โ
Fund Manager Skill
Alpha Calculator
Measure How Much a Fund Manager Beats the Market
Calculate Jensen's Alpha, Treynor Ratio, Sharpe Ratio, and Information Ratio for any mutual fund or portfolio. Separate skill from luck โ find out if your returns are earned or just beta-riding the market.
Jensen's AlphaSharpe RatioTreynor Ratio
BetaInformation RatioRisk-Adjusted Return
PRESETS:
Calculate Jensen's Alpha
Portfolio / Fund Return
Actual CAGR delivered by the fund
%
-20%+50%
Benchmark / Market Return
Nifty 50 / Sensex CAGR over same period
%
-20%+50%
Risk-Free Rate
10-yr G-Sec yield / T-Bill rate
%
0%20%
Beta (ฮฒ)
Fund's sensitivity to market moves
ฮฒ
03.0
Portfolio Std Dev (ฯp)
Annual volatility of the fund's returns
%
0.1%60%
Optional โ for Tracking Error & Info Ratio
Tracking Error
Std dev of (Fund return โ Benchmark return)
%
Portfolio Return
Actual annualised return of the portfolio
%
-20%+50%
Risk-Free Rate
Government bond / T-Bill yield
%
0%20%
Portfolio Std Dev (ฯp)
Annual volatility / standard deviation
%
0.1%60%
Market Return
Benchmark CAGR over same period
%
-20%+50%
Beta (ฮฒ)
Fund sensitivity to market
ฮฒ
03.0
Market Std Dev (ฯm)
Annual volatility of the benchmark
%
Risk-Free Rate
Applied to all years
%
Annual Returns Data
YearFund Return (%)Benchmark (%)Alpha
Alpha Analysis
โ
Jensen's Alpha
โ
โ
Sharpe Ratio
โ
โ
Treynor Ratio
โ
โ
Info Ratio
โ
โ
Beta
โ
โ
๐ Risk-Adjusted Performance Gauges
Portfolio Return
โ
โ
Expected Return
โ
CAPM expected
Jensen's Alpha
โ
โ
Skill Assessment
โ
โ
Return Decomposition: Beta vs Alpha
Risk-Free Rate
Beta Return
Alpha (Skill)
๐ Full Risk-Adjusted Metrics Breakdown
What is Alpha in Investing?
Alpha is the excess return a fund or portfolio generates above and beyond what would be predicted by its risk (beta) and the market environment. A positive alpha means the fund manager added value through stock selection or timing โ skill, not just luck. Zero alpha means the fund delivered exactly what its risk level predicted. Negative alpha means the manager actually destroyed value compared to a passive index.
The most widely used formulation is Jensen's Alpha, named after economist Michael Jensen. It uses the Capital Asset Pricing Model (CAPM) to determine the "expected" return for a given level of systematic risk (beta), and then compares the actual return to that expected return.
