Equity Portfolio Management

Question 1

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Benchmark Concentration metrics

Answer 1

1. Herfindahl-Hirschman Index (HHI) = ∑ (market cap weights)²
2. Effective # stocks = 1 / HHI (# of stocks in an equally weighted portfolio that mimics the concentration of the index)

Question 2

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Approaches to Passive Investing

Answer 2

1. Pooled investments: Open-end mutual funds and ETFs
2. Derivatives-based strategies: Futures, Options and Swaps
3. Passively managed equity index-based portfolios
   
   1. Full Replication
   2. Stratified Sampling - when tracking indexes with a large number of constituents, hold a limited sample in subgroupings
   3. Optimization - max a desirable characteristic or min undesirable, subject to constraints.
   4. Blended Approach

Question 3

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Tracking Error_P

Answer 3

Tracking Error_P = | Std Dev (R_P - R_B) |

Question 4

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Active Equity Investing Portfolio Construction

Behavioral biases + 2 Traps

Answer 4

1. Behavioral Biases (CAROLIna)

• Confirmation,
• Availability,
• Regret aversion,
• Overconfidence,
• Loss aversion,
• Illusion of control

1. Value Trap and Growth Trap

Question 5

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Active Return, Share and Risk

Answer 5

a) Active Return (R_A) – excess return generated ∑(W_Pi - W_Bi) * R_i

b) Active Share = ½ * ∑ |W_Pi - W_Bi| - For the same level of fees, choose the fund with the highest Active Share!

c) Active Risk (σ_RA) = √[R_{Active return}² / (T-1)] T = # of periods or √[σ² (∑(β_pk – β_bk) × F_k) + σ²_e] - higher covariance with the benchmark helps to reduce active risk

Question 6

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Ex-post active return & Sources of Active Returns

Answer 6

Ex-post active return: R_A = ∑(β_pk – β_bk) × F_k + (α + ε);

where = β is the sensitivity to the rewarded factor k

1. Rewarded factors (k): risks that offer long-term premiums (β, size, value, liquidity, etc)
2. Alpha skills (α): Tactical exposures to mispriced securities, sectors, and rewarded risks
3. Luck (ε): Idiosyncratic risk (from concentrated active positions). Highest influence of Position Sizing

Question 7

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Fundamental law of active management (Exp active return)

Answer 7

Fundamental law of active management: E(R_A) = I_nformationC_oefficient * √BR_eadth * σ_RA * T_ransferC_oefficient

Question 8

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Total Portfolio Variance & Asset’s contribution to Variance (ơ²)

Answer 8

ơ = Std Dev = Volatility / ơ² = Variance

1. Total Portfolio Variance (2 assets port) = ơ_P² = w_A²ơ_A² + w_B²ơ_B² + 2w_Aw_B(COV_AB)

• Cov_AB = ơ_A*ơB*ρ_AB

2. Asset A Contribution to Var = w_Aw_A(COV_AA) + w_Aw_B(COV_AB)

3. % = (2) / (1) = w_A(COV_AP)

• 4. Factor A Contribution to Portfolio Var = β_Aβ_A(COV_AA)

Question 9

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Equity Investment Style Classification – Ways for classifying the portfolio’s overall style

Answer 9

Equity Investment Style Classification - used to compare portfolio with index

• Holdings-Based Style Analysis: Bottom-up approach, find were portfolio holds higher weight on style box (mkt cap vs value/growth) - PREFERED
• Returns-Based Style Analysis: identify the style of a fund through multivariate regression of the funds returns against a set of passive style indices. Does not require information on holding (less accurate, but easier).

Question 10

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VAR-based measures

Answer 10

• Conditional VaR (CVaR): avg. loss if VaR is exceeded (i.e. expected shortfall)
• Incremental VaR (IVaR): Δ in VaR when new asset is added
• Marginal VaR (MVaR): VaR effect in position size