Equity Portfolio Management (2)

www.levelupbootcamps.com 5/3/21

Level Up, LLC©2021 All rights reserved 1

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


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


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


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


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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Equity Portfolio Management (2)