Jensen's Alpha = Rp โ [Rf + ฮฒ ร (Rm โ Rf)]
Sharpe Ratio = (Rp โ Rf) รท ฯp
Treynor Ratio = (Rp โ Rf) รท ฮฒ
Information Ratio = (Rp โ Rm) รท Tracking Error
Where: Rp = Portfolio Return ย ยทย Rf = Risk-Free Rate ย ยทย Rm = Market Return ย ยทย ฮฒ = Beta ย ยทย ฯp = Portfolio Std Dev
Sharpe Ratio = (Rp โ Rf) รท ฯp
Treynor Ratio = (Rp โ Rf) รท ฮฒ
Information Ratio = (Rp โ Rm) รท Tracking Error
Where: Rp = Portfolio Return ย ยทย Rf = Risk-Free Rate ย ยทย Rm = Market Return ย ยทย ฮฒ = Beta ย ยทย ฯp = Portfolio Std Dev
Interpreting Alpha, Sharpe, Treynor & Information Ratio
| Metric | What It Measures | Good Value | Limitation |
|---|---|---|---|
| Jensen's Alpha | Excess return over CAPM expectation | > 1% (active funds) | Depends heavily on beta accuracy |
| Sharpe Ratio | Return per unit of total risk (ฯ) | > 1.0 | Penalises upside & downside equally |
| Treynor Ratio | Return per unit of market risk (ฮฒ) | > market Treynor | Only meaningful for diversified portfolios |
| Information Ratio | Active return per unit of active risk | > 0.5 (excellent: > 1.0) | Needs reliable tracking error estimate |
| Beta (ฮฒ) | Market sensitivity | 0.8โ1.1 (stable equity) | Backward-looking; changes over time |
Typical Alpha Values for Indian Mutual Funds
| Fund Category | Typical Alpha (3-yr) | Typical Sharpe | Typical Beta |
|---|---|---|---|
| Large-Cap Active Funds | 0% to +2% | 0.7โ1.0 | 0.9โ1.0 |
| Mid-Cap Funds | +2% to +5% | 0.8โ1.2 | 0.9โ1.1 |
| Small-Cap Funds | +3% to +8% | 0.6โ1.0 | 1.1โ1.4 |
| Flexi-Cap Funds | +1% to +4% | 0.8โ1.1 | 0.85โ1.0 |
| Index Funds (Nifty 50) | โ0.1% to โ0.5% | 0.7โ0.9 | ~1.0 |
| Debt / Liquid Funds | +0.5% to +1.5% | 1.2โ2.5 | 0.0โ0.2 |
Frequently Asked Questions
Is a high alpha always good?โผ
Not necessarily. Very high alpha (e.g., 10%+) in a single period is often statistical noise and unlikely to persist. Alpha is most meaningful when it is: (a) consistent across multiple periods (3โ5 years), (b) achieved with low tracking error, (c) higher than expense ratio โ since TER directly eats into alpha. An index fund with -0.2% alpha beats an active fund with +1% alpha if the active fund charges 1.5% TER but the index fund charges only 0.1%.
What is beta and why does it matter for alpha?โผ
Beta measures how much a fund moves relative to the market. A beta of 1.0 means the fund moves in lockstep with Nifty 50. Beta of 1.2 means it rises 12% when Nifty rises 10%, and falls 12% when Nifty falls 10%. In alpha calculation, beta determines the "expected return" โ a high-beta fund is expected to earn more in bull markets simply because it takes more market risk. Alpha strips out this beta-driven return, leaving only the skill component. A fund returning 18% with beta of 1.5 may have zero alpha, while a fund returning 14% with beta of 0.8 may have positive alpha.
What is the difference between Sharpe and Treynor ratios?โผ
Both measure risk-adjusted return, but they define "risk" differently. Sharpe uses total risk (standard deviation of returns) โ measuring all volatility, both systematic and unsystematic. Treynor uses only systematic risk (beta) โ measuring only market-related volatility. For a well-diversified fund, both give similar rankings. For concentrated portfolios, Sharpe is more conservative because it penalises stock-specific volatility. Use Sharpe when evaluating a single fund; use Treynor when comparing funds that are all part of a diversified portfolio.
Can alpha be negative even if a fund beats Nifty?โผ
Yes. If a fund has a beta of 1.4 and the Nifty returned 12%, the fund was expected to return at least 14โ15% just from market beta. If it actually returned 13% โ which beats Nifty โ its alpha is still negative because it underperformed what its risk level predicted. This is why beta context is critical: a fund beating Nifty but with high beta may be taking disproportionate risk for its outperformance.
What is Information Ratio and how is it used?โผ
The Information Ratio (IR) divides active return (fund return minus benchmark) by tracking error (standard deviation of that difference). It answers: "For every unit of active risk taken, how much active return did the manager deliver?" An IR above 0.5 is considered good; above 1.0 is excellent. A fund with 3% active return and 6% tracking error has an IR of 0.5. A fund with 3% active return and 3% tracking error has an IR of 1.0 โ same return, but achieved with less deviation from the benchmark, indicating more consistent skill.
