Diversification Beyond Stocks and Bonds: A Mean-Variance Assessment of Gold and Real Estate in a Multi-Asset Portfolio

Abstract

Modern portfolio construction increasingly extends beyond the traditional combination of equities and fixed income to include alternative assets such as gold and real estate. This study evaluates whether the inclusion of these alternatives improves the risk-return efficiency of a conventional two-asset portfolio. Using representative long-run annualized estimates of returns, volatilities, and correlations for five asset classes, including domestic equities, international equities, investment-grade bonds, gold, as well as real estate investment trusts, the study uses a mean-variance optimization framework to construct efficient frontiers, global minimum-variance portfolios, and tangency portfolios under a long-only constraint. The results show that alternative assets provide different diversification benefits. Gold receives an allocation of approximately 15% in the optimal risky portfolio despite its low standalone Sharpe ratio, as its low correlation with equities reduces portfolio risk. In contrast, the allocations to real estate and international equities remain limited due to high correlation with domestic equities. At the portfolio level, the expanded opportunity set increases the maximum Sharpe ratio by approximately 4-5% and lowers the volatility required for a given return target. The results confirm that diversification benefits depend more on covariance with existing holdings than on standalone performance.