# Beta and R-Squared

A fund’s market sensitivity, and how much the market explains it.

Source data: AMFI daily NAV (17,900+ schemes) + Nifty benchmark indices. Last updated: 2026-07-02. Interactive tool: https://mfpro.tigzig.com

## What is Beta?



Beta measures how sensitive a fund is to market movements (Nifty 50).
 A beta of 1.0 means the fund moves in lockstep with the market.
 Beta > 1 means the fund amplifies market moves (goes up more in bull markets,
 down more in bear markets). Beta 0
),
bench_daily AS (
 SELECT date,
 (nav / LAG(nav) OVER (ORDER BY date) - 1) * 100 AS ret
 FROM index_nav WHERE index_name = 'INDEX_NIFTY50'
)
SELECT
 REGR_SLOPE(f.ret, b.ret) AS beta,
 REGR_R2(f.ret, b.ret) AS r_squared
FROM fund_daily f
JOIN bench_daily b ON f.date = b.date
WHERE f.ret IS NOT NULL AND b.ret IS NOT NULL 
 


## Worked Example


 HDFC Flexi Cap - Full History


Beta = 0.92, R² = 0.88


The fund captures 92% of Nifty 50's moves (slightly defensive). 88% of its variance
 is explained by the market - this is a strong fit, so the beta is reliable.

 

Axis Focused 25 - Last 3Y


Beta = 0.78, R² = 0.71


More defensive (only 78% of market moves), and 71% fit. The concentrated
 portfolio (25 stocks) means more stock-specific risk, hence lower R².

 
 


## Edge Cases





- **Low R²:** When R² is below 0.40, the beta becomes unreliable -
 the fund's returns aren't driven by the benchmark, so the regression is a poor fit.
 We still show beta but in grey italic to flag this.

- **Minimum observations:** We require at least 60 daily returns. With fewer,
 the regression is statistically meaningless.

- **Benchmark choice matters:** The default benchmark is Nifty 50, but you can
 select a different one via the Benchmark dropdown. A midcap fund benchmarked against Nifty 50 may show lower R² than if
 benchmarked against Nifty Midcap 150. This doesn't mean the fund is bad - it means the
 benchmark isn't ideal for that fund. Try switching to a more appropriate benchmark for better insight.


 


## Beta Confidence Intervals



The beta value from the regression is a point estimate. Confidence intervals tell you the
 range within which the true beta is likely to fall. A narrow CI means the beta is precisely
 estimated; a wide CI means there is more uncertainty.

 
 SE(Beta) = |Beta / t-stat|

CI = Beta ± t critical × SE(Beta)

t critical values:
 90% CI → 1.645
 95% CI → 1.960
 99% CI → 2.576
 

We derive the standard error directly from the beta and t-statistic that are already
 computed. No additional regression is needed. The t-critical values assume a large sample
 (250+ daily observations), where the t-distribution closely approximates the normal.


Beta CI - Worked Example


Beta = 0.92, t-stat = 28.4


SE = |0.92 / 28.4| = 0.0324


95% CI = 0.92 ± 1.960 × 0.0324 = **[0.856, 0.984]**


We are 95% confident the true beta lies between 0.856 and 0.984. The interval is
 narrow because we have many observations and a high t-stat.

 

When the t-stat is low (e.g., below 2), the CI becomes wide and may include zero -
 meaning we cannot be confident the fund has any systematic relationship with the benchmark.
 This aligns with the R² color coding: low t-stat typically accompanies low R².

## Related metrics

More Risk Metrics methodology from the MFPRO analytics tool:

- [Alpha and t-statistic](/mfpro/alpha-and-t-stat)

- [Sharpe Ratio](/mfpro/sharpe-ratio)

- [Sortino Ratio](/mfpro/sortino-ratio)

- [Tracking Error and Information Ratio](/mfpro/tracking-error-information-ratio)

- [Capture Ratios (Upside and Downside)](/mfpro/capture-ratio)

- [Win Rate](/mfpro/win-rate)

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Source: https://www.tigzig.com/mfpro/beta-and-r-squared