Your portfolio returned +20% this year. The S&P 500 returned +15%. Is that simple +5pp gap proof you outperformed? Honest answer: not yet. Whether that gap is luck, stock-picking skill, or just a reward for taking more risk is exactly what alpha tries to separate. This article walks through the 4-step frame — beta adjustment, Information Ratio, Tracking Error, benchmark selection — to compare against a benchmark honestly.
The most intuitive definition is:
Calling this "I beat the S&P by 5%" feels natural. But in academia and the industry, alpha (α) means something stricter.
Key assumption: "Returns proportional to market beta (β) are available to anyone." Buy S&P 500 with 1.5× leverage and when the market does +10%, you naturally see ~+15%. That extra 5% is not stock-selection skill — it's just the cost of doubling your exposure. Counting it as alpha would be dishonest.
The standard definition:
The bracketed expression is what CAPM (Capital Asset Pricing Model) predicts as "the expected return that matches your beta." Subtracting that from actual return gives alpha — the "excess return that beta cannot explain." That residual is what real stock-picking skill looks like.
Compare two investors. Risk-free rate rf = 3%, S&P 500 = +15%.
| Investor | Return | Beta (β) | Simple gap | Alpha (α) |
|---|---|---|---|---|
| A — Diversified value | +20% | 0.9 | +5pp | +6.2pp |
| B — Leveraged ETF | +20% | 2.0 | +5pp | −4.0pp |
Math:
Same +20% return, same +5pp simple gap, but A has positive alpha (skill) while B has negative alpha (under-rewarded for risk). B is just a bigger bet that wins more when markets are up and loses more when they're down — at the same risk level, simply leveraging the market 1.5× would have been more efficient.
Beta comes from regression — regress your daily return series on the benchmark's return series; the slope is beta.
Practical rule: use at least 1 year of daily data. Less than 6 months gets too noisy. Single-stock beta is available on Yahoo Finance / Bloomberg; portfolio beta is the weighted average of holdings' betas.
If alpha is +6% but it swings ±15pp every year, is that skill or luck? The metric introduced to answer this is the Information Ratio (IR).
Here Tracking Error is the standard deviation of (portfolio − benchmark) return differences. That is, "how varied was your divergence from the benchmark."
Why this matters: if you only look at alpha, a "lucky big year" still shows positive alpha. IR measures "how repeatable that alpha is" — where Sharpe Ratio is risk-adjusted absolute return, IR is risk-adjusted excess-over-benchmark return.
→ Deep dive on Information Ratio — what 0.5/1.0/2.0 actually mean, plus 4 calculation pitfalls
TE of 5pp means on average you diverged from the benchmark by 5pp per year. TE itself is neither good nor bad — judge it against intent.
| TE level | Interpretation | Type |
|---|---|---|
| < 2pp | Near benchmark | Index / smart-beta |
| 2–6pp | Moderately active | Large-cap active fund |
| > 6pp | High-conviction active | Concentrated / thematic / hedge fund |
If "tracking the S&P 500" is the goal but TE is 10%, the strategy drifted from intent. Conversely, if "concentrated bets on next-gen AI" is the goal but TE is 1%, you just rode the benchmark.
Pick the wrong benchmark and all the math above is meaningless. Two principles:
US large-cap portfolio? S&P 500. Korea-heavy? KOSPI or KOSPI 200. Global diversified? MSCI World or ACWI. Heavy EM? MSCI EM. The benchmark must have the same market / currency exposure as your portfolio for the comparison to be honest.
Comparing a USD-based portfolio to KOSPI (KRW) mixes currency moves into your alpha. Compare against KRW-converted S&P 500 (or a hedged S&P 500 ETF) to isolate real stock alpha.
The Asset Chart in Multifolios automatically shows a dashed S&P 500 line in Return mode (blue dashed line). Korea-heavy? Toggle to KOSPI.
Note: simple visual comparison doesn't resolve beta / IR / TE in sections 1–4. That needs separate statistical tools (R, Python, or a future Multifolios alpha-analytics card).