Efficient Regression Basis Construction via Random Networks: A Novel Approach

Investment management is like cooking a meal – you want to strike the right balance between flavor and nutrition. But, just as too much salt can ruin a dish, too much risk can sink your portfolio. That’s where the 1/n portfolio comes in – an age-old rule of thumb that distributes investments equally among a set number of funds. Markowitz won a Nobel Prize for this simple yet powerful concept, but is it still relevant today?
To explore this question, we dive into the world of randomized signature methods and neural networks. These techniques offer efficient regression bases for path space functionals, outperforming classical neural networks in high-dimensional spaces. But, what does this mean for investors? In essence, these methods provide a way to balance risk and reward, much like a skilled chef adjusts spices to create the perfect dish.
In practice, we compare the 1/n strategy with our proposed approach using simulated data, showcasing how our method performs better in the first two years of an algorithm’s "burn-in" period. We also examine real-world data and transaction costs, revealing how our technique can help mitigate risks while maintaining returns.
Ultimately, this article demonstrates that while the 1/n portfolio may have been groundbreaking in its time, there are more effective ways to manage investments today. By leveraging cutting-edge techniques and a deep understanding of risk management, we can create a balanced portfolio that satisfies both flavor and nutrition – or in this case, returns and risk.