Rebalancing blueprint

Quantitative finance scholars are creating better optimizers.

Robert Engle, at New York University's Stern School of Business, and Michael Brandt, at Duke University's Fuqua School of Business, proposed a new quantitative model that would give investors a blueprint on how to rebalance their portfolios monthly to produce higher risk-adjusted returns without increasing risk. It would also give investors a simple way of optimizing their portfolios. Messrs. Engle and Brandt presented their findings at a recent conference hosted by The Chicago Quantitative Alliance, a money management industry group dedicated to quantitative research.

Most pension plans face funding shortfalls. As a result, many are demanding better returns with less risk from their money managers.

Mr. Engle, who won the Nobel Memorial Prize in Economic Sciences in 2003 for creating his Autoregressive Conditional Heteroskedasticity, or ARCH, model, proposed an extension to the ARCH model that he calls dynamic conditional correlation. This new model would allow an investor to forecast correlation and covariance (the measure of the degree to which two volatile asset classes are associated), and to build a rebalancing strategy that slightly increases risk-adjusted returns. At least one money management executive labeled DCC a breakthrough.

"Ten years ago, even five years ago, no one was able to forecast correlations and covariances," said Ken Kroner, managing director of the Advanced Strategies and Research Group at Barclays Global Investors, San Francisco. According to Mr. Kroner — a former student of Mr. Engle's — BGI is one of the only firms to use a model similar to the ARCH model. BGI developed its model last year, based on Mr. Engle's work.

"Engle's model hasn't been discussed among pension plans because it's quite complex," Mr. Kroner said. "But as risk becomes more of a concern at institutions, I suspect you'll see a lot more managers implementing a similar model in the future."

Mr. Engle developed the new model along with finance professors Pedro Santa-Clara and Ross Valkanov, both at the Anderson School of Management at the University of California at Los Angeles.

The original ARCH model says a portfolio's volatility can be predicted based on weighted standard deviations (a measure of volatility of comparing the returns of a security or portfolio to its mean over time).

A heavier weighting is placed on short-term standard deviations — e.g., during the past five days — while a lighter weighting is placed on long-term standard deviations — e.g., the past five years. Mr. Engle also factors value at risk — a statistical estimation of the probability of losses in a portfolio. In the case of the ARCH model, Mr. Engle defines VAR as a past loss of a security or portfolio that an investor is 99% certain is worse than any future loss.

In Mr. Engle's DCC model, he applies the ARCH model to multiple asset classes. By calculating the correlation between two or more asset classes over time, the risk-adjusted returns of each one can be reasonably predicted. By forecasting the risk-adjusted returns on a monthly basis, investors can use futures in their overall portfolio to produce slightly better returns and not increase volatility.

Michael Brandt, an assistant professor of finance at the Fuqua school, proposed simplifying the capital asset pricing model, which can now involve millions of calculations.

Some current CAPM models factor in beta, or systematic risk (a stock or portfolio's correlation to an index), while others use the famous Fama-French model, developed by Eugene F. Fama and Kenneth R. French. The Fama-French model is designed to find undervalued securities by factoring in a stock's market capitalization and its book-to-market-price ratio in addition to beta.

In Nobel Laureate Harry Markowitz's efficient frontier model — the first model to quantify the risk/return levels of model portfolios — if an investor calculates beta on each security in a portfolio of, say, 100 stocks, by the third set of calculations, the investor could end up with more than 300,000 points of data.

"By the fourth set, it could run into the millions," Mr. Brandt said. "It's simply unfeasible for an investor to work with that." He noted this is a problem quantitative portfolio managers and consultants have run into for decades with this model.

Instead, Mr. Brandt's model, called "parametric weights in portfolio optimization," proposes that the weightings of securities in a portfolio can be calculated simply by factoring in any 10 fundamental characteristics of a stock that the investor chooses, such as dividend income, lagging 12-month return, book value to market price, etc. Also factored into the equation is the number of stocks in the given universe (e.g., Microsoft Corp. is in the U.S. equity universe, which contains about 6,000 stocks) and the weight of the stock in its given index (e.g., Microsoft is in the Standard & Poor's 500 index).

"This is something that can be done on a laptop in two minutes," he said.

One money manager at the CQA conference, who did not want to be identified, said, "(Mr.) Brandt's model could be extremely useful if it were ever used. More testing must be done of it, but if it can produce valid results with fewer calculations, it could make life for money managers much easier."

"(Mr.) Brandt's model is brand new to me," said BGI's Mr. Kroner. "It is definitely something that warrants more research. Essentially, he and his colleagues found a way to combine all moments of distribution (the levels of calculations required in both the CAPM and the Fama-French models) into one equation by setting up parameters for each of the securities in a portfolio."