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When Kelly and Tangency Portfolios Can Share Weights

Article Quant Q&A · Author: KIM Kyuhyong
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Summary

The document asks why empirical studies may find Kelly portfolios concentrated in fewer stocks, with higher returns and variance, despite a reported theoretical result that Kelly and tangent portfolios have the same weights. The answer describes Kelly as maximizing long-run wealth growth and the tangent portfolio as maximizing risk-adjusted return along the capital market line. It suggests their weights can coincide under certain conditions, but gives no derivation of those conditions.

The response attributes differences between theory and empirical results to market variation, data limitations, investor behavior, simplifying assumptions, and anomalies. These are broad possibilities rather than evidence tied to a particular study, dataset, or model. The document therefore highlights the importance of matching theoretical assumptions and empirical definitions, but does not establish that the reported portfolio differences contradict a specific theorem or explain their source.

Key ideas

  • Kelly allocation targets long-run growth, while tangency allocation is framed around risk-adjusted return.
  • The answer says the portfolios can share weights only under certain conditions, without deriving them.
  • Empirical portfolio composition and performance may differ because of data, market conditions, behavior, or model assumptions.
  • The discussion offers possible explanations but cites no study details or quantitative evidence.

Tags

Portfolio constructionStatisticsRisk management
Full text
# If Kelly and tangent portfolios have the same weights, do they differ only empirically?


# If Kelly and tangent portfolios have the same weights, do they differ only empirically?












I studied Kelly portfolio and tangent portfolio and found that they have the same weights. But the empirical studies that I have seen so far show that Kelly portfolio has a smaller number of stocks with higher returns and higher variances. I do not understand why this happens, because the empirical study has to be based on theoretical results. Is there any one who understands this phenomenon?

## Answer by Shivam Singh (score 2)

https://quant.stackexchange.com/a/76502

So to begin with the terms mentioned ,The Kelly portfolio is based on optimizing the growth rate of wealth over the long term, considering the probabilities of different outcomes. On the other hand, the tangent portfolio is a part of the Capital Market Line (CML) that represents the best combination of the risk-free asset and risky assets, aiming to maximize the risk-adjusted return.

I think the Kelly portfolio and the tangent portfolio can have the same weights but only under certain conditions. This could occur when the marke's risk-free rate aligns with the expected return of the risky assets, making the tangent portfolio's weight distribution similar to that of the Kelly portfolio.

However, your confusion arises from the empirical studies that show a different scenario. It's important to note that empirical studies are based on real-world data, which may not always perfectly align with theoretical assumptions. Factors such as market dynamics, investor behavior, and unexpected events can influence portfolio performance in ways that theoretical models might not capture accurately.

The discrepancy between theoretical expectations and empirical observations could be due to various reasons:

Market Dynamics: Real-world market conditions can vary significantly from theoretical models. Factors like market volatility, liquidity constraints, and changing economic conditions can impact portfolio behavior.

Data Limitations: Empirical studies are based on historical data, which might not perfectly represent future market behavior. The dataset's scope, quality, and the period considered can affect results.

Behavioral Biases: Investor behavior and sentiment can lead to deviations from theoretical expectations. Investors may not always act rationally or in accordance with theoretical models.

Model Simplifications: Theoretical models often make assumptions to simplify complex realities. These assumptions might not hold true in all circumstances.

Market Anomalies: Empirical studies might uncover anomalies or patterns that challenge theoretical predictions, leading to further research and exploration.

I hope this helps :)

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.