Diversification is one of the pillars of asset allocation. The authors argue, however,
that investors typically assess correlations for a full sample, which masks an
asset’s diversification properties in various market environments. They claim that
downside correlation is the important measure to consider and demonstrate that full-scale
optimization is better than standard mean–variance optimization because it can
generate portfolios with lower downside correlation but higher upside correlation.
The authors argue that assets chosen to complement a portfolio’s main engine of growth
should diversify on the downside (i.e., when the main asset performs poorly). They point out,
however, that upside diversification is, in fact, an undesirable property because it is more
efficient for assets to be correlated on the upside. When investors take the correlation of
the full sample into account, this nuance is lost, which leads to inferior portfolio
construction.
The authors derive conditional correlations analytically under the assumption that returns
are jointly normally distributed to measure the theoretical bias that should be expected from
conditional correlations. They then conduct an empirical study in which the conditional
correlations are contrasted to a wide variety of asset classes to demonstrate that significant
asymmetry exists. Finally, the authors present a portfolio construction technique called
“full-scale optimization.” They demonstrate that this technique is able to produce
portfolios in which the constituent assets exhibit relatively lower correlation on the
downside and higher correlation on the upside than portfolios produced by traditional
mean–variance optimization.
Several asset classes and indices are included in their analysis. For the equity markets, the
authors use MSCI indices for the United States, the United Kingdom, France, Germany, Japan,
and World ex-United States for January 1970–February 2008. To capture style and size
data, the Russell 3000 Value (U.S. value), Russell 3000 Growth (U.S. growth), S&P 500
(U.S. large cap), and Russell 2500 (U.S. small plus mid-cap) indices are included. Several
hedge fund styles from the Hedge Fund Research database are also considered, including event
driven, relative value arbitrage, convertible arbitrage, equity market neutral, merger
arbitrage, and global hedge. The fixed-income markets included are U.S. bonds, government
bonds, and high-yield, mortgage-backed, and investment-grade credit.
The authors find that observed correlations are higher than normal on the downside while
lower on the upside. For example, in considering the correlation between the U.S. Russell 3000
and MSCI World ex-United States, they find that when both markets are up one standard
deviation, correlation between them is –17 percent, whereas when both markets are down
more than one standard deviation, correlation between them is 76 percent. They find that these
correlation asymmetries prevail, including for such hedge fund styles as market-neutral
equity. In fact, they find that only a few asset classes offer desirable downside
deviation—mortgage-backed securities, high yield, and credit, which all failed to
diversify during the financial crisis of 2007–2008.
The authors then construct a portfolio using full-scale optimization. Unlike
mean–variance analysis, which assumes normally distributed inputs, full-scale
optimization uses the distribution features of the empirical sample, so assets’
skewness, kurtosis, and correlation asymmetries are taken into account. Hence, full-scale
optimization implicitly minimizes downside correlation and maximizes upside correlation. The
authors demonstrate that using full-scale optimization reduces correlation asymmetry by more
than half compared with using mean–variance optimization. Although the results show
consistent increases in the utility of the portfolio generated by full-scale optimization, the
biggest uplift is achieved in the subsample in which hedge funds are included and utility is
improved by 254 percent.
In summary, the authors present an analytical framework to show how conditional correlations
vary under the assumption that returns are jointly normally distributed. This result is used
to highlight the correlation asymmetry that is prevalent among a variety of asset pairs. The
authors then present a portfolio construction technique that is able to take advantage of this
asymmetry, and they note that traditional mean–variance is unable to do so.