What's My Return?

Key Concepts

• Return on Investment (ROI): The gain or loss on an investment relative to its cost. Calculated as (Ending Value - Beginning Value) / Beginning Value or Ending Value / Beginning Value - 1.
• Total Return: The overall gain or loss over a period, reflecting the cumulative effect of all investments, regardless of individual trade performance.
• Geometric Return: A more accurate measure of investment performance over time, accounting for compounding. Calculated by raising the product of periodic returns to the power of 1/n (where n is the number of periods).
• Arithmetic Average: A simple average of returns, often misleading as it doesn’t account for compounding or the size of investments.
• Time-Weighted Return: Measures the performance of an investment itself, removing the impact of investor cash flows (deposits and withdrawals).
• Dollar-Weighted Return (Internal Rate of Return - IRR): Measures the performance experienced by the investor, considering the timing and size of cash flows.
• Volatility Drag: The negative impact of high volatility on returns, particularly in leveraged investments.

Understanding Investment Returns: A Deep Dive

The core message of this discussion centers on the critical importance of understanding how investment returns are calculated, and recognizing that a simple average can be profoundly misleading. The speakers, Bill Johnson and Stu, highlight a common issue: traders seeing impressive individual trade returns (e.g., 80%, 150%) yet experiencing stagnant or declining overall account balances. This discrepancy stems from a misunderstanding of different return calculation methods.

The Pitfalls of Simple Averages

The discussion begins by debunking the common practice of simply adding up percentage gains and losses and dividing by the number of trades (arithmetic average). This method is presented as “highly misleading” and can create a false sense of confidence. The example of earning 50% on one position and losing 50% on another illustrates this point. While the arithmetic average suggests a zero return, the actual result is a 25% loss if starting with a $1 investment (ending with $0.75). This highlights the importance of considering the impact of losses on a diminishing principal.

Return on Investment (ROI) Explained

ROI is defined as the net gain or loss per investment, calculated as (Ending Value - Beginning Value) / Beginning Value. An example is provided: a $1,000 investment growing to $1,200 yields a 20% ROI. While straightforward, the speakers note that this calculation can become cumbersome with larger numbers. An alternative, and often easier, method is to divide the ending value by the beginning value and subtract 1 (Ending Value / Beginning Value - 1), achieving the same result. A cautionary note is added: accurately knowing the initial investment amount is crucial, as traders often misremember or miscalculate this figure.

Total Return: The Big Picture

Total return focuses on the overall gain or loss over time, typically applied to the entire account. It’s calculated as (Ending Value / Starting Value - 1). This metric provides a broader perspective on performance, independent of individual trade outcomes. The speakers emphasize that total return is a more meaningful indicator of long-term success than focusing solely on individual trade percentages.

Geometric vs. Arithmetic Return: A Crucial Distinction

The discussion then delves into the difference between geometric and arithmetic returns. The geometric return is presented as a more accurate measure of investment performance, particularly when compounding is involved. It answers the question: “What constant return would produce the same end result?” The formula involves raising the product of periodic returns to the power of 1/n (where n is the number of periods). The example of a three-month period with returns of 20%, -80%, and 200% demonstrates the discrepancy: the arithmetic average suggests a 100% return, while the geometric return reveals a more realistic 22%. This difference is attributed to the effects of compounding and the impact of losses on a smaller principal.

Time-Weighted and Dollar-Weighted Returns: Advanced Considerations

The conversation extends to more sophisticated return calculations: time-weighted and dollar-weighted returns.

• Time-Weighted Return: This method isolates the performance of the investment itself by removing the influence of investor cash flows (deposits and withdrawals). It’s commonly used by mutual funds to provide a standardized performance metric.
• Dollar-Weighted Return (Internal Rate of Return - IRR): This calculation considers the timing and size of cash flows, reflecting the investor’s actual experience. It’s particularly relevant when significant deposits or withdrawals occur during the investment period. The speakers caution that IRR can be complex to calculate and requires specialized tools (like financial calculators).

The Danger of Misleading Returns & The Beardstown Ladies Example

The speakers warn against blindly accepting reported returns, especially those found in newsletters or online. They cite the example of the “Beardstown Ladies,” an investment club whose reported astronomical returns were later found to be inflated due to improper accounting of deposits. This anecdote underscores the importance of scrutinizing the methodology behind any reported return figures.

The Importance of Probability and Risk

Throughout the discussion, the speakers implicitly emphasize the role of probability and risk. They caution against relying on the expectation of consistently high returns, highlighting the potential for significant losses. The example of compounding a small account to a large sum is presented as unrealistic and requiring an unsustainable level of risk. They reiterate that understanding the probabilities involved is paramount to making informed investment decisions.

Conclusion

The core takeaway is that calculating and interpreting investment returns is far more complex than it appears. Traders must move beyond simple arithmetic averages and embrace more sophisticated methods like geometric return to accurately assess performance. Understanding the nuances of time-weighted and dollar-weighted returns provides a deeper insight into investment outcomes. Ultimately, the speakers advocate for a cautious and informed approach, emphasizing the importance of questioning reported returns and focusing on the overall impact on the account balance rather than individual trade percentages. The message is clear: knowledge is power, and a solid understanding of return calculations is essential for achieving long-term market success.