The Hidden Cost of Volatility Drag: How to Compute Portfolio Returns Badly

The world of finance is full of complex concepts, often shrouded in technical jargon. One such concept that can be particularly misleading is the idea of computing portfolio returns badly. As a seasoned financial writer, it's essential to unpack this notion and explore why it matters.

The Tale of Two Returns: A Misconception

The phrase "A tale of two returns" comes from economics and finance literature. It refers to the observation that stock prices in different countries exhibit distinct patterns when trading across borders. However, this concept can be applied to portfolio returns as well. When computing portfolio returns, it's crucial to consider how the returns of individual assets might interact with each other.

One of the most common misconceptions is multiplying weights times log returns and comparing them with actual log returns of the portfolio. This approach, while straightforward, has several flaws. For instance, it ignores the concept of correlation between assets, which can significantly impact overall portfolio performance.

The Power of Correlation: Understanding the Interplay

Correlation is a statistical measure that describes how closely two variables are related. In the context of portfolio returns, correlation refers to the tendency for assets with similar characteristics (e.g., asset class) to move in tandem. When computing portfolio returns, it's essential to account for this correlation. By doing so, you can avoid the pitfalls of a "volatility drag" and create a more accurate picture of your investment portfolio.

A Case Study: The S&P 500

To illustrate the concept of correlation, consider a case study involving the S&P 500 index. Suppose we generate random portfolios with exactly 20 assets, no more than 10% weight for any asset, and sum to 40%. We then compute the returns for each portfolio using the formula: (weights log returns) / weights times log returns.

The Results of the Random Portfolios

The results of these computations reveal a pleasing downward bias in the computed returns. This means that, on average, we expect the returns of individual assets to be lower than their actual returns when compared with the portfolio as a whole. To understand why this occurs, let's transform the weights times log returns back into simple returns using an exponential function: exp(ret2008) - 1.

A Transformation That Reveals a Hidden Pattern

By applying this transformation, we can see that the correlation between assets is indeed driving down overall portfolio returns. This pattern holds true for both positive and negative correlations. Understanding how to account for correlation in portfolio returns is crucial for making informed investment decisions.

The Risks of Not Accounting for Correlation

Ignoring correlation when computing portfolio returns can lead to poor investment outcomes. By failing to consider the interplay between assets, you may miss out on potential opportunities or neglect to capitalize on favorable market conditions.

An Example of a Portfolio with Excessive Correlation

Consider an example involving the following random portfolios:

Portfolio A: 30% long-only S&P 500 index, 20% BAC stock Portfolio B: 40% long-only BAC stock, 10% GS stock Portfolio C: 50% long-only TIP bond, 30% Treasury ETF

By analyzing the returns of these portfolios using our formula from earlier, we can see that they exhibit excessive correlation. This leads to a "volatility drag" effect on portfolio returns.

The Benefits of Accounting for Correlation

To mitigate this risk, it's essential to consider the correlation between assets when computing portfolio returns. By doing so, you can create more accurate investment models and reduce the likelihood of poor performance.

A Practical Approach to Accounting for Correlation

One practical approach is to use a correlation matrix to visualize the relationships between individual assets. This will help you identify areas where your portfolio might be most correlated and adjust your strategy accordingly.

Conclusion: The Importance of Accounting for Correlation

Computing portfolio returns badly can have serious consequences for investment outcomes. By accounting for correlation, you can create more accurate models and make informed decisions that align with your investment goals. Remember to consider the relationships between assets and adjust your strategy to maximize returns while minimizing risk.