Correlation Ambiguity and Under-Diversification

We study effects of correlation ambiguity on portfolio choice when the number of risky assets is large. We find that the optimal portfolio contains only a fraction of available risky assets. With 100 stocks randomly selected from the S&P 500, less than 20 stocks will be held in the optimal portfolio. Thus, correlation ambiguity provides an explanation for under-diversification documented in empirical studies. In particular, correlation ambiguity can generate anti-diversification in the sense that the optimal portfolio consists of only one risky asset. Even though the optimal portfolio under correlation ambiguity is less diversified, it is less risky in the sense that it has smaller variance and fewer extremely large positions than the standard mean-variance portfolio. Our results suggest that correlation ambiguity has important implications for portfolio choice