Mathematical Finance

Carry Strategies Across Asset Classes: Mathematical Foundations

Imagine borrowing money at 1% and lending it at 5%. The 4% difference seems like an obvious profit, yet financial theory suggests this opportunity shouldn’t exist. Markets should quickly eliminate such discrepancies through arbitrage. But across currencies, bonds, and stocks, these “carry” opportunities persist with remarkable consistency.

Read More

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.

Read More