Lecture 16: Indexes 4

Fund Performance Metrics

Objective: Evaluating performance of funds against benchmarks for informed investor decisions.

Key Metrics:

  • Correlation: Measures how fund returns relate to benchmark returns; passive funds should show high correlation (close to 1); active funds typically show lower correlation.

  • Alpha: Indicates excess return relative to benchmark; passive funds near zero, while positive alpha in active funds shows outperformance.

  • Beta: Reflects fund volatility related to benchmarks; beta of 1 matches market, >1 indicates higher risk, <1 lower risk.

  • R-squared (R²): Proportion of fund return variation explained by benchmark returns; passive funds have high R², while active funds have lower.

  • Average Difference in Returns: Measures deviation of fund returns from benchmarks; passive funds near zero divergence.

Comparison of Funds:

  • Passive Fund: Vanguard 500 Index Fund (VFINX) aims to mirror S&P 500.

  • Active Fund: Fidelity Large Cap Stock Fund (FLCSX) seeks to outperform S&P 500 at higher risk/expense.

Graphical Analysis:

  • VFINX shows close tracking of S&P 500 with high correlation; FLCSX shows variability.

Single-Index Model:

  • Used for detailed fund performance analysis via linear regression: [ R_i = \alpha + \beta(R_b) + \epsilon ]

Excel Implementation:

  • Analyzes fund returns from January 2010 to 2024; key functions include CORREL and STDEV.P for correlation and standard deviation.

Results:

  • VFINX: alpha near 0, beta of 1.005, and R² at 0.997.

  • FLCSX: negative alpha, higher beta (1.08), R² at 0.935, indicating underperformance vs benchmarks.

Conclusion: Passive funds reliably track benchmarks, whereas active funds show higher volatility and potential underperformance.