The True Meaning of Alpha (α) — What "Beating the S&P 500" Actually Means
Suppose your portfolio returned +20% this year and the S&P 500 returned +15%. That is a +5 percentage-point gap, but is it proof of stock-picking skill? Not by itself. Beta adjustment can identify a difference relative to a model; it cannot on its own separate skill from luck. This article explains CAPM alpha, Information Ratio, Tracking Error and the comparison conditions that matter, including currency and cash flows.
1. Simple difference is not CAPM alpha — account for beta
The most intuitive definition is:
In this example, "I beat the S&P 500 by 5 percentage points" describes the simple gap. The CAPM alpha (α) discussed here adjusts the comparison for market beta.
More market exposure can explain a larger return. In a single period, ignoring borrowing costs and fees, 1.5× exposure to the S&P 500 turns a +10% market return into about +15%. The extra 5pp can be explained by increasing market exposure by 50%, rather than stock-selection skill. A daily-reset leveraged ETF's longer-term return can differ from this simple multiple. This exposure-related difference is not evidence of stock-selection alpha.
For the single-period example below, hold beta fixed and calculate a CAPM-based comparison difference:
CAPM relates expected returns to beta. Here, the bracket substitutes the benchmark's realized return to form a comparison value, not a forecast. In a regression of excess returns over multiple periods, alpha is the estimated intercept; each period's difference includes that alpha plus a residual. A positive single-period difference does not establish stock-picking skill. Use the same period and currency for the portfolio, chosen market proxy and risk-free return. CFA Institute: CAPM's expected-return relationship
2. Example — same +5pp gap, different alpha
Compare two hypothetical investors over the same single period. Risk-free rate rf = 3%, S&P 500 = +15%, with the betas below held fixed. The table's alpha column reports each investor's difference from the CAPM comparison value for that period.
| Investor | Return | Beta (β) | Simple gap | Alpha (α) |
|---|---|---|---|---|
| A — Diversified value | +20% | 0.9 | +5pp | +6.2pp |
| B — Leveraged ETF | +20% | 2.0 | +5pp | −7.0pp |
Math:
- A's CAPM comparison = 3% + 0.9 × (15% − 3%) = 13.8%
αA = 20% − 13.8% = +6.2pp - B's CAPM comparison = 3% + 2.0 × (15% − 3%) = 27.0%
αB = 20% − 27.0% = −7.0pp
Same +20% return and +5pp simple gap, but A is +6.2pp above the model's comparison value while B is −7.0pp below it. B is compared with the 27.0% CAPM comparison value for its assumed β = 2.0; 1.5× market exposure does not have the same beta. This is a fixed-beta illustration for the period, not proof of skill or future performance.
2-1. How do you compute beta (β)?
In a single-factor regression with an intercept, beta is the slope of portfolio excess returns on benchmark excess returns. Both subtract the risk-free return for the same observation period.
Use matching dates, frequency and currency, and a positive variance for the benchmark's excess returns. Estimates depend on the sample and portfolio composition; a fixed minimum such as one year does not guarantee reliability. Weighting holdings' betas by current portfolio weights can describe the current mix when the betas use the same market and estimation conditions. It need not equal a historical portfolio regression if the holdings changed.
3. Information Ratio — active return and variability
The Information Ratio (IR) divides mean active return by its variability. Active return is portfolio return minus benchmark return for the same period, not the CAPM alpha above.
TE is the standard deviation of active returns. Use matching observation frequencies and annualization conventions for the numerator and denominator. CFA Institute: active return, active risk, and IR
- IR > 0.5 — Mean active return exceeds half the TE. That alone does not establish skill.
- IR ≈ 0 — Mean active return is small relative to TE. This is not a statistical significance test.
- IR < 0 — Mean active return was negative over the measurement period, not necessarily in every period.
