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Key Takeaways
- In a return regression, alpha is the intercept and the period-specific residual is a separate term.
- Jensen’s alpha compares average portfolio excess return with beta times average market excess return.
- Positive alpha is the return left after the market exposure is paid for, 2.8 points a year in the example.
- Calculate gross and net alpha from the corresponding return series, counting fees and execution costs once.
- Compare alpha with factor exposures, residual variation, drawdown and capital usage.
What is alpha?
Alpha is the part of a portfolio’s return left after accounting for its exposure to the market or other selected factors. Jensen’s alpha is the fitted intercept in a regression of portfolio excess returns on market excess returns. A positive alpha means the portfolio’s mean return exceeded the risk-free baseline plus its beta-scaled market excess return over the measured period.
How is alpha calculated?
In a market regression, portfolio excess return equals alpha plus beta times market excess return plus a period-specific residual. Alpha is the fitted intercept; the residual is the observation’s remaining deviation.
For an ordinary least-squares regression with an intercept, alpha equals mean portfolio excess return minus fitted beta times mean market excess return.
Formula
Portfolio excess return at t = alpha + beta × market excess return at t + residual at t; fitted alpha = mean(portfolio excess return) − fitted beta × mean(market excess return)- Use matching portfolio, benchmark and risk-free return observations. The formula uses arithmetic means of those periodic returns.
- Beta is the slope from regressing portfolio excess returns on benchmark excess returns.
- CAPM says what a portfolio should earn for its beta; the regression measures what it did earn on the realized excess returns, fitting alpha and beta together.
- A multifactor model replaces the single bracketed term with several factor exposures, which changes the alpha it reports.
Alpha example: alpha vs active return
Use the same return record to estimate beta and annualized arithmetic means: portfolio 12%, benchmark 8%, risk-free baseline 2%, and beta 1.2. The portfolio series is net of its included costs.
- Mean market excess return: 8% − 2% = 6% annualized
- Beta contribution: 1.2 × 6% = 7.2 percentage points
- Mean return accounted for by baseline and beta: 2% + 7.2% = 9.2%
- Annualized fitted alpha: 12% − 9.2% = 2.8 percentage points
- Mean active return over the index: 12% − 8% = 4 percentage points
The fitted alpha is 2.8 annualized percentage points, while mean active return over the benchmark is 4 points. The 1.2-point difference comes from the portfolio’s beta above one applied to the 6% market premium.
Gross alpha, net alpha and the return basis
Use the portfolio’s actual net-return series when measuring net alpha. Calculate a separate gross version from the corresponding gross-return series. Include each fee, financing charge and execution cost once.
A single year’s compounded return is distinct from an annualized arithmetic mean used in the fitted regression. Keep the observation frequency and scaling convention aligned across the example.
How factor models change alpha
A multifactor regression adds selected factor returns and estimates their exposures with the intercept. Adding a factor can move alpha in either direction, depending on the fitted relationship.
Review the attributed returns and residual variation alongside alpha. Before sizing up a strategy the regression credits with alpha, check its position payoffs and the capital it ties up.
Alpha vs the information ratio and Sharpe ratio
The Information Ratio uses mean active return and tracking error. The appraisal-ratio construction uses alpha and regression residual volatility. Sharpe uses mean excess return and its standard deviation.
Sharpe scores return per unit of total volatility, the information ratio scores consistency against the benchmark, and the appraisal ratio scores alpha per unit of residual risk.
Limitations of alpha
- The 2.8 points belong to the measured period, and a shorter record carries wider estimation error. Confirm alpha across more periods before allocating more capital to the strategy.
- Fit a benchmark that matches the strategy before crediting alpha. Changing the benchmark or adding factors refits the exposures, and alpha can rise, fall or stay the same.
- Match the return basis before comparing two alphas. Gross and net series, observation frequency and annualization each change the figure.
- Check whether market exposure moved during the window. When it did, the single 1.2 beta averages it, and alpha picks up whatever part of the mismatch the average misses.
- Read alpha beside the risk taken to earn it. Residual volatility, drawdown and capital usage each get their own measure.
Bottom line
Alpha measures the return a portfolio earned beyond what the risk-free baseline and its market or factor exposure account for. Use it to separate return that beta explains from return it does not, and read it with the model, return basis and sample that produced it, alongside residual volatility, costs and drawdown.
Clear answers
Frequently Asked Questions
Sources and Further Reading
- CFA Institute: Portfolio Risk and Return, Part II
- Fidelity: Alpha, Beta, and Smart Beta
- Fidelity: What Is a Benchmark?
How entries are sourced, calculated and updated: editorial methodology.