Excess return, also known as abnormal or alpha return, measures the performance of an investment compared to a benchmark index or another suitable reference. It is commonly used by investors, portfolio managers, and financial analysts to evaluate the effectiveness of investment strategies, identify outperforming assets, and analyze risk-adjusted returns. In this article, we will explain how to calculate excess return and provide practical examples that will help you better understand this essential financial concept.

Step 1: Identify the Components Needed for the Calculation

To calculate excess return for an investment or portfolio, you’ll need the following components:

1. Investment Return: The actual return generated by the asset, expressed as a percentage.

2. Benchmark Return: The return on a benchmark index or reference asset against which we’ll compare the performance of the investment.

3. Excess Return (α): The difference between the investment return and benchmark return.

Step 2: Calculate Investment Return

Investment return is calculated based on your initial capital investment and any gains or losses generated by the asset over a specific period. This can be done using one of two methods:

a. Simple Rate of Return:

Investment Return = (Ending Value – Initial Value) / Initial Value

b. Compound Annual Growth Rate (CAGR):

Investment Return = ((Ending Value / Initial Value)^(1/n) – 1) * 100

where `n` is the number of years invested.

Step 3: Determine Benchmark Return

To accurately assess excess return, you should compare your investment against a benchmark index that represents a passive alternative. For example, if you are analyzing a U.S. equity fund, you might use the S&P 500 Index as your benchmark.

Benchmark Return = (Benchmark Ending Value – Benchmark Initial Value) / Benchmark Initial Value

Step 4: Calculate Excess Return

After determining the investment return and benchmark return, you can now calculate the excess return. The formula is:

Excess Return (α) = Investment Return – Benchmark Return

Example:

Suppose an investor has a portfolio of U.S. stocks with an initial value of $10,000 and an ending value of $12,500 after three years. The S&P 500 Index increased from 2,500 to 3,000 over the same period. Calculating the excess returns for this portfolio would involve the following steps:

1. Calculate the CAGR for the portfolio:

Investment Return (%) = ((12,500 / 10,000)^(1/3) – 1) * 100 = 7.72%

2. Calculate the benchmark return using the Simple Rate of Return:

Benchmark Return (%) = (3,000 – 2,500) / 2,500 * 100 = 20.0%

3. Calculate Excess Return:

Excess Return (α) = Investment Return – Benchmark Return

Excess Return (α) = 7.72% – 20.0%

Excess Return (α) = -12.28%

Conclusion

Having calculated the excess return for our example portfolio (-12.28%), we can infer that it underperformed the S&P 500 benchmark index over three years in this case. By consistently monitoring and calculating excess returns, investors can make informed decisions on rebalancing their portfolios to maximize risk-adjusted performance and achieve long-term investment goals.