Revisiting Equity–Bond Diversification: Tail Risk, Extreme Events and Option–Implied Evidence from Global ETFs.

Balanced equity–bond portfolios face challenges during periods of inflation, monetary tightening, and changing market dependence. This study examines thirty balanced and multi-asset exchange-traded funds listed in the United States, Canada, and Australia using daily U.S.-dollar returns over 2020–2024. A rolling-window framework compares minimum-variance and Conditional Value-at-Risk (CVaR) allocations under long-only and constrained long–short specifications with an equally weighted benchmark. The analysis evaluates cumulative performance, risk-adjusted returns, maximum drawdown, Value-at-Risk (VaR), and CVaR, complemented by filtered extreme-tail estimation and conditional volatility modeling. Over the reported evaluation period, optimized portfolios exhibit lower empirical VaR and CVaR than the equally weighted benchmark, while long–short portfolios exhibit lower tail-loss measures than their corresponding long-only strategies. The long–short 95% CVaR portfolio records the smallest maximum drawdown and the highest reported Sharpe, Sortino, and Rachev ratios, although all reported Sharpe and Sortino ratios are negative. GARCH and FIGARCH comparisons indicate substantial volatility persistence, with information criteria favoring GARCH and squared-residual diagnostics showing no significant remaining autocorrelation at the examined lags. A historically estimated Normal Inverse Gaussian model provides an illustrative framework for European option valuation and model-generated implied-volatility surfaces. These surfaces represent implications of the specified pricing model rather than observed option-market expectations. The findings highlight the value of evaluating multiple dimensions of portfolio risk, while investment interpretations remain subject to trading costs, short-selling costs, and leverage considerations.