As a finance professional, I often analyze investment strategies to determine their effectiveness. One approach that stands out is buy and hold, a passive strategy where investors purchase securities and hold them for an extended period. However, what interests me more is abnormal buy and hold returns (ABHR), which measure performance deviations from expected benchmarks. In this article, I dissect ABHR, its calculation, significance, and real-world applications.
Table of Contents
Understanding Buy and Hold Returns
Before diving into abnormal returns, I need to establish a baseline. Buy and hold returns (BHR) represent the cumulative gain or loss from holding an asset over a specific period. The formula for BHR is:
BHR = \prod_{t=1}^{T} (1 + R_t) - 1Where:
- R_t = return at time t
- T = total holding period
For example, if I hold a stock for three years with annual returns of 5%, 10%, and -2%, the BHR is:
BHR = (1.05 \times 1.10 \times 0.98) - 1 = 0.1289 \text{ or } 12.89\%Defining Abnormal Buy and Hold Returns
Abnormal returns measure performance beyond what a market model predicts. If I expect a stock to return 8% annually based on the Capital Asset Pricing Model (CAPM), but it returns 12%, the abnormal return is 4%. Extending this to a multi-period scenario, ABHR is calculated as:
ABHR = \prod_{t=1}^{T} (1 + R_{it}) - \prod_{t=1}^{T} (1 + E(R_{it}))Where:
- R_{it} = actual return of asset i at time t
- E(R_{it}) = expected return based on a benchmark (e.g., market index)
Example Calculation
Suppose I invest in a tech stock over two years:
| Year | Actual Return (R_{it}) | Expected Return (E(R_{it})) |
|---|---|---|
| 1 | 15% | 10% |
| 2 | 20% | 12% |
The ABHR is:
ABHR = (1.15 \times 1.20) - (1.10 \times 1.12) = 1.38 - 1.232 = 0.148 \text{ or } 14.8\%This means the stock outperformed expectations by 14.8% over two years.
Why ABHR Matters in Finance
ABHR helps me assess whether an investment strategy, event, or market anomaly generates excess returns. Common applications include:
- Event Studies – Measuring the impact of earnings announcements, mergers, or regulatory changes.
- Fund Performance – Evaluating if active managers beat their benchmarks.
- Market Anomalies – Identifying patterns like the January Effect or momentum strategies.
Statistical Significance of ABHR
To determine if ABHR is not due to random chance, I use a t-test:
t = \frac{ABHR}{\sigma(ABHR) / \sqrt{N}}Where:
- \sigma(ABHR) = standard deviation of abnormal returns
- N = number of observations
If the t-statistic exceeds critical values (e.g., 1.96 for 95% confidence), the ABHR is statistically significant.
Comparing ABHR Across Different Strategies
Let’s examine how ABHR varies between investment styles.
| Strategy | Average ABHR (5-Year Period) | Volatility |
|---|---|---|
| Value Investing | 6.2% | 12.1% |
| Growth Investing | 4.5% | 18.3% |
| Momentum Trading | 8.1% | 22.7% |
From this table, I infer that momentum strategies generate higher ABHR but with greater risk, while value investing offers steadier excess returns.
Criticisms and Limitations
While ABHR is useful, it has flaws:
- Benchmark Sensitivity – Results change if I use CAPM vs. Fama-French models.
- Survivorship Bias – Excluding delisted stocks inflates ABHR.
- Transaction Costs – Ignoring fees overstates net returns.
Adjusting for Risk Factors
To refine ABHR, I incorporate multi-factor models like Fama-French:
E(R_{it}) = R_f + \beta (R_m - R_f) + s \cdot SMB + h \cdot HMLWhere:
- SMB = Small Minus Big (size factor)
- HML = High Minus Low (value factor)
This helps me isolate whether ABHR stems from skill or exposure to risk factors.
Real-World Case: ABHR in Tech Stocks
Consider the performance of FAANG stocks (2015-2020):
| Stock | Actual BHR | Expected BHR (S&P 500) | ABHR |
|---|---|---|---|
| Apple | 325% | 85% | 240% |
| Amazon | 400% | 85% | 315% |
| Netflix | 450% | 85% | 365% |
The massive ABHR suggests tech stocks significantly outperformed the market. However, was this due to skill, luck, or speculative bubbles? Further risk-adjustment would clarify.
Practical Implications for Investors
If I rely on ABHR for decision-making, I should:
- Use Robust Benchmarks – Compare against sector-specific indices.
- Factor in Taxes & Fees – High turnover strategies may erode ABHR.
- Avoid Data Mining – Overfitting historical data leads to false positives.
Conclusion
Abnormal buy and hold return analysis provides a powerful lens to evaluate investment performance. By isolating excess returns, I can distinguish luck from skill and refine my strategies. However, I must account for risk factors, benchmarks, and real-world costs to avoid misleading conclusions. Whether I’m assessing a mutual fund, a trading strategy, or market anomalies, ABHR remains an indispensable tool in my financial toolkit.
