Optimizing Indexed Portfolios By John Spence April 4, 2002

In many cases, holding every stock in an index isn't cost effective. One reason is that some thinly traded securities, such as small-cap or international stocks, are illiquid and carry higher transaction costs and wider bid-ask spreads. Therefore, index fund managers often take an optimized sample of the index that doesn't include every stock, but still behaves like the real benchmark. The idea is to cut down on transaction costs and save money while still tracking the index to a reasonable degree.

Sounds easy enough, but how do you actually pull that off? The optimization programs are proprietary and confidential, but San Francisco-based Barclays Global Investors (BGI) did fill us in on some of the general techniques and strategies involved.

"When you're optimizing, the first task is to go back and look at past volatility, correlations, and returns," says Binu George, principal and global equity strategist at BGI. "But how far back to you go, and how in-depth do you get? For example, do you look at daily, monthly, or annual returns? The answer depends in part on how stable you believe the data is. More data is better, but the fundamental market rules may have changed over time, rendering the data irrelevant. All good quantitative analysis involves looking at the data in the context of history. It's here where art meets science."

Optimized sampling involves balancing "benchmark risk" and transaction costs, which leads to some rather involved quantitative analysis.

"Risk isn't necessarily best measured by a stock's volatility," said George. "The fund manager must look at how the stock behaves relative to the entire portfolio. You can't just look at individual stocks in isolation. This leads to some complex analysis when comparing a stock against all the others. For example, there are roughly 500,000 possible pairs of stocks in a 1,000 stock portfolio."

Like other index fund managers that use portfolio optimization, BGI isn't overly concerned about perfect tracking if it comes at too high a price.

"We're willing to tolerate a certain level of tracking error," said George. "However, the incentive isn't to increase returns, but rather cut down on transaction costs. Zero tracking error naturally results in higher transaction costs."

George said the concept is not a new one, but the technology required to perform the analysis wasn't always easily accessible.

"The concept of portfolio optimization is actually quite old, and was developed in the late 1950s by [1990 Nobel Laureate in Economics] Harry Markowitz. However, it took over 20 years for the idea to be widely accepted. The main reason is that the computers and technology required to perform the complex analysis weren't readily available until later," said George.

Before optimized sampling was widely used, less sophisticated strategies were employed to mimic an index.

"Prior to optimization and factor models, stratified sampling was the norm," said George. "Under this methodology, the portfolio is broken into strata [or cells], for example different industries. The stocks within a stratum are examined against each other, but correlation between strata isn't taken into account. This is a rather crude method that only allows you to come close to tracking a benchmark."

Optimized sampling is particularly important in managing the iShares MSCI EAFE because the fund holds international stocks and because of its exchange-traded fund structure.

Mind if we sample?
	iShares MSCI EAFE	MSCI EAFE index
Total # of holdings:	794	1,021

Source: iShares.com, MSCI - data as of 4/4/2002

I'll follow your lead . . .
Returns	iShares MSCI EAFE	MSCI EAFE index
YTD	-4.54%	-4.57%
1 month	0.72%	0.70%
3 month	-3.87%	-3.93%
6 month	-8.01%	-8.01%
Fund inception (8/14/01)	-10.59%	-10.67%

Source: iShares.com - data as of 2/28/2002

"The iShares MSCI EAFE makes heavy use of optimization, and tracking the index in a cost effective way is the primary objective," said Feng Ding, emerging markets portfolio manager for BGI. "However, since it is an ETF there are additional concerns. We have to ensure the tradability of the ETF at all times, and we have to take into account that market makers must be able to hedge their positions. Ideally, we want the best of both worlds: a highly liquid portfolio with minimal tracking error."