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35-1 portfolio performance evaluation (2 components (performane …

- - - - commonly used on an ex post basis to evaluate historical risk-adjusted returns
      - S_A = (R_A - r_f) / σ_A
      - weakness - indifferent bw upside and downside volatility
    - - excess return per unit of systematic risk
      - T_A = (R_A − r_f) / ‸β_A
      - relation to the volatility it bring to a well-diversified portfolio
      - most useful whose performance being evaluation combined in a broader fulluy diversified portfolio
    - - assess performance relative to benchmark, scaled by risk
      - IR = [E(r_p) − E(r_B)] / σ(r_p − r_B)
    - - a returns-based measure
      - annualized alpha / annualized residual risk
        computed from a factor regression
      - AR = α / σε
        σε: standard deviation of ε_t
    - - a modificaiton of sharpe ratio
      - ex ante:
        SR_D = [E(r_p) − r_T] / σ_D
        r_T: MAR min acceptable return / target rate of return
      - σ_D: target semi-standard deviation / target senideviation
        σ_D^2 = ∑[min((r_t - r_T), 0)^2] / N
      - to accurately assess performance when return distributiosn not symmetrical
      - not a risk premium
        most relevant when primary objectives is capital preservation
    - - upside capture
        ratio UC:
        
        measures capture when benchmark return positive
        
        UC(m,B,t) = R(m,t) / R(B,t) if R(B,t) ≥ 0
      - downside capture
        ratio DC:
        
        measures capture when benchmark return negative
        
        DC(m,B,t) = R(m,t) / R(B,t) if R(B,t) < 0
      - upside/downside
        capture
        / captue ratio CR:
        
        = upside capture / downside capture
        CR(m B,t) = UC(m,B,t) / DC(m,B,t)
        
        1 → positive asymmetry, a convex return profile → benchmark returns increase, portfolio returns increase at an increasing rate
        
        <1 → negative asymmetry, a concave return profile → benchmark returns increase, portfolio returns increase at an decreasing rate
      - useful in evaluating consistency issues -
        bw stated investment process and reported performance
    - - drawdown: cumulative peak-to-through loss during continuous period
      - drawdown duration: total time from start of drawdown until cumulative drawdown recovers to zero
      - Maximum DD(m,t) = min([V(m,t) – V(m,t)/V(m,t)], 0)
      - an asymmetrical return profile or avoiding large drawdowns
        →higher absolute and risk-adjusted returns in certain markets
      - manager responses to large drawdown → robustness and repeatabiity of investment / construction / risk manage / implementing
      - should also consider horizon and its relationship with risk capacity - dynamic asrises if perception of risk is path dependent or drawdown chagnes risk tolerance
  - - - how outperformance achieved, distinguishing stcok selection from country allocation
    - - a long track record necessary - statistical certainty in conclusion
      - additional studies / qualitative analyses
      - must understand and acknowledge the limits of all tools