Alpha

Overview

Alpha measures the portion of return that cannot be explained by an asset’s or portfolio’s beta exposure to its benchmark. It represents skill‑based, idiosyncratic performance — the return generated above or below what the benchmark would predict.

ClearLedger Analytics computes alpha deterministically using a regression between the asset’s (or portfolio’s) daily adjusted returns and the benchmark’s daily adjusted returns. Beta is the slope of the regression line; alpha is the intercept — the value of the asset’s return when the benchmark’s return is zero.

1. What Alpha Represents

Alpha answers one question:

“Did this portfolio earn more or less than what the market alone would explain?”

Interpretation:

• Positive alpha → outperformed expectations

• Zero alpha → performed exactly as expected

• Negative alpha → underperformed expectations

Alpha isolates the portion of return driven by manager decisions, not market exposure.

2. Conceptual Definition

Alpha represents the excess return an asset or portfolio generates after accounting for its sensitivity (beta) to the benchmark.

It is the purest measure of value added beyond systematic market movement.

3. Deterministic Regression‑Based Formula

ClearLedger Analytics uses the standard institutional regression‑based definition of alpha:

Alpha = Portfolio Return − (Beta × Benchmark Return)

This ensures alpha reflects:

• the portfolio’s actual sensitivity to the market

• the benchmark’s actual realized return

• the portion of return not explained by systematic risk

No forecasting. No assumptions. No noise. Just deterministic math.

4. How ClearLedger Analytics Computes Alpha

Step‑by‑Step Calculation:

• Build a stable date spine based on the selected calendar range.

• Retrieve daily adjusted returns for both the asset/portfolio and the benchmark.

• Compute mean returns for both series.

• Compute regression components: ΣX, ΣY, ΣXY, ΣX².

• Compute beta (slope):

β = (n·ΣXY − ΣX·ΣY) / (n·ΣX² − (ΣX)²)

• Compute alpha (intercept):

α = μY − β·μX

This regression‑based method is the same mathematical convention used in institutional portfolio risk systems. ClearLedger Analytics applies it consistently across attribution, performance decomposition, and optimization workflows.

5. What Drives Alpha

Alpha changes when:

• weights shift

• diversification improves

• risk exposures change

• individual securities outperform or underperform

• constraints limit or enhance opportunity

Alpha is not a property of a stock — it is a property of portfolio construction.

6. Portfolio Alpha vs. Security Alpha

ClearLedger Analytics focuses on portfolio‑level alpha, not security‑level alpha.

Why?

• security alpha is unstable

• security alpha depends heavily on benchmark choice

• security alpha ignores interactions between holdings

• portfolio alpha is what clients actually experience

Portfolio alpha is the only alpha that matters for advisors.

7. How ClearLedger Analytics Uses Alpha

Alpha is used to:

• quantify value added beyond market exposure

• compare current vs optimized portfolios

• support risk‑adjusted performance diagnostics

• help advisors communicate the impact of weight changes

Conclusion

Alpha measures the portion of return that comes from decisions — not from the market.

ClearLedger Analytics computes alpha using deterministic, regression‑based methods, giving advisors a clear, transparent measure of value added.

This makes performance attribution simple, explainable, and actionable.