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Portfolio Construction OverviewActive equity portfolio construction attempts to implement and realize value-added insights about expected returns while understanding both the return objective & risk
(1) Active Share (AS)• Difference b/w portfolio wgts & BM wgts• Complete control by mgr.• Assess fees per unit active mgt.• Captures number & sizing positions in
the portfolio that differ from BM – easy J• If AS = 0%, then 100% portfolio matches
BM. If AS = 80% then 20% BM match
(2) Active Risk (AR)• Tracking error (TE) - historical• Measure of volatility of portfolio returns
relative to volatility of BM returns• Influenced by volatility of securities
with highest active weights & predicted variances & correlations (GARCH) that differ from the BM
2 Sources of Active Share1.Hold different portfolio stocks vs. BM2.Holding BM securities but with different
weights (different than zero)Concentrated portfolio has higher active share vs. diversified portfolio with lower AS
AS = ½ S|WeightPortfolio – WeightBM |n
AR (sRA) = ⎷s2(S(Bpk-Bbk) x Fk) + s2e
___________________CME
2 Predicted Sources of Active Risk1.Variance attributed to factor exposure2.Variance of idiosyncratic risk (& alpha) 3.AR depends on cross correlations &
variance, outside the control of mgr.4.Controllable via portfolio structure
ii i
Eq. 2, 3 & 6
Benchmark relative risk arises from the portfolio manager taking active weights different from the BM & different forecasted/predicted risk than the BM – Level of BM Activism
EOC 6EOC 7
CFA errata
3
Active Risk & Factor Exposure
Active Risk (AR) Contributors• Active risk attributable to active
share will be smaller when a portfolio holds greater number of securities and/or idiosyncratic risk is small
• Active risk increases with an increase in factor & idiosyncratic volatility
• Active risk increases when a portfolio becomes moreuncorrelated with BM – CASH!
Predicted Active Risk (AR)• Requires forward looking
estimates of correlations & variances
• Requires var-covar matrix• Affected by cross-correlations• Not controllable by Pmgr.• Variance of factor exposure• Variance of idiosyncratic risk
Sources• Portfolio holds different
stocks than the BM• Holding stocks weights
different than the BM• Diversification does not
matter
Portfolio Structure• High net exposure to a risk factor lead to high level of AR• If factor exposure is neutralized, AR is all active share• AR is smaller if # of stocks is large or avg idiosyncratic risk
is small• AR will rise with increase in factor or idiosyncratic volatility
Active share & active risk provide insights as to the manager’s activism against their benchmark. AS can be used to assess the fees paid per unit of active mgt.
Asset A Contribution to Portfolio Variance = wAwA(CovAA) + wAwB(CovAB) + wAwC(CovAC) Asset A Contribution to Portfolio Variance = (40% x 40% x 0.0400) + (40% x 50% x 0.0096) + (40% x 10% x 0.0024) = 0.006 + 0.00192 + 0.000096 = 0.008416
Eq. 8b
Exh 10
Eq. 8a
ProportionsAsset B 39.35%Asset C 1.44%White Text pg. 492