PORTFOLIO OPTIMIZATION BETWEEN CRYPTOCURRENCIES AND SOUTH ASIAN STOCK INDICES USING MODERN PORTFOLIO THEORY

Abstract

This paper investigated the mean-variance properties of Markowitz's portfolio selection for a diversified portfolio of major cryptocurrencies and South Asian stock indices, and whether short-run diversification gains persist after accounting for long-run time-series properties. Descriptive statistics of the daily returns for 2014-2025, respectively, for 5 cryptocurrencies BTC, ETH, USDT, BNB, and XRP and 5 South Asian indices Nifty 50, BSE Sensex, PSX 100, DSE Broad Index, and ASPI indicate that cryptocurrencies offer significantly higher returns and volatility than the South Asian equity indices, with USDT being an outlier given the infrequent de-pegging events. The stationarity of the ten series has been verified by the Augmented Dickey-Fuller and Phillips-Perron tests, with USDT being the only series that still contains a trend at both levels and first differences. Even though short-run correlations are low, the Johansen trace test shows that there are two cointegrating vectors between the long-run subset of cryptocurrencies and South Asian equities. All ten equations are highly significant, as confirmed by a Vector Error Correction Model (VECM), with the cryptocurrency equations having greater explanatory power. The results are incorporated into two mean-variance optimizations: one with a static sample covariance matrix and one with an estimate based on the residuals of a VECM model. The efficient frontier, the minimum-variance portfolio, and the tangency portfolio are constructed. Results suggest that correlation-only models may overestimate diversification benefits when accounting for long-run equilibrium dynamics; therefore, these dynamics should be incorporated into the portfolio guidelines of South Asian investors.