These interpretations require positive TE. If TE = 0, the ratio is undefined; using the portfolio itself as its benchmark gives 0/0. IR evaluates benchmark-relative performance; it does not prove repeatable skill. It depends on the measurement period, benchmark, and outliers. CFA Institute: Sharpe Ratio and Information Ratio
→ Information Ratio — Measuring Active Return and Its Variability
4. Tracking Error — how different was your path?
Annualized TE of 5pp means the annualized standard deviation of active returns is 5pp. It does not mean the average active return or average absolute gap is 5pp. Judge its size against the portfolio mandate.
With the same benchmark, period and calculation method, larger TE means more variable active returns. There is no universal 2pp or 6pp boundary that identifies a strategy type or proves good or bad management. Compare index-tracking results with the mandate's permitted deviations, and active strategies with the risks they intended to take.
Low TE does not require zero mean active return or the same holdings as the benchmark. TE alone cannot reveal the manager's intent or explain what caused the result.
5. Which benchmark should you pick?
The benchmark changes what a comparison tells you. Choose it in advance to reflect the investment mandate, and check these conditions:
① Match the asset class
For US large caps, the S&P 500 is a candidate; for Korean equities, KOSPI or KOSPI 200; for global equities, MSCI World or ACWI; for emerging markets, MSCI EM. Their coverage and weights differ, so check the index methodology against your holdings and mandate. These are general examples, not all options available in Multifolios.
② Align the currency
Comparing a USD-based portfolio with a KRW-based KOSPI return mixes reporting currencies. Convert both to the same currency, and align the period, dividend treatment and fee basis. Currency conversion is not currency hedging. Conversion changes the reporting unit while retaining FX effects; hedging changes FX exposure. Match the benchmark's hedging policy to the mandate. Neither matching currencies nor choosing a hedged ETF isolates stock-selection alpha by itself. CFA Institute: benchmark currency and hedging conditions, pp. 10–11
6. Hands-on — comparing asset values and benchmark prices
The Asset Chart in Multifolios initially selects S&P 500 (SPY) in Return mode. Its benchmark buttons offer S&P 500 (SPY) / QQQ / KOSPI, not every index discussed above (checked October 7, 2026).
- Dashboard → Asset Chart top: select "Return" mode
- Use the benchmark buttons to select S&P 500 (SPY) / QQQ / KOSPI
- Compare changes in portfolio asset value and benchmark price, each normalized to its own starting value
- Select a range such as 1m / 3m / 6m / YTD / All. All covers up to the last 5 years; available records and price history also affect the displayed range
This chart does not adjust for external cash flows. Deposits, withdrawals and changes in recorded holdings can affect the asset-value line. It estimates historical values from recorded holdings and available prices and FX rates; it does not reconstruct a complete transaction and cash-balance history. When snapshots exist or every holding has at most one purchase record, it uses current holding quantities for historical dates.
The benchmark line normalizes fetched closing prices without converting them to the portfolio's display currency or adjusting for dividend reinvestment. The portfolio line also does not add dividend cash flows to calculate a total return. Missing dates can carry forward the last available benchmark price, and the two lines can have different starting observations. Choosing the same range therefore does not guarantee identical valuation times or comparison conditions.
To remove the effect of external cash flows from an investment-performance comparison, calculate a measure such as time-weighted return separately. CFA Institute: GIPS Handbook, Provision 2.A.24, on time-weighted returns and external cash flows. The chart itself does not calculate CAPM alpha, beta, IR or TE, and cannot establish investment skill.
Summary
- A return gap and CAPM alpha are different. Beta-adjusted comparisons still depend on the chosen model and estimation conditions.
- Positive alpha or IR does not prove skill. Consider the sample, period and benchmark as well.
- Judge Tracking Error against the mandate. Its size alone does not identify a strategy or its quality.
- Currency conversion and hedging are different. Also align asset classes, dividends, fees, dates and cash-flow treatment.
- Multifolios Return mode visually compares asset values with benchmark prices. It does not calculate cash-flow-adjusted performance or alpha.