โ
Fund Manager Skill
Alpha Calculator
Measure How Much a Fund Manager Beats the Market
Calculate Jensen's Alpha, Treynor Ratio, Sharpe Ratio, and Information Ratio for any mutual fund or portfolio. Separate skill from luck โ find out if your returns are earned or just beta-riding the market.
Jensen's AlphaSharpe RatioTreynor Ratio
BetaInformation RatioRisk-Adjusted Return
PRESETS:
Calculate Jensen's Alpha
Portfolio / Fund Return
Actual CAGR delivered by the fund
%
-20%+50%
Benchmark / Market Return
Nifty 50 / Sensex CAGR over same period
%
-20%+50%
Risk-Free Rate
10-yr G-Sec yield / T-Bill rate
%
0%20%
Beta (ฮฒ)
Fund's sensitivity to market moves
ฮฒ
03.0
Portfolio Std Dev (ฯp)
Annual volatility of the fund's returns
%
0.1%60%
Optional โ for Tracking Error & Info Ratio
Tracking Error
Std dev of (Fund return โ Benchmark return)
%
Portfolio Return
Actual annualised return of the portfolio
%
-20%+50%
Risk-Free Rate
Government bond / T-Bill yield
%
0%20%
Portfolio Std Dev (ฯp)
Annual volatility / standard deviation
%
0.1%60%
Market Return
Benchmark CAGR over same period
%
-20%+50%
Beta (ฮฒ)
Fund sensitivity to market
ฮฒ
03.0
Market Std Dev (ฯm)
Annual volatility of the benchmark
%
Risk-Free Rate
Applied to all years
%
Annual Returns Data
YearFund Return (%)Benchmark (%)Alpha
Alpha Analysis
โ
Jensen's Alpha
โ
โ
Sharpe Ratio
โ
โ
Treynor Ratio
โ
โ
Info Ratio
โ
โ
Beta
โ
โ
๐ Risk-Adjusted Performance Gauges
Portfolio Return
โ
โ
Expected Return
โ
CAPM expected
Jensen's Alpha
โ
โ
Skill Assessment
โ
โ
Return Decomposition: Beta vs Alpha
Risk-Free Rate
Beta Return
Alpha (Skill)
๐ Full Risk-Adjusted Metrics Breakdown
What is Alpha in Investing?
Alpha is the excess return a fund or portfolio generates above and beyond what would be predicted by its risk (beta) and the market environment. A positive alpha means the fund manager added value through stock selection or timing โ skill, not just luck. Zero alpha means the fund delivered exactly what its risk level predicted. Negative alpha means the manager actually destroyed value compared to a passive index.
The most widely used formulation is Jensen's Alpha, named after economist Michael Jensen. It uses the Capital Asset Pricing Model (CAPM) to determine the "expected" return for a given level of systematic risk (beta), and then compares the actual return to that expected return.
