Expected Return

Overview

Expected return is the forward‑looking estimate of how much an investment is projected to earn on an annual basis after adjusting for the risk‑free rate. ClearLedger Analytics calculates expected return using daily log excess returns, which measure the difference between the stock’s return and the risk‑free return in continuous compounding space.

This approach is mathematically stable, avoids compounding distortions, and aligns with standard practices used in institutional portfolio management.

1. What Expected Return Represents

Expected return answers a simple question:

“How much annualized growth is this asset expected to achieve after accounting for the risk‑free rate?”

Expected return is a core input into:

• efficient frontier modeling
• portfolio optimization
• risk‑adjusted performance analytics
• return attribution

2. Conceptual Definition

Expected return represents the annualized growth rate an asset is expected to achieve, based on its historical performance relative to the risk‑free rate.

By using log returns, ClearLedger ensures that expected return is:

• stable across different time horizons
• free from compounding distortions
• consistent with institutional risk engines

3. How ClearLedger Analytics Computes Expected Return

Step‑by‑step calculation:

• Compute daily log returns for the stock and the risk‑free asset
• Calculate daily log excess return (stock minus risk‑free)
• Average the daily excess returns over the selected date range
• Annualize the result by multiplying by 252 trading days
• Convert back to a normal annual return using the exponential function

Formula:

Expected Return = exp(252 × AvgDailyLogExcessReturn) − 1

This produces a stable, annualized expected return that feeds directly into ClearLedger Analytics optimization engine, efficient frontier modeling, and risk‑adjusted performance analytics.

4. Why Expected Return Matters

Expected return is one of the most important inputs in portfolio construction. It helps advisors understand:

• how much return each asset contributes to the portfolio
• how optimization balances return vs. risk
• how different assets behave relative to the risk‑free rate
• how expected return interacts with covariance to shape the efficient frontier

Clients understand expected return intuitively:

“This asset is expected to earn X% per year after accounting for the risk‑free rate.”

5. Expected Return in Optimization

ClearLedger Analytics uses expected return to:

• construct the μ vector for efficient frontier optimization
• evaluate optimized vs. current portfolios
• support risk‑adjusted performance diagnostics
• quantify the impact of weight changes on expected growth

Expected return is a foundational component of deterministic portfolio optimization.

Conclusion

Expected return provides a forward‑looking estimate of annualized growth after adjusting for the risk‑free rate. ClearLedger Analytics computes expected return using daily log excess returns, producing a stable, mathematically sound measure that integrates directly into optimization, efficient frontier modeling, and risk‑adjusted analytics.