# Alpha

Alpha is the difference between an investment’s realized return and the return predicted by a specified risk-adjusted benchmark model, usually expressed in percentage points.

## What it means

A stock or portfolio can outperform a market index simply because it takes more market risk. Alpha asks how much of a realized return remains unexplained after accounting for risk under a specified model. It is usually evaluated over a stated historical period, not known in advance.

In the single-factor capital asset pricing model (CAPM), alpha compares realized return with the return implied by the risk-free rate, the market’s return and the investment’s beta. A positive result means realized return exceeded that model’s prediction; a negative result means it fell short. Neither establishes skill or predicts future results. Alpha depends on the chosen benchmark, risk model, measurement period and return data.

## How it is calculated

For a single measurement period, a CAPM-based calculation is:

`Alpha = R_i − [R_f + β_i × (R_m − R_f)]`

- `Alpha`: realized return minus the model-predicted return, in percentage points for the period.
- `R_i`: the investment’s realized return over that period, in percent.
- `R_f`: the risk-free return for the same period, in percent.
- `β_i`: the investment’s beta relative to the chosen market benchmark; it has no units.
- `R_m`: the market benchmark’s realized return over the same period, in percent.

Returns must cover matching periods and use consistent conventions. For example, compare total returns, including dividends where applicable, rather than a stock’s price-only return with an index’s total return. Beta must also be estimated against the stated benchmark. In a regression, Jensen’s alpha is commonly estimated as the intercept of the investment’s excess returns regressed on the benchmark’s excess returns; that estimate need not equal a calculation using an independently estimated beta and period totals.

## Worked example

Suppose, hypothetically, a portfolio returned 12% over one year, the risk-free return was 2%, the selected market benchmark returned 8% and the portfolio’s estimated beta was 1.25.

1. Find the market’s excess return: `8% − 2% = 6 percentage points`.
2. Adjust it for beta: `1.25 × 6 = 7.5 percentage points`.
3. Add the risk-free return: `2% + 7.5% = 9.5%` model-predicted return.
4. Subtract that prediction from the portfolio’s realized return: `12% − 9.5% = +2.5 percentage points` of alpha.

The result describes this hypothetical period under this particular model. If the 12% portfolio return excludes trading costs, the calculated alpha also does not account for those costs.

## Why it matters before you trade

Alpha is often used to evaluate a strategy after returns are observed. Before a trade, a claimed *expected alpha* is only an estimate, sensitive to assumptions and model error. Historical alpha may reflect chance, a changing risk exposure or an unsuitable benchmark rather than a repeatable advantage.

Execution costs can reduce any return available to an investor. The bid-ask spread, market impact and other transaction costs therefore matter when assessing whether a proposed trade makes sense under an investor’s own assumptions. Alpha is a return measure; it does not describe an order’s liquidity, likely fill or short-term price volatility.

## How PreTrAIde uses it

PreTrAIde does not list alpha calculation or alpha forecasting among its stated features. Its pre-trade analysis instead assesses a proposed stock basket before the user places any order. It estimates factors including spread, market impact and volatility, then returns a GO, NO-GO or MODIFY verdict with a model-estimated success probability, risk assessment, suggested execution strategy and plain-language reasoning. Those outputs are decision support, not an alpha estimate, a return forecast or an investment recommendation.

## Common mistakes

- **Calling every return above an index “alpha.”** A simple difference from an index does not adjust for beta or specify a risk model.
- **Mixing time periods or return conventions.** Annual and monthly returns, or price and total returns, cannot be combined directly in the formula.
- **Treating positive historical alpha as proof of skill.** A short sample, benchmark choice or statistical noise can change the result.
- **Ignoring implementation.** A gross-return calculation can overstate what remains after spreads, market impact and other costs.
- **Confusing alpha with beta.** Beta measures sensitivity to benchmark movements; alpha is the return left unexplained by the specified model.

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Source: https://pretraide.com/glossary/alpha