Jensen's Alpha = Rp โ [Rf + ฮฒ ร (Rm โ Rf)]
Sharpe Ratio = (Rp โ Rf) รท ฯp
Treynor Ratio = (Rp โ Rf) รท ฮฒ
Information Ratio = (Rp โ Rm) รท Tracking Error
Where: Rp = Portfolio Return ยท Rf = Risk-Free Rate ยท Rm = Market Return ยท ฮฒ = Beta ยท ฯp = Portfolio Std Dev
Sharpe Ratio = (Rp โ Rf) รท ฯp
Treynor Ratio = (Rp โ Rf) รท ฮฒ
Information Ratio = (Rp โ Rm) รท Tracking Error
Where: Rp = Portfolio Return ยท Rf = Risk-Free Rate ยท Rm = Market Return ยท ฮฒ = Beta ยท ฯp = Portfolio Std Dev
Interpreting Alpha, Sharpe, Treynor & Information Ratio
| Metric | What It Measures | Good Value | Limitation |
|---|---|---|---|
| Jensen's Alpha | Excess return over CAPM expectation | > 1% (active funds) | Depends heavily on beta accuracy |
| Sharpe Ratio | Return per unit of total risk (ฯ) | > 1.0 | Penalises upside & downside equally |
| Treynor Ratio | Return per unit of market risk (ฮฒ) | > market Treynor | Only meaningful for diversified portfolios |
| Information Ratio | Active return per unit of active risk | > 0.5 (excellent: > 1.0) | Needs reliable tracking error estimate |
| Beta (ฮฒ) | Market sensitivity | 0.8โ1.1 (stable equity) | Backward-looking; changes over time |
Typical Alpha Values for Indian Mutual Funds
| Fund Category | Typical Alpha (3-yr) | Typical Sharpe | Typical Beta |
|---|---|---|---|
| Large-Cap Active Funds | 0% to +2% | 0.7โ1.0 | 0.9โ1.0 |
| Mid-Cap Funds | +2% to +5% | 0.8โ1.2 | 0.9โ1.1 |
| Small-Cap Funds | +3% to +8% | 0.6โ1.0 | 1.1โ1.4 |
| Flexi-Cap Funds | +1% to +4% | 0.8โ1.1 | 0.85โ1.0 |
| Index Funds (Nifty 50) | โ0.1% to โ0.5% | 0.7โ0.9 | ~1.0 |
| Debt / Liquid Funds | +0.5% to +1.5% | 1.2โ2.5 | 0.0โ0.2 |
Frequently Asked Questions
Is a high alpha always good?โผ
Not necessarily. Very high alpha (e.g., 10%+) in a single period is often statistical noise and unlikely to persist. Alpha is most meaningful when it is: (a) consistent across multiple periods (3โ5 years), (b) achieved with low tracking error, (c) higher than expense ratio โ since TER directly eats into alpha. An index fund with -0.2% alpha beats an active fund with +1% alpha if the active fund charges 1.5% TER but the index fund charges only 0.1%.
What is beta and why does it matter for alpha?โผ
Beta measures how much a fund moves relative to the market. A beta of 1.0 means the fund moves in lockstep with Nifty 50. Beta of 1.2 means it rises 12% when Nifty rises 10%, and falls 12% when Nifty falls 10%. In alpha calculation, beta determines the "expected return" โ a high-beta fund is expected to earn more in bull markets simply because it takes more market risk. Alpha strips out this beta-driven return, leaving only the skill component. A fund returning 18% with beta of 1.5 may have zero alpha, while a fund returning 14% with beta of 0.8 may have positive alpha.
What is the difference between Sharpe and Treynor ratios?โผ
Both measure risk-adjusted return, but they define "risk" differently. Sharpe uses total risk (standard deviation of returns) โ measuring all volatility, both systematic and unsystematic. Treynor uses only systematic risk (beta) โ measuring only market-related volatility. For a well-diversified fund, both give similar rankings. For concentrated portfolios, Sharpe is more conservative because it penalises stock-specific volatility. Use Sharpe when evaluating a single fund; use Treynor when comparing funds that are all part of a diversified portfolio.
Can alpha be negative even if a fund beats Nifty?โผ
Yes. If a fund has a beta of 1.4 and the Nifty returned 12%, the fund was expected to return at least 14โ15% just from market beta. If it actually returned 13% โ which beats Nifty โ its alpha is still negative because it underperformed what its risk level predicted. This is why beta context is critical: a fund beating Nifty but with high beta may be taking disproportionate risk for its outperformance.
What is Information Ratio and how is it used?โผ
The Information Ratio (IR) divides active return (fund return minus benchmark) by tracking error (standard deviation of that difference). It answers: "For every unit of active risk taken, how much active return did the manager deliver?" An IR above 0.5 is considered good; above 1.0 is excellent. A fund with 3% active return and 6% tracking error has an IR of 0.5. A fund with 3% active return and 3% tracking error has an IR of 1.0 โ same return, but achieved with less deviation from the benchmark, indicating more consistent skill.