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You’re right that traditional beta does not account for the liability of ETF fees or expense ratios. To incorporate the impact of fees into the risk assessment of an ETF, you can use a few additional methods or considerations:

1. Adjusted Returns for Fees

• Impact: Fees directly reduce the net returns of the ETF, so they affect the total return risk.
• Method: Adjust the ETF's historical returns by deducting the annual expense ratio from the reported returns.
• Result: Analyze the beta or volatility of these net returns instead of the gross returns to get a more realistic risk measure.

2. Sharpe Ratio with Fees

• The Sharpe Ratio measures risk-adjusted returns.
• Adjustment: Calculate using net returns (after fees). Compare this against similar ETFs or benchmarks. A lower Sharpe Ratio after fees indicates less efficient risk-adjusted performance.

3. Expense Drag in Scenario Analysis

• Impact: Expense ratios act as a guaranteed loss percentage annually.
• Method:
  • Model hypothetical scenarios (e.g., market gains/losses) and incorporate the impact of the expense ratio.
  • Example: If an ETF earns 7% annually but has a 1% expense ratio, the investor effectively earns 6%. This creates a compounding drag over time.

4. Fee Risk as a Sensitivity Factor

• Treat fees as a fixed liability in sensitivity analysis.
• Measure how the presence of fees affects long-term portfolio growth or magnifies risk during down markets (e.g., market losses still incur fees).

5. Expense-Adjusted Alpha

• Alpha typically measures excess returns over a benchmark.
• Calculate alpha after subtracting fees. A negative expense-adjusted alpha indicates the ETF may not be adding value after accounting for costs.

6. Monte Carlo Simulations

• Use Monte Carlo simulations to project the impact of the expense ratio over various market conditions and holding periods.
• Evaluate the probability of underperformance due to compounding expenses.

7. Tracking Error Adjusted for Fees

• Tracking Error: Measures how closely an ETF tracks its benchmark.
• Incorporate fees into tracking error analysis to see how they distort alignment with the benchmark.

Example Consideration:

Imagine an ETF with a gross return of 7% and a 1% expense ratio:

• Net Beta: Adjust historical returns for the 1% fee, then recalculate beta relative to a benchmark.
• Sharpe Ratio After Fees: Use net returns in the Sharpe Ratio formula.

In conclusion, while beta measures systematic market risk, incorporating the expense ratio into risk measures provides a more comprehensive view of the true liability of investing in an ETF. Adjusted returns, scenario analysis, and Sharpe ratios with fees are practical ways to account for this liability.