The Role of Cryptocurrencies in Portfolio Diversification and Optimization

Abstract

Denne afhandling undersøger kryptovalutaers rolle som diversifikationsinstrumenter i traditionelle aktieporteføljer bestående af danske og amerikanske aktier. Ved brug af et omfattende datasæt, der dækker perioden fra februar 2019 til januar 2025, anvender studiet mean-variance optimering, risikojusterede præstationsmål (Sharpe-, Sortino- og Calmar-ratioer), nedadgående risikomål (VaR, CVaR og maksimalt drawdown), faktormodeller (Fama-French 3- og 5-faktor modeller) samt en bred vifte af statistiske tests, herunder Wilcoxon Signed-Rank, ikke-parametriske benchmark tests, bootstrap-metoder og regimespecifik bootstrapping. Resultaterne viser, at inkludering af kryptovalutaer generelt øger porteføljeeffektiviteten ved at forbedre de risikojusterede afkast på tværs af flere porteføljekonstruktioner, både in-sample og out-of-sample. Porteføljer med kryptovaluta udviser konsekvent højere Sharpe- og Sortino-ratioer sammenlignet med traditionelle porteføljer, selvom ikke alle forbedringer når formel statistisk signifikans ved bootstrap-testning. Faktormodel-analyser viser signifikante positive alpha-værdier for porteføljer med kryptovalutaeksponering, hvilket indikerer, at afkastet ikke udelukkende kan forklares af konventionelle systematiske risikofaktorer. Diversifikationsfordelen ved kryptovalutaer er dog regimesensitiv. Mens korrelationerne med aktier forbliver lave i stabile perioder, stiger de under markedsuro, hvilket reducerer deres beskyttende effekt under finansiel stress. Porteføljer med kryptovaluta udviser desuden øget nedadgående risiko, især i ubegrænsede og gearede strategier, hvilket understreger vigtigheden af at anvende realistiske porteføljebegrænsninger. Samlet konkluderer studiet, at kryptovalutaer kan fungere som effektive diversifikationsværktøjer, der kan forbedre porteføljeeffektiviteten, når de integreres i velkonstruerede porteføljer med passende risikostyring, samtidig med at deres regimespecifikke karakteristika kræver forsigtighed under markedsuro.

This thesis investigates the role of cryptocurrencies as diversification instruments within traditional equity portfolios consisting of Danish and U.S. stocks. Using a comprehensive dataset spanning February 2019 to January 2025, the study applies mean-variance optimization, risk-adjusted performance metrics (Sharpe, Sortino, and Calmar ratios), downside risk measures (VaR, CVaR, and maximum drawdown), factor models (Fama-French 3- and 5-factor models), and a robust battery of statistical tests, including Wilcoxon Signed-Rank, non-parametric benchmark, bootstrap procedures, and regime-dependent bootstrapping. The findings demonstrate that including cryptocurrencies generally enhances portfolio efficiency by increasing risk-adjusted returns across multiple portfolio constructions, both in-sample and out-of-sample. Crypto-inclusive portfolios consistently show superior Sharpe and Sortino ratios relative to traditional portfolios, although not all improvements reach formal statistical significance under bootstrap testing. Factor model analyses reveal significant positive alphas for portfolios with cryptocurrency exposure, suggesting that their returns are not fully attributable to conventional systematic risk factors. However, the diversification benefit of cryptocurrencies exhibits regime dependency. While they maintain low correlations with equities during stable periods, these correlations rise during market crises, reducing their protective function during financial stress. Crypto-inclusive portfolios also exhibit heightened downside risk, particularly in unconstrained and leveraged strategies, emphasizing the importance of applying realistic portfolio constraints. Overall, the study concludes that cryptocurrencies can serve as effective diversification tools that improve portfolio efficiency when integrated into thoughtfully constructed portfolios with appropriate risk management, while their regime-dependent characteristics necessitate caution during periods of market turmoil.

A master thesis from Aalborg University

The Role of Cryptocurrencies in Portfolio Diversification and Optimization