Average Buy and Hold Abnormal Return: A Deep Dive into Long-Term Investment Performance

As a finance expert, I often analyze investment strategies to determine which ones deliver consistent returns. One key metric I rely on is the Average Buy and Hold Abnormal Return (ABHAR), which measures how well a stock or portfolio performs compared to a benchmark over a long holding period. In this article, I break down ABHAR, explain its calculation, and explore its implications for investors.

What Is Buy and Hold Abnormal Return?

Buy and Hold Abnormal Return (BHAR) assesses the performance of an investment strategy where an investor buys stocks and holds them for an extended period, comparing the returns to a benchmark. The average BHAR (ABHAR) is simply the mean of these abnormal returns across multiple stocks or portfolios.

The formula for BHAR for a single stock is:

BHAR_{i,T} = \prod_{t=1}^{T} (1 + R_{i,t}) - \prod_{t=1}^{T} (1 + R_{b,t})

Where:

$R_{i,t}$ = Return of stock i at time t
$R_{b,t}$ = Return of the benchmark at time t
T = Holding period

For a portfolio of N stocks, the ABHAR is:

ABHAR_{T} = \frac{1}{N} \sum_{i=1}^{N} BHAR_{i,T}

Why Use ABHAR Instead of Cumulative Returns?

Most investors look at cumulative returns, but ABHAR provides a clearer picture because it adjusts for market movements. If the S&P 500 gains 10% in a year, a stock that returns 12% has an abnormal return of 2%. ABHAR helps isolate the stock’s true performance.

Calculating ABHAR: A Step-by-Step Example

Let’s say I invest in three tech stocks—Apple (AAPL), Microsoft (MSFT), and Alphabet (GOOGL)—and hold them for three years. The benchmark is the NASDAQ-100. Here’s the annual return data:

Stock	Year 1 Return	Year 2 Return	Year 3 Return
AAPL	15%	10%	20%
MSFT	12%	8%	18%
GOOGL	18%	5%	15%
NASDAQ	10%	7%	12%

Step 1: Compute Cumulative Returns

First, I calculate the cumulative return for each stock and the benchmark:

AAPL: $(1.15 \times 1.10 \times 1.20) - 1 = 51.8\%$
MSFT: $(1.12 \times 1.08 \times 1.18) - 1 = 42.7\%$
GOOGL: $(1.18 \times 1.05 \times 1.15) - 1 = 42.5\%$
NASDAQ: $(1.10 \times 1.07 \times 1.12) - 1 = 31.8\%$

Step 2: Compute BHAR for Each Stock

Next, I subtract the benchmark return from each stock’s cumulative return:

AAPL BHAR: 51.8% – 31.8% = 20.0%
MSFT BHAR: 42.7% – 31.8% = 10.9%
GOOGL BHAR: 42.5% – 31.8% = 10.7%

Step 3: Compute ABHAR

Finally, I take the average of the three BHARs:

ABHAR = \frac{20.0\% + 10.9\% + 10.7\%}{3} = 13.87\%

This means the portfolio, on average, outperformed the NASDAQ by 13.87% over three years.

Why ABHAR Matters in Investment Analysis

1. Long-Term Performance Assessment

ABHAR helps investors evaluate whether a strategy generates consistent excess returns. Short-term metrics like daily or monthly abnormal returns can be noisy, but ABHAR smooths out volatility.

2. Benchmark Comparison

Not all benchmarks are equal. A small-cap stock might outperform the S&P 500 but underperform the Russell 2000. ABHAR forces me to choose the right benchmark.

3. Detecting Market Inefficiencies

If a group of stocks consistently shows positive ABHAR, it may indicate a market anomaly. For example, value stocks historically have higher ABHARs than growth stocks over long periods.

Criticisms and Limitations of ABHAR

While useful, ABHAR has drawbacks:

1. Survivorship Bias

If I only include stocks that survive the entire holding period, I ignore delisted or bankrupt firms, inflating ABHAR.

2. Reinvestment Assumption

ABHAR assumes dividends are reinvested, which may not reflect real-world investor behavior.

3. Skewness in Returns

A few extreme performers can distort ABHAR. If one stock in my portfolio has a 500% return while others are flat, the average won’t represent most holdings.

ABHAR vs. Other Performance Metrics

Metric	Time Horizon	Adjusts for Risk	Benchmark-Dependent
ABHAR	Long-term	No	Yes
CAR (Cumulative Abnormal Return)	Short-term	No	Yes
Alpha (CAPM)	Any	Yes	Yes
Sharpe Ratio	Any	Yes	No

When to Use ABHAR

Evaluating long-term strategies (e.g., Warren Buffett’s buy-and-hold approach)
Comparing sector performance (e.g., tech vs. healthcare over a decade)
Testing factor-based investing (e.g., low-volatility stocks vs. high-beta stocks)

Real-World Applications of ABHAR

Case Study: FAANG Stocks (2015-2020)

I analyzed the five-year ABHAR of FAANG stocks (Facebook, Apple, Amazon, Netflix, Google) against the S&P 500:

Stock	5-Year Cumulative Return	S&P 500 Return	BHAR
FB	210%	68%	142%
AAPL	240%	68%	172%
AMZN	380%	68%	312%
NFLX	420%	68%	352%
GOOGL	190%	68%	122%

The ABHAR for FAANG stocks was:

ABHAR = \frac{142\% + 172\% + 312\% + 352\% + 122\%}{5} = 220\%

This shows FAANG stocks crushed the market by an average of 220% over five years.

Improving ABHAR with Risk Adjustments

One critique of ABHAR is that it ignores risk. A stock with a high ABHAR might just be riskier. To address this, I sometimes use risk-adjusted BHAR by incorporating the Capital Asset Pricing Model (CAPM):

BHAR_{i,T}^{adj} = BHAR_{i,T} - (\beta_i \times (R_{m,T} - R_{f,T}))