Mathematical Finance
- Home /
- Categories /
- Mathematical Finance
Why Nobody Should Use Sample Covariance Matrices
- Fabio Capela
- Portfolio optimization , Risk management , Quantitative finance , Covariance estimation , Modern portfolio theory , Statistical methods , Asset management , Mathematical finance
Since Harry Markowitz introduced mean-variance optimization in 1952, portfolio managers have faced a persistent and frustrating problem. The mathematical elegance of Modern Portfolio Theory promises optimal asset allocation, but in practice, portfolios constructed using traditional methods often perform worse than simple equal-weight strategies. The culprit? A seemingly innocuous component that lies at the heart of every optimization: the sample covariance matrix.
Read MoreCarry Strategies Across Asset Classes: Mathematical Foundations
- Fabio Capela
- Carry trading , Quantitative finance , Asset pricing , Risk premia , Cross asset strategies , Mathematical finance , Alternative beta , Systematic trading
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 MoreThe Efficient Frontier is a Beautiful Lie: Why 'Optimal' Portfolios Fail in Real Markets
- Fabio Capela
- Portfolio theory , Quantitative finance , Modern portfolio theory , Risk management , Mathematical finance , Investment mathematics , Portfolio construction , Academic finance
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