Lagged return: Meaning, Criticisms & Real-World Uses

What Is Lagged Return?

A lagged return refers to the past performance of an asset, portfolio, or economic variable measured over a specific period preceding the current observation point. In the realm of investment analysis, it signifies the return generated in a prior period that is then used as an input for current analysis or prediction. This concept is fundamental in quantitative analysis and various financial modeling techniques, often serving as an independent variable to explain or forecast future outcomes. Lagged returns are distinct from contemporary or forward-looking returns, as they always pertain to a historical timeframe. They are crucial for understanding how past market behavior might influence subsequent movements, particularly in strategies like momentum strategy.

History and Origin

The concept of using past data to inform future expectations, including lagged returns, has roots in both economic theory and empirical finance. In economics, the classification of economic indicators into leading, coincident, and lagging categories was formalized by institutions like the National Bureau of Economic Research (NBER) to better understand the business cycle. Lagging indicators, by definition, confirm trends after they have already occurred.⁵

In financial markets, the explicit study of lagged returns gained significant traction with the emergence of empirical research into market anomalies and predictability. A seminal contribution came from Narasimhan Jegadeesh and Sheridan Titman, whose 1993 paper "Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency" provided strong evidence for the profitability of strategies based on past stock returns.⁴ Their work demonstrated that stocks with strong past returns (i.e., high lagged returns over a 3- to 12-month period) tended to continue performing well over subsequent periods, challenging strict interpretations of market efficiency.

Key Takeaways

A lagged return is the historical performance of an asset or variable over a defined prior period.
It is a critical component in quantitative investment strategies, especially momentum.
Lagged returns are used to identify patterns and relationships between past and future performance.
In economic analysis, lagged indicators confirm trends after they have unfolded.
The study of lagged returns has contributed to insights into market predictability.

Formula and Calculation

The calculation of a simple lagged return is identical to calculating a standard return, but the "lagged" aspect refers to the specific historical period chosen for the calculation. For an asset's price, the simple lagged return (RL) over a period (t-n) to (t-1) can be expressed as:

R_L = \frac{P_{t-1} - P_{t-n}}{P_{t-n}}

Where:

(P_{t-1}) = Price of the asset at the end of the lagged period (e.g., end of the previous month)
(P_{t-n}) = Price of the asset at the beginning of the lagged period (n) periods ago
(n) = The length of the lagged period (e.g., 3 months, 6 months, 1 year)

This formula measures the percentage change in price over a past interval. For example, a "6-month lagged return" would use the price from six months ago as (P_{t-n}) and the price from one month ago as (P_{t-1}), reflecting the return generated in that specific six-month window. Such calculations are foundational for various investment performance assessments.

Interpreting the Lagged Return

Interpreting a lagged return involves understanding what the past performance implies for future behavior. A positive lagged return indicates that an asset or variable performed well in the recent past, while a negative one indicates underperformance. In financial modeling, analysts might examine whether assets with strong positive lagged returns tend to continue their positive trajectory (as in momentum), or if those with negative lagged returns tend to reverse (as in contrarian strategies). The duration of the lag is crucial; a short-term lagged return (e.g., one week) might suggest different implications than a long-term lagged return (e.g., three years). Furthermore, the magnitude of the lagged return provides insight into the strength of the historical trend. For instance, a very high positive lagged return could signal overextension or, conversely, a strong, persistent trend.

Hypothetical Example

Consider an investor analyzing a stock, XYZ Corp., to determine if it exhibits momentum. They decide to look at the 6-month lagged return.

On June 30, 2024, XYZ Corp. stock price is $105.
On December 31, 2023 (six months prior), XYZ Corp. stock price was $90.

Using the formula for lagged return:

R_L = \frac{P_{t-1} - P_{t-n}}{P_{t-n}} = \frac{\$105 - \$90}{\$90} = \frac{\$15}{\$90} \approx 0.1667 \text{ or } 16.67\%

This means XYZ Corp. had a 6-month lagged return of approximately 16.67%. If the investor is employing a portfolio construction strategy based on momentum, this positive lagged return would suggest that XYZ Corp. is a "winner" and might be considered for inclusion in a long portfolio, assuming other criteria are met.

