Optimizing Portfolios Based on Hurst Exponent

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Portfolio optimization is an important aspect of investment management, aiming to construct portfolios that offer the best risk-return trade-off based on an investor’s objectives and constraints. Various optimization techniques, such as mean-variance optimization, Black-Litterman model, and risk parity, are employed to generate optimal portfolios tailored to different investment goals and risk preferences.

Additionally, advancements in computational methods and access to extensive datasets have enabled investors to implement more sophisticated optimization strategies, incorporating factors like market trends, volatility, and correlations among assets.

Reference [1] introduces a novel portfolio optimization technique aimed at maximizing the signal-to-noise ratio. This is achieved by developing an objective function based on the Hurst exponent. Essentially, the authors seek to maximize the Hurst exponent of a portfolio, creating what they term a synthetic asset. Assets with a high Hurst exponent are deemed suitable for trend-following strategies. They pointed out,

In this paper, we set out to find a control mechanism that can find a linear superposition of financial signals (a portfolio) that is smooth, has positive auto-correlation, and has long memory. Such a technique could be used as a sort of pre-processing step that generates a predictable portfolio that could be used as an artificial asset in another trading strategy. We found that maximizing the Signal-to-noise ratio of relative portfolio increments achieves this goal. We also found that minimizing the variance instead can have a similar effect, but its effectiveness is significantly lower, and can even become worse than random choice. As a direct consequence, we concluded that the well-known maximum Sharpe-ratio portfolio (coming from the classical mean-variance portfolio optimization framework) also exhibits such beneficial properties, and so do portfolios obtained based on Taguchi’s Quality Engineering principles, as these are closely related to the S/N ratio. As expected, shorting also proved to significantly increase the effectiveness of achieving more predictable portfolios.

The article offers a fresh perspective on portfolio design. However, similar to other studies, such as those focusing on pairs trading where cointegration is maximized, the authors did not conduct out-of-sample tests. Therefore, they did not address whether the trend-following property of the synthetic asset will persist in the future.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Adam Zlatniczki, Andras Telcs, Application of Portfolio Optimization to Achieve Persistent Time Series, Journal of Optimization Theory and Applications, April 2024

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