Financial Mathematics

The Efficient Frontier is a Beautiful Lie: Why 'Optimal' Portfolios Fail in Real Markets

If you’ve ever opened up an investing textbook, you’ve seen the chart. A smooth, upward-curving line — the efficient frontier — showing a perfect relationship between risk and return. All you need to do is plug in your estimates for expected returns, volatilities, and correlations, and voilà: the optimal portfolio is right there in front of you.

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How Fractional Differencing Revolutionized My Feature Engineering for Investment Strategies

As a theoretical physicist turned systematic investor, I’ve always been fascinated by the mathematical structures underlying financial markets. While most investors focus on price movements and traditional technical indicators, I discovered that the real edge comes from understanding the deeper statistical properties of market data—particularly how to extract meaningful features that preserve both trend information and stationarity.

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