Excess Return

Core Description

• Excess return represents the portion of an investment’s performance that surpasses a relevant benchmark or the risk-free rate.
• It is a fundamental measure for assessing portfolio manager skill, adjusted for risk and fees, and helps investors assess value added compared with the market.
• Evaluating excess return supports more informed investment decisions by providing objective, benchmark-relative analysis.

Definition and Background

What is Excess Return?
Excess return refers to the performance of an investment that exceeds a chosen benchmark, usually a broad market index (such as the S&P 500 or MSCI World Index) or the risk-free rate (such as U.S. Treasury bills). It is calculated as the investment’s total return minus the benchmark’s return for the same period.

Historical Perspective
The concept of excess return is rooted in the early development of financial theory. Before formal models were developed, early traders recognized that riskier investments required a return premium over safer options. The introduction of Modern Portfolio Theory by Markowitz, as well as the Capital Asset Pricing Model (CAPM) by Sharpe, Lintner, and Mossin, formalized the idea that portfolio returns should be compared to relevant benchmarks and risk-adjusted expectations.

Evolution of the Excess Return Concept

• CAPM and Alpha: Within the CAPM, excess return beyond what is explained by market exposure (beta) is referred to as “alpha,” which is an important metric for evaluating active manager value.
• Multi-factor Models: As more complex asset-pricing models developed, excess return attribution expanded, recognizing that exposures to factors (such as value, momentum, or size) might explain returns previously identified as alpha.
• Behavioral Perspectives: Behavioral finance and anomaly studies suggested that some consistent excess returns may reflect mispricing rather than risk premia.

Calculation Methods and Applications

How to Calculate Excess Return

Basic Formula
Excess Return = Investment Return – Benchmark Return

• Both returns must be measured over the same period, and all relevant dividends or income should be reinvested.
• Returns are typically expressed as percentages and should be net of any fees or costs for investor relevance.

Geometric Compounding for Multiple Periods
When evaluating multiple periods:

• Use compounded returns to account for the effect of compounding.
• Example:
  If your investment grows 5 percent one year and 4 percent the next, and the benchmark grows 3 percent and 2 percent respectively:
  • Investment cumulative: (1 + 0.05) * (1 + 0.04) = 1.092
  • Benchmark cumulative: (1 + 0.03) * (1 + 0.02) = 1.0506
  • Cumulative excess return: 1.092 / 1.0506 - 1 ≈ 3.95 percent

Annualization of Excess Return
To express periodic excess returns as annual values:Annualized Excess Return ≈ (1 + Cumulative Excess Return)^(12 / N) – 1
where N is the number of months in the measurement period.

Practical Uses

• Skill Attribution:
  By isolating performance above passive benchmarks, investors can determine whether active management is generating value (commonly referred to as “alpha” in investment literature).
• Compensation and Incentives:
  Some asset management contracts and incentive structures are tied to persistent positive excess returns.
• Portfolio Construction:
  Excess return data can inform allocations and risk budgeting across various strategies.

Comparison, Advantages, and Common Misconceptions

Comparison With Related Terms

Advantages

Objective Measurement:
Excess return provides an objective basis for comparing strategies and managers, showing value beyond passive exposure.

Risk-Adjusted Evaluation:
When combined with measures such as the Sharpe ratio or Information ratio, excess return reflects the risk taken to achieve outperformance.

Enhanced Client Communication:
Benchmark-relative reporting enables transparent disclosure and sets clear expectations for investors.

Common Misconceptions

Confusing Excess with Total Return:
A gain of 10 percent is not a 10 percent excess return if the benchmark also rose 8 percent; the true excess return in this case is 2 percent.

Using Inappropriate Benchmarks:
Comparing results from a small-cap strategy to a large-cap index can distort excess return assessment.

Ignoring Fees, Costs, and Taxes:
Excess returns should be measured net of management fees, transaction costs, and, where relevant, after tax.

Practical Guide

Constructing and Interpreting Excess Return

Step 1: Select a Suitable Benchmark
Choose an investable index that matches the investment’s style, geography, sector, and currency exposure.

Step 2: Calculate Returns (Net of Fees)
Use total returns (including dividends and coupons) and be consistent with reinvestment conventions.

Step 3: Apply Risk Adjustments
Consider risk-adjusted metrics such as alpha, Sharpe ratio, and information ratio for comprehensive assessment.

Step 4: Assess Persistence and Reliability
Check whether excess returns are maintained across different periods and market cycles.

Sample Case Study (Hypothetical Example)

A US large-cap equity fund earns a 9 percent net return in one year, while the S&P 500 returns 6 percent.

• Excess Return: 9 percent – 6 percent = 3 percent
• Tracking Error: 4 percent
• Information Ratio: 3 percent / 4 percent = 0.75

A regression analysis over 36 months shows the fund’s alpha (risk-adjusted excess) is statistically significant, indicating the manager added value beyond simple index exposure.
This is a hypothetical example for educational purposes only and does not constitute investment advice.

Addressing Pitfalls

• Ensure the chosen benchmark remains relevant as fund strategy or market conditions change.
• Decompose total excess return into factors (such as sector allocation or security selection) to understand sources of performance.
• Evaluate performance net of all explicit (fees, taxes) and implicit costs (such as slippage and spreads).

Resources for Learning and Improvement

Textbooks & Seminal Papers

• Investments by Bodie, Kane, and Marcus – foundational for risk and return concepts.
• Active Portfolio Management by Grinold & Kahn – detailed discussion on alpha and information ratio.
• Asset Pricing by John Cochrane – links excess return to risk premia and factor models.
• Jensen, M. C. (1968) – introduces “alpha” as abnormal return.
• Fama and French (1993) – explores size and value factor effects.
• Carhart (1997) – examines momentum factors.

Online Courses

• Yale’s “Financial Markets” by Robert Shiller – available free via Coursera.
• University of Geneva’s “Investment Management” on Coursera.
• CFA Institute readings on GIPS and manager evaluation.

Data and Benchmarks

• Kenneth R. French Data Library – provides open access to factor series.
• MSCI or S&P indices for benchmarking.
• FRED for accurate and current risk-free rates.

Practical Tools

• Python: pandas/numpy (data analysis), statsmodels (regression), PyPortfolioOpt (optimization), alphalens (signal analysis).
• R: PerformanceAnalytics, quantmod.
• Backtrader for portfolio backtesting.

Blogs, Research, and Podcasts

• AQR blog and research – insights on market trends and alpha decomposition.
• Damodaran’s Musings on Markets.
• Podcasts: Masters in Business, Capital Allocators.

FAQs

What is excess return?

Excess return is the portion of an investment’s performance above a chosen benchmark, such as a market index or risk-free rate. For example, if a fund gains 11 percent while the benchmark gains 8 percent, its excess return is 3 percent.

How do you calculate excess return?

Subtract the return of the relevant benchmark from the return of the investment over the same period. Both returns should be calculated net of fees on a total return basis.

What benchmark should I use?

Choose a benchmark that accurately reflects the investment’s universe and style, for example, the MSCI World Index for global equities or a government bond index for fixed income portfolios.

How does excess return differ from Sharpe or Information ratio?

Excess return is the raw difference above a benchmark, while the Sharpe ratio divides excess return by volatility and the Information ratio divides it by tracking error. These provide risk-adjusted perspectives.

Can negative excess return still be acceptable?

Yes. For defensive or low-volatility strategies, negative excess return in a strong bull market may be acceptable if the strategy achieves its risk management goals.

Do excess returns persist over time?

Consistent and persistent excess return is uncommon. Research suggests that after considering fees and strategy popularity, excess returns may diminish. Long-term and out-of-sample analysis is important.

How do fees and taxes impact excess return?

Fees, trading costs, and taxes all decrease realized excess return. Only net, after-tax and after-fee figures accurately reflect value added over benchmarks.

Conclusion

Excess return is a key metric for separating investment skill from market exposure. It allows for objective, risk-adjusted evaluation of performance and informs asset allocation, compensation, and risk management. To use excess return effectively, it is important to select appropriate benchmarks, account for all costs, and assess results over complete market cycles. By combining excess return analysis with risk-adjusted measures and statistical tools, investors can make informed, transparent, and diligent decisions in the investment landscape.