Equity Portfolio Management (2)
Transcript of Equity Portfolio Management (2)
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Equity Portfolio Management (2)
5/3/21 1LevelUp, LLC©2021 All rights reserved
Active Equity Investing: Portfolio Construction
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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
Portfolio Building Blocks1.O/U weight exposure to
rewarded & unrewarded factors - market, size, style, & price momentum
2.Alpha skills – timing factors, securities & markets
3.Sizing positions4.Breadth of expertise
Allocating Risk Budget• Risk mgt. process• Absolute vs. relative risk• Asset or factor contribution
to portfolio variance• Segmentation of portfolio
variance; factor exposure & unexplained risk
• Effect of constraints & leverage on risk & IR
• Heuristic & formal risk constraints
Well Constructed Portfolio
• Meets investor expectations & constraints with low unexplained risk
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Approaches to Implement Core Beliefs
• Systematic vs. discretionary• Top-down vs. bottom-up• Benchmark aware or agnostic
Specialized Strategies• Merits of long only• Long short strategies• Long extension• Market Neutral• Benefits & drawbacks
Implicit Costs• Market impact• Position size• UAM & turnover• Slippage
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2 Measures of BM Relative 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
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Eq. 5
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
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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!
• O/(U) weight energy firms vs. technology firms
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AR (sRA) = ⎷s2(S(Bpk-Bbk) x Fk) + s2e
___________________
Exhibit 7
Active Risk & Active Share• Controllable by decreasing
security concentration
Low active risk &narrow sector deviation
Portfolio Mgr Characterizations1. Factor neutral, diversified, or concentrated2. Diversified (low security concentration & low
idiosyncratic risk) or concentrated (high security concentration & high idiosyncratic risk)
Multi-factor product High AS = 0.70, Low AR = +/-3%
BBox 2 Q3*
Factor Exposure• High net exposure to a risk factor, leads to
high active risk regardless of stock selection• If factor exposure is neutral, active risk is
attributable to active share (D weights)Concentrated Stock-picker High AS = 0.90 & High AR 8%-12%
High idiosyncratic risk & high active risk
EOC 6
Eq. 6
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Benchmark Relative Risk Measures
Realized Active Risk• Actual, historical
standard deviation between portfolio return and BM return
• Equation 3 pg. 470• AR rises when its
uncorrelated with its BM
Active Share (AS)• Weight driven• Difference b/w portfolio
& benchmark weights• Port wgt – BM wgt• Function of number of
stocks & position sizing• Controlled by manager
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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.
Two types of Active Risk
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Single Asset Contribution/Proportion to Portfolio s2
Asset Wgt. St. Dev.
A 40% 20%
B 50% 12%
C 10% 6%
Portfolio 100% 11.92%
A B C
1 0.40 0.20
0.40 1 0.20
0.20 0.20 1
0.88 0.78 0.20
Pairwise Correlations
Absolute %
0.008416 59.22%
0.005592 39.35%
0.000204 1.44%
0.014212 100%
Portfolio Risk Attribution – s2
A B C
0.0400 0.0096 0.0024
0.0096 0.0144 0.0014
0.0024 0.00144 0.0036
0.0209 0.0111 0.0014
Covariance Matrix3 Asset Class Portfolio
Asset A’s proportion to total portfolio variance = Asset A proportion to portfolio variance/total portfolio variance = 0.008416/0.014212 = 59.22%
Portfolio Variance = wA2sA2 + wB2sB2 + wC2sC2 + 2wAwB(CovAB) + 2wAwC(CovAC) + 2wBwC(CovBC) sP2 = 40%220%2 + 50%212%2 + 10%26%2 + 2(40%)(50%)(0.0096) + 2(40%)(10%)(0.0024) + 2(50%)(10%)(0.00144) = 0.0142123 Asset Portfolio St. Dev s = 11.92%
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
EOC 12 CFA errata
Think combinations = AB, BC & AC
Causes & Sources of Absolute Risk
Absolute Variance
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Single Asset Contribution to Portfolio Variance
Asset Wgt. St. Dev.
1 30% 25%
2 45% 14%
3 25% 8%
Portfolio 100%
1 2 2
0.06250 0.01050 0.00800
0.01050 0.01960 .00224
0.00800 0.00224 0.00640
Covariance Matrix3 Asset Class Portfolio
Asset 2 Contribution to Portfolio Variance = w2w2(Cov2,2) + w2w1(Cov2,1) + w2w3(Cov2,3) Asset 2 Contribution to Portfolio Variance = (45% x 45% x 0.01960) + (30% x 45% x 0.01050) + (45% x 25% x 0.00224) = 0.003969 + 0.001418 + 0.000252 = 0.005639
Eq. 8b
EOC 12 CFA errata3/2021
“Contribution” not“proportion”
EOC 12
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