CAPM Regression Analysis: Testing Risk, Return and Market Efficiency Across US Equities

Overview

A project centred on the Capital Asset Pricing Model (CAPM), examining the relationship between systematic risk and expected return for four US stocks - Adobe, Ford, Chevron, and Caterpillar - against the S&P 500 and the risk-free rate. The project moved from distributional analysis, through formal hypothesis testing on variance and regression parameters, to a forward-looking return forecast with a confidence interval.

What I did

• •Sourced monthly closing prices from Bloomberg for four US equities, the S&P 500 index, and the FEDL01 risk-free rate, and calculated holding period returns
• •Converted the annualised risk-free rate to monthly terms and assessed the normality of each stock's return distribution, discussing the implications of non-normality for the validity of CAPM
• •Conducted a formal F-test at both 5% and 1% significance levels to compare the variance of each stock against the market index, stating the null and alternative hypotheses and interpreting how the results shifted across significance levels
• •Related each company's beta to the variance ratio between the stock and the index
• •Estimated the CAPM regression (excess stock return against excess market return) for each company and interpreted the alpha and beta coefficients
• •Ran a one-sample t-test at 1% significance on the regression intercept to test whether each company was undervalued, explaining the test statistic, critical value, and economic rationale
• •Ran a further hypothesis test on beta to assess whether each company was riskier than the market, with the same statistical and economic interpretation
• •Plotted the Security Market Line for all four stocks and evaluated their relative profitability and mispricing
• •Forecasted Adobe's next-month expected return under a projected 10% market move, constructing a 95% confidence interval around the prediction
• •Proposed methodological improvements (e.g. additional explanatory factors) to strengthen the model's explanatory power

Skills & tools