The very high rates of return observed, until recently, on many stock markets around the world and their superior performance over managed domestic portfolios has led to increased interest in investment funds whose performance mirrors that of a specific index. This increased interest is seen in the large number of new index funds that have been introduced based on domestic and foreign markets. Of the 63 Canadian-based index funds covering Canadian and foreign indexes (including segregated funds), 63% have been in operation less than three years.

With this increased interest, do investors know exactly what they are purchasing when they buy an index fund? Are there some elements of index funds and their construction that should be understood before purchase?

It is my contention that a careful analysis of index funds is needed, or the investor may have an unexpected surprise.

What is an index fund?
An index fund is a portfolio of securities chosen to replicate the performance of a specific benchmark portfolio, such as a stock market index (either broadly or narrowly defined), or a bond market index. Indexing is a passive strategy in which portfolio rebalancing occurs only when the benchmark composition changes. The divergence of the index fund's performance from that of the benchmark is an indication of how effectively the fund has performed its replication. This divergence is referred to as tracking error and can be the result of a number of factors, including the management expense ratio (MER), uninvested cash, or the replication strategy used by the fund.

It is important to note that performance in the index fund context is not the same as performance for non-index portfolios. For the latter funds, performance is related to observed return over a benchmark relative to the risk incurred. For the index fund, excluding the management expense ratio, perfect replication would result in no excess return over the benchmark, no difference in risk, and complete alignment of movement in index values and rates of return between the replicating fund and the benchmark.

Who uses index funds?
The list of index fund users is large and includes institutional investors, who often manage their own replication strategies, and individual investors who purchase either mutual funds or closed-end investment funds that provide units replicating the composition of the benchmark. These latter portfolios are called Index Participation Units (IPUs).

What are the uncertainties?
First, the investor must fully understand the benchmark used. The benchmark can vary from a small subset of available stocks on a domestic market, such as the i60 found on the Toronto Stock Exchange, to a large set of stocks such as SPDRs which replicate the S&P 500 index, to a combination of bond, domestic and foreign stock indexes.

Depending on the investor's rationale for purchasing an index fund, the choice of index can be very important. For example, the investor may want to use the index fund as a base upon which to place an overlay portfolio built on her own expectations concerning certain stocks or sectors. If the index fund does not match the benchmark, the investor may end up with an overall portfolio strategy that is not what was expected.

To further confuse the issue, some funds are not "pure" index funds, but add an overlay equity port-folio; these are often referred to as enhanced index funds. For example, National Bank Mutual Funds has an open-end index fund called Canadian Index Plus that invests between 70% to 80% of its funds in the i60, with the remainder actively managed. The fund has an MER between that of a pure index fund and a non-index fund.

If an investor believes that mutual fund managers are "closet indexers," then an index fund strategy is sensible. However, purchasing an enhanced index fund will generate a portfolio that due to its lack of correlation with the benchmark does not track it well, and will over- or underperform the benchmark based on the bets taken within the portfolio.

Tracking error
Tracking uncertainty exists based on the replication methodology. Each replication method has a set of transaction costs. For example, consider the strategy where the fund buys all of the stocks in the benchmark portfolio in their existing proportions. This eliminates tracking error, but increases transaction costs by the purchase of small capitalization stocks in the benchmark, which will increase bid-ask cost and could have an impact on the share price. As well, if the fund is not sufficiently large, this strategy will lead to rounding error as it forces expensive odd lot transactions.

At the other extreme is a partial replication strategy that uses a subset of the stocks in the benchmark. The replicating portfolio usually includes the stocks with the greatest weight and invests a smaller amount, if any, in the small cap stocks in the benchmark. Since the benchmark portfolio