March 3, 2009
Markedly different optimal asset allocations result, depending on whether down-down or up-up correlations are used. Unconditional correlations smoothes results between these sets of assumptions.
Instead of mean-variance, the co-authors recommend “full-scale optimization” as the preferred approach.
Full-scale optimization finds the optimal portfolio by testing various combinations of asset classes against the historical data, which reflects asymmetrical correlations, as well other statistical properties, such as skewness, kurtosis, and other peculiarities.
Traditional mean-variance optimization uses a quadratic utility function, which means that it assumes investors have constant risk aversion – they are equally risk averse regardless of their wealth.
A more realistic approach is to assume that investors’ risk aversion increases once they reach a certain level of wealth. Such an approach is reflected in a “kinked” utility function, and full-scale optimization constructs the optimal portfolio under these circumstances.
Implications for advisors
The guiding message of this research is that advisors should focus more on hedging than diversifying, according to Page. But identifying, implementing, and measuring the effectiveness of proper hedges requires more research. Page said the concept of portfolio insurance offers some promise. Shorting the historically undesirable asset classes (like relative value arbitrage) might work, but shorting negates the returns along with the diversification properties, so a more sophisticated approach is necessary.
The key is finding assets that decouple, especially in down markets. And just because traditional assets have failed to decouple in the past does not mean they will behave this way in the future. Proper diversification requires an understanding of the fundamentals driving the returns of each asset class, analyzing whether these fundamentals are influenced by truly independent economic relationships, and insuring that this independence is exhibited primarily in down markets.
Does this research mean that advisors should scrap the concept of diversification altogether, and rely on a portfolio of plain-vanilla equities? Absolutely not. But it does send a stern warning to advisors paying substantial fees for portfolio construction and optimization tools that do not incorporate correlation asymmetries. If you are using such tools, an important question to ask is whether they optimize based on averages across all historical data, or over primarily down markets when diversification is most valuable.
Portfolios should be built to withstand turbulence, knowing that investors cannot predict when that turbulence will occur. Proper diversification is an important ingredient toward reaching this goal. Other research by Kritzman shows that once turbulence occurs, it tends to persist on a daily basis, and active managers can profit from this behavior. [See our earlier article on this topic.]
If the co-authors had constructed a portfolio two years ago, it would have been heavily laden with mortgage-backed securities, in retrospect one of the worst possible choices of asset classes. But Page advises against placing too much faith in the historical data. “Mathematics is there to help us make the best use of our judgments,” he said. Many people warned about the dangers of the real-estate bubble, which were not reflected in the co-authors’ data, and good judgment would have avoided the most exposed asset classes.
Page likened portfolios built with traditional mean-variance optimization to “driving a car with the air bag deployed, except when the car crashes.” Full-scale optimization, based on empirical data reflecting the asymmetric nature of correlations, does the opposite. It deploys diversification when it is needed most (in market crashes) and gets it out of the way when it is not needed (in up markets).
Display article as PDF for printing.
Would you like to send this article to a friend?
Remember, if you have a question or comment, send it to .
