What is Portfolio / Index Regression?

Portfolio or index regression refers to the statistical technique used to analyze the relationship between a portfolio's returns and the returns of a benchmark index. By performing regression analysis, investors can determine how much of the portfolio's performance can be explained by the benchmark and assess the portfolio's sensitivity to market movements. The regression helps in estimating alpha and beta, which are key performance metrics.

Regression Formula: In the context of portfolio analysis, the linear regression model is typically expressed as:

Portfolio Return = Alpha + Beta * (Benchmark Return) + Error Term Where:
  • Alpha: The excess return of the portfolio relative to the benchmark
  • Beta: The sensitivity of the portfolio to market movements
  • Error Term: The portion of the portfolio's returns not explained by the benchmark

Understanding Portfolio Regression

Portfolio regression provides insight into how the portfolio behaves in relation to the benchmark:
  • Alpha: A positive alpha indicates that the portfolio has outperformed the benchmark after adjusting for market risk, while a negative alpha shows underperformance.
  • Beta: A beta greater than 1 suggests the portfolio is more volatile than the market, while a beta less than 1 indicates less volatility. A beta of 1 means the portfolio moves in line with the benchmark.
  • Error Term: Represents the part of the portfolio’s returns that cannot be explained by the market index, highlighting the presence of other factors affecting performance.

Example Calculation

Suppose a portfolio has a regression equation of:

Portfolio Return = 2% + 1.1 * (Benchmark Return) + Error This means the portfolio has an alpha of 2% (outperforming the benchmark) and a beta of 1.1 (more volatile than the market). For every 1% change in the benchmark, the portfolio's return is expected to change by 1.1%, plus the error term.

Evaluation

Regression analysis helps investors understand the drivers behind portfolio performance. Alpha provides insights into the portfolio manager's skill, while beta reveals the portfolio's sensitivity to market risk. By examining the regression equation, investors can make more informed decisions about whether the portfolio aligns with their risk tolerance and market expectations. However, it is important to note that regression is based on historical data and may not predict future performance accurately. Combining regression with other performance metrics like Sharpe ratio and volatility can provide a more comprehensive evaluation.