Practical Applications

Lagged returns are extensively used in various financial and economic analyses:

Momentum Strategies: A primary application is in momentum strategy, where investors buy assets that have performed well in the recent past (positive lagged returns) and sell those that have performed poorly (negative lagged returns). This relies on the premise that past trends tend to persist for a certain period.
Factor Investing: Lagged returns, especially those related to price or earnings momentum, are often treated as a "factor" in factor-based asset pricing models.
Economic Analysis: In macroeconomics, government agencies and research bodies use lagging economic indicators to confirm the presence of a specific trend, such as a recession or recovery. These indicators, including corporate profits or unemployment rates, reflect conditions after the general economy has already shifted.³ The Federal Reserve Bank of San Francisco, for example, conducts extensive economic research and provides data and indicators, some of which are inherently lagged in their confirmation of economic states.²
Risk Management: Analyzing lagged returns can help in assessing the historical volatility and drawdown of an asset, informing risk-adjusted returns calculations.
Technical Analysis: While not strictly a formulaic calculation of "lagged return," many indicators in technical analysis (e.g., moving averages) are based on averaged past prices, effectively incorporating lagged data to smooth out noise and identify trends in capital markets.

Limitations and Criticisms

Despite their utility, lagged returns and strategies based on them come with limitations. One significant criticism in finance is that while momentum strategies based on lagged returns have historically shown statistical significance, their future profitability is not guaranteed and can be subject to regime shifts or market changes. The "momentum crash" phenomenon, where momentum strategies suffer severe losses, highlights this risk.

From an economic perspective, relying solely on lagged indicators can lead to delayed policy responses, as these indicators confirm what has already happened. While useful for historical context and confirming trends, they do not offer predictive power for immediate action. For instance, an unemployment rate (a common lagging indicator) might only signal a recession months after it has begun. The National Bureau of Economic Research (NBER) provides comprehensive information on how various indicators perform in relation to the business cycle, noting the inherent delays in lagging indicators.¹

Furthermore, the effectiveness of using lagged returns in prediction can vary based on the asset class, market conditions, and the specific lag period chosen. Overfitting models to historical time series data can also lead to poor out-of-sample performance, where the model performs well on past data but fails to predict future outcomes.

Lagged Return vs. Leading Indicator

The distinction between a lagged return (or lagging indicator) and a leading indicator lies in their timing relative to the phenomenon they describe or predict.

Lagged Return/Lagging Indicator: These measures reflect conditions or performance that have already occurred and are used to confirm a trend. For example, a company's past quarterly earnings, representing its lagged return, or the unemployment rate, a lagging economic indicator, provide a historical view. They confirm that a shift has taken place in the economy or an asset's performance.
Leading Indicator: In contrast, a leading indicator attempts to forecast future events or trends. Examples include new housing starts, consumer confidence, or specific elements of the yield curve. These indicators are designed to change before the broader economy or a specific market trend shifts, offering insights into potential future conditions. While a lagged return looks backward to confirm, a leading indicator looks forward to anticipate.

The confusion often arises because both are used in analysis, but for different purposes: lagged returns/indicators provide confirmation and historical context, while leading indicators aim for foresight.

FAQs

What is the primary purpose of analyzing lagged returns?

The primary purpose of analyzing lagged returns is to identify historical patterns and relationships that might offer insights into future asset performance or economic trends. This forms the basis for various quantitative trading strategies and economic analysis.

Are lagged returns the same as historical returns?

Yes, lagged returns are a subset of historical returns. "Historical returns" is a broad term for any past performance. "Lagged return" specifically refers to the past return used as an input for a current analysis or predictive model, often with a defined time gap or "lag" before the period being predicted.

Can lagged returns predict future stock prices?

Lagged returns can indicate tendencies or probabilities for future price movements, especially in the context of phenomena like momentum. However, they do not guarantee future performance. Financial markets are complex, and past results do not definitively predict future outcomes. Models using lagged returns are often assessed for their regression analysis capabilities and predictive power.

Why are lagged returns important in momentum investing?

In momentum investing, lagged returns are critical because they are the direct input used to identify "winner" and "loser" assets. The strategy explicitly assumes that assets that have shown strong positive lagged returns will continue to outperform, and those with negative lagged returns will continue to underperform for a subsequent period.

Do economists use lagged returns?

Yes, economists frequently use lagging indicators, which are essentially economic variables reflecting "lagged returns" in the broader sense. These indicators, such as corporate profits, average duration of unemployment, or the Consumer Price Index for services, confirm shifts in the business cycle after they have already begun.