Investment Analysis

This project analyzes a portfolio of 10 major U.S. stocks using CAPM and Fama-French models to estimate alpha, beta, and risk metrics. It constructs optimized portfolios single index, active-passive, and tangent, then compares their Sharpe Ratios. The goal is to assess performance, risk-adjusted returns, and the impact of margin on portfolio efficiency

Objective


Conducted a comprehensive analysis of U.S. equities using CAPM, multi-factor models, and portfolio theory. Applied real market data to build, test, and compare asset allocation strategies.

Part 1: CAPM & Multi-Factor Model Analysis

  • Selected a diversified set of U.S. publicly listed stocks: Apple, Microsoft, Alphabet, Amazon, Tesla, NVIDIA, Meta, AMD, Procter & Gamble, Visa, and SPDR S&P 500 ETF (SPY as benchmark)

  • Collected 5 years of monthly price data and computed monthly log-returns

  • Constructed the variance-covariance matrix for all asset returns

  • Estimated CAPM alpha and beta for each stock using SPY as the market index

    • Compared computed betas with Yahoo Finance values for validation

    • Found that most alphas were statistically insignificant at 95%, indicating noise

    • NVIDIA was the only stock with statistically significant alpha

Extended Regression with Fama-French and Momentum Factors

  • Integrated SMB, HML, and MOM factors into the regression model

    • Observed changes in alpha, but most remained statistically insignificant

    • Reinforced that additional factors improved explanatory power but didn’t introduce strong alpha for most stocks

Single Index Model (SIM) Portfolio Construction

  • Used alpha and tracking error to compute:

    • Active portfolio weights (based on excess return per unit of risk)

    • Passive portfolio weights (SPY-based market index)

    • Overall portfolio composition (blend of active + passive)

  • Calculated the expected Sharpe Ratio of the SIM portfolio and compared it to SPY

    • SIM Sharpe Ratio: 0.144

    • SPY Sharpe Ratio was lower, but SIM underperformed compared to the tangent portfolio later

Part 2: Case-by-Case Portfolio Optimization

  • Selected 4 stocks from the larger group and explored multiple portfolio construction scenarios

  • Solved for weights under varying assumptions, including constraints and different optimization cases

  • Final outputs computed and visualized using Excel for clarity and validation

Part 3: Tangent Portfolio & Margin Analysis

  • Built the tangent portfolio using the return vector and sigma matrix

  • Achieved a Sharpe Ratio of 0.215, outperforming the SIM portfolio

  • Simulated investor allocation:

    • For a $10,000 portfolio under 50% margin requirement, computed actual capital and loaned amounts per stock

    • Recomputed portfolio Sharpe Ratio under 75% initial margin constraint

    • Assessed impact of leverage on risk-adjusted performance