Alpha and beta
Jensen's alpha quantifies manager skill as excess return above CAPM prediction; beta measures a fund's sensitivity to benchmark moves via covariance/variance.
Alpha and beta are the two outputs of a single linear regression of a fund's excess returns against a benchmark's excess returns. Beta describes the slope — how much the fund moves for each unit of benchmark movement. Alpha describes the intercept — the return left over after stripping out what beta explains. Together they answer: how exposed is this fund to the market, and what has the manager added beyond that exposure?
Beta — market sensitivity
What it measures
Beta (β) quantifies how much a fund's return tends to move relative to its benchmark. A beta of 1.0 means the fund has moved in lockstep with the benchmark historically. A beta of 1.2 means the fund amplifies benchmark moves by 20% — if the benchmark falls 10%, the fund tends to fall 12%. A beta of 0.8 means the fund absorbs only 80% of benchmark movement.
Beta is not a measure of quality. High beta is neutral — it reflects higher market exposure. In rising markets, a high-beta fund outperforms; in falling markets, it underperforms. It is a description of positioning, not an endorsement of it.
How beta is computed
Beta is the covariance of the fund's excess return with the benchmark's excess return, divided by the variance of the benchmark's excess return — the standard OLS slope estimator from Sharpe (1964) and CAPM:
β = Cov(R_p − R_f, R_b − R_f) / Var(R_b − R_f)
Where:
R_p= monthly fund returnR_b= monthly benchmark return (Total Return Index, per SEBI 2017/126 mandate)R_f= monthly risk-free rate (91-day T-bill / 12)
The computation uses 36 monthly return pairs (minimum 24). All returns are in excess of the risk-free rate to align with CAPM's formulation.
Example: Over 36 months, Cov(fund excess, benchmark excess) = 0.00182; Var(benchmark excess) = 0.00154. Beta = 0.00182 / 0.00154 = 1.18. The fund amplifies benchmark moves by 18%.
Benchmark assignment
SEBI circular SEBI/HO/IMD/DF2/CIR/P/2017/126 (December 2017) mandated Total Return Index (TRI) benchmarks for all mutual fund schemes — the benchmark must include dividend reinvestment, not just price movement. MintByte uses TRI benchmark data for all beta and alpha calculations. Category-to-benchmark mapping follows SEBI's 2023 recategorisation circular:
| SEBI Category | Benchmark used |
|---|---|
| Large Cap | Nifty 50 TRI |
| Mid Cap | Nifty Midcap 150 TRI |
| Small Cap | Nifty Smallcap 250 TRI |
| Flexi Cap / Multi Cap | Nifty 500 TRI |
| Debt: Short Duration | CRISIL Short Term Bond Index |
| Debt: Liquid | CRISIL Liquid Fund Index |
Alpha — active manager contribution
What it measures
Jensen's alpha (Jensen, 1968) is the intercept of the CAPM regression — the return a fund generates that cannot be explained by its beta-weighted benchmark exposure. A positive alpha means the manager added value; a negative alpha means passive benchmark exposure would have been more rewarding after adjusting for the fund's own risk level.
How alpha is computed
From the CAPM identity:
α = R_p − [R_f + β × (R_b − R_f)]
This is the Jensen (1968) formulation — the same as computing the OLS intercept in the excess-return regression. Both methods are algebraically equivalent; MintByte uses the regression intercept directly, expressed in annualised percentage points.
Example: Large-cap fund. R_p = 14.2%, R_f = 6.8%, R_b = 12.5%, β = 0.92.
Expected return = 6.8 + 0.92 × (12.5 − 6.8)
= 6.8 + 5.24
= 12.04%
Alpha = 14.2 − 12.04 = +2.16%
The fund earned 2.16 percentage points more than its level of market exposure would predict.
Interpreting alpha
| Alpha (annualised) | Reading |
|---|---|
| > +3% | Strong — sustained alpha at this level is rare in Indian large-cap |
| +1% to +3% | Good — manager contributing meaningfully over market exposure |
| −1% to +1% | Neutral — consider whether TER justifies active management |
| < −1% | Negative — market exposure would have outperformed |
Alpha figures should be evaluated over multiple rolling 3-year windows, not a single period. A single window may be dominated by a secular trend (e.g. one heavy sector bet that paid off). Persistent alpha across rolling periods is a more meaningful signal of manager skill.
Relationship between alpha and beta
Alpha and beta are not independent. A high-beta fund has a wider variance of possible alpha outcomes — it can generate very high positive alpha in a bull run by being more exposed, but the same positioning will produce deeply negative alpha in a bear run. This is why funds should not be compared on alpha without first verifying that their betas are in the same range.
A fund with beta 1.4 and alpha +4% is not necessarily better than a fund with beta 0.8 and alpha +3% — the first fund is taking substantially more market risk to generate slightly more excess return. The Sharpe Ratio or Treynor Ratio (a variant that normalises by beta) are the appropriate comparison tools.
Statistical caveats
The 36-month OLS regression has limited degrees of freedom for equity funds that change their style over time. The R² of the regression (coefficient of determination) tells you how well the single-factor model fits: a high R² (> 0.90) means most fund return variation is explained by the benchmark — alpha and beta are reliable estimates. A low R² (< 0.70) means the fund is driven by idiosyncratic exposures the single-factor model cannot capture; multi-factor decomposition via Factor Exposure is more appropriate in that case.
Primary sources
- Sharpe, W.F. (1964). "Capital asset prices: A theory of market equilibrium under conditions of risk." Journal of Finance, 19(3), 425–442. — Establishes CAPM and the beta concept.
- Jensen, M.C. (1968). "The performance of mutual funds in the period 1945–1964." Journal of Finance, 23(2), 389–416. — Introduces Jensen's alpha as the CAPM intercept for evaluating manager skill.
- SEBI/HO/IMD/DF2/CIR/P/2017/126 (December 2017) — TRI benchmark mandate for all mutual fund performance reporting.
Monthly NAV and benchmark returns: AdvisorKhoj API. Risk-free rate: RBI 91-day T-bill monthly average. Computations run monthly after NAV refresh; minimum 24 months required for inclusion.