying objectives in terms of risk
      - Maximizing exposure to rewarded factors
      - Maximizing exposure to securities having specific characteristics custom-defined by a discretionary manager
      - Heuristic approaches that use less scientific methods (i.e weighting based on ranking of some multiples...)
- - - - active risk is a function of the variance due to factor exposures and the variance due to idiosyncratic risk
      - (https://bit.ly/2UkdDhg)
- - - - The contribution of asset i to portfolio variance(CVi) is given by the equation(https://bit.ly/2H7zMHU)
        The portfolio variance is the sum of each asset's contribution to portfolio variance
      - Extended covariance attributed to factor exposures https://bit.ly/39caxAn
      - (https://bit.ly/388WfAo)
        [Factor-based risk budgeting example]