Project Overview
Implemented the CAPM market model in R to estimate the systematic risk (beta) of stock ABC relative to the S&P 500. The project quantifies how much of the stock's return variability is attributable to market-wide movements versus idiosyncratic factors — a fundamental tool in equity research, portfolio construction, and risk budgeting.
📋Problem Statement
Estimate the market beta of stock ABC to determine its systematic risk exposure, assess whether it generated positive risk-adjusted return (alpha), and quantify how much of its return variance is explained by market movements versus firm-specific factors.
🎯Analytical Approach
Applied the CAPM single-factor market model: excess return of stock ABC regressed on S&P 500 excess return using OLS. Estimated α (Jensen's alpha) and β (systematic risk coefficient), evaluated model fit via R², and ran full regression diagnostics to validate OLS assumptions.
💾Data & Variables
Monthly excess returns for stock ABC and the S&P 500 index over the same observation period. Excess returns computed as raw returns minus the risk-free rate. Data imported from Excel (Project1_data_3.xlsx). Both series are mean-zero centered for the regression specification.
🔧Methods & Tests
OLS via lm(): (R_ABC − R_f) = α + β(R_SP500 − R_f) + ε. Standard errors computed using heteroskedasticity-robust estimators. Residual diagnostics: Q-Q normality plot, residuals vs fitted (linearity check), scale-location (homoskedasticity), and Cook's distance (influential observations).
✨Key Results
β = 0.6487: Stock ABC moves 0.65% for every 1% move in the S&P 500 — a defensive, low-beta equity. α = 0.005506: Generated ~0.55% monthly excess return above CAPM prediction, suggesting mild positive abnormal performance. R² = 0.1916: Only 19.2% of ABC's variance is explained by market factor — idiosyncratic risk dominates.
🧠Key Learnings
Low beta does not imply low total risk — high idiosyncratic variance (R² ≈ 19%) means diversification is critical for this stock. Jensen's alpha interpretation requires caution: statistical significance depends on sample length. The CAPM single-factor model is a starting point; multi-factor models (Fama-French 3/5 factor) typically improve explanatory power for individual stocks.