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Portfolio Selection with Hedge Funds

We use the Markowitz framework to consider hedge funds as an asset class, and make two observations: First, even if hedge funds offered zero diversification benefit (perfectly positively correlated with traditional asset classes), the efficient frontier of exclusively stocks and bonds would still be completely dominated by the frontier which includes hedge funds. Second, it is critical to consider conditional correlations in addition to unconditional correlations. I extend an argument made by Roll (1980) about orthogonal portfolios to those which include hedge funds, in order to suggest that institutions, when evaluating potential new alternative asset classes for potential portfolio inclusion, should attach more importance to the vector of returns and the diagonal of the covariance matrix than to the off-diagonal terms. However, the off-diagonals should nonetheless be considered carefully, and I present a multi-regime conditional correlation methodology which utilizes a statistic we call the conditional correlation ratio, and show a simple example of its usefulness.