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07 · Active Equity · Optimization

Active Equity — Treynor–Black Model

StatusCompletedTypeActive equity

Can residual alpha from five large-cap equities improve a diversified market portfolio after factor adjustment?

CAPM and Fama–French three-factor regressions with alpha-weighted active-portfolio construction.

0.74Sharpe ratio
0.93portfolio beta
60months of returns

Objective

Apply the Treynor–Black framework to five S&P 100 equities and test whether security-specific alpha can improve the risk-adjusted profile of a market portfolio.

Analytical approach

  1. 01

    Collect 60 months of returns for five S&P 100 equities and the market.

  2. 02

    Estimate CAPM and Fama–French three-factor regressions.

  3. 03

    Separate systematic exposure from residual alpha and idiosyncratic risk.

  4. 04

    Weight the active sleeve by alpha relative to residual variance.

  5. 05

    Combine the active and passive portfolios and evaluate beta and Sharpe ratio.

Key inputs and outputs

UniverseFive S&P 100 equities
Estimation window60 monthly observations
Final portfolio beta0.93
Final Sharpe ratio0.74

What the analysis showed

  • The optimized portfolio maintained below-market beta at 0.93.
  • Alpha weighting improved the portfolio’s risk-adjusted profile to a 0.74 Sharpe ratio.
  • Factor regressions provided a disciplined separation of market exposure from security-selection signals.

Investment conclusion

The model demonstrates a systematic bridge between security analysis and portfolio construction: active weights are earned through residual alpha and constrained by idiosyncratic risk rather than conviction alone.

Boundaries of the work

  • The five-name universe is small and sensitive to the estimation window.
  • Historical factor relationships may not persist out of sample.
  • Transaction costs, turnover, and estimation error are not fully modeled.
  • This project is not yet documented in the public GitHub repository.

Capabilities demonstrated

Technology

RMicrosoft ExcelFama–French factor data

Finance

CAPMFactor regressionPortfolio optimizationAlpha estimationRisk-adjusted performanceActive portfolio construction