Scenario Comparison
Active vs. Passive ETF Performance Comparison
Compare hypothetical active and passive ETFs using annual net total returns, benchmark gaps, simplified CAPM alpha and Sharpe ratios.
Set comparison conditions
All figures are hypothetical, not FBCG, IWF or any real fund data. Edit an input to compare returns, alpha and Sharpe ratios immediately.
Common market assumptions
AActive ETF A
BPassive ETF B
Enter annual total returns already reflecting fund-level expenses and reinvested distributions. Expense ratios are informational and are not deducted again. Returns, beta, volatility and the common benchmark must use consistent periods and frequencies; this tool does not annualize inputs.
Comparison results
Each group has its own scale; the center line is zero and negatives extend left. Numeric labels provide the full comparison.
Annual net total return
Return relative to the common benchmark
Illustrative CAPM alpha
AActive ETF A
- Illustrative CAPM alpha
- -0.50 pp
- CAPM required return
- 12.50%
- Sharpe Ratio
- 0.4000
- Assumed annual fee (not deducted again)
- 1.00%
Calculation steps
Required return = 2.00% + 1.50 × (9.00% − 2.00%) = 12.50%
Alpha = 12.00% − 12.50% = -0.50 pp
Sharpe = (12.00% − 2.00%) ÷ 25.00% = 0.4000
BPassive ETF B
- Illustrative CAPM alpha
- -0.20 pp
- CAPM required return
- 9.00%
- Sharpe Ratio
- 0.4533
- Assumed annual fee (not deducted again)
- 0.20%
Calculation steps
Required return = 2.00% + 1.00 × (9.00% − 2.00%) = 9.00%
Alpha = 8.80% − 9.00% = -0.20 pp
Sharpe = (8.80% − 2.00%) ÷ 15.00% = 0.4533
Change only beta and observe alpha
Keep every other input fixed while changing ETF A's assumed market exposure. This isolates a model variable; a real fund's beta, returns and volatility do not vary independently in this way.
- CAPM required return
- 12.50%
- Illustrative CAPM alpha
- -0.50 pp
With other inputs fixed, ETF A's CAPM required return is 12.50% and illustrative alpha is -0.50 pp. The market risk premium is +7.00 pp; its sign determines how beta changes affect alpha.
How to read the results
ETF A has the higher annual net total return, by +3.20 pp. That direct difference is not risk-adjusted.
Alpha compares the assumed return with the CAPM return required for market exposure; Sharpe compares return above the risk-free rate with total volatility. Beta is not standard deviation, so the measures can rank scenarios differently.
Under these assumptions, ETF B has the higher Sharpe ratio. This model comparison alone cannot establish fund quality or manager skill.
This uses one assumed period and beta to illustrate CAPM alpha; it is not a regression on a common historical time series or a reliable estimate of real Jensen's alpha. Negative Sharpe rankings can also be affected by the denominator, so read excess return and volatility together.
Method and assumptions
Rp is the ETF annual net total return, Rm the common market return, Rf the risk-free rate, β market exposure and σ annualized return volatility. Returns and risk inputs must refer to one period. Returns already reflect fund-level expenses; expense ratios provide cost context and are not deducted again.
Scope and model limitations
This compares one-period assumptions rather than estimating a historical regression. Beta is not total risk, and Sharpe leaves out liquidity and tail losses. A single result establishes neither manager skill nor future performance.