Investment Mathematics
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The Minimum Correlation Algorithm: Rethinking Portfolio Diversification Through Mathematical Elegance
- Fabio Capela
- Portfolio optimization , Quantitative finance , Diversification strategies , Risk management , Algorithmic trading , Modern portfolio theory , Asset allocation , Investment mathematics
“Don’t put all your eggs in one basket” – this timeless wisdom has evolved into one of finance’s most fundamental principles. Yet despite diversification’s universal acceptance, its mathematical underpinnings remain poorly understood by most practitioners. The conventional approach treats diversification as simply holding many assets, but this perspective misses the profound mathematical reality that drives risk reduction in portfolios.
Read MoreThe Hidden Reality of High Sharpe Ratios: Why Even Elite Strategies Face Monthly Losses
- Fabio Capela
- Risk management , Investment strategy , Portfolio management , Quantitative finance , Statistical analysis , Performance evaluation , Investment mathematics , Risk assessment
The Sharpe ratio stands as one of finance’s most celebrated metrics, elegantly capturing risk-adjusted returns in a single number. An annualized Sharpe ratio of 2.0 sounds impressive—it represents exceptional risk-adjusted performance that places a strategy in the top tier of investment approaches. Yet here lies a reality that surprises many investors: even strategies with outstanding annualized Sharpe ratios experience negative months far more frequently than intuition suggests.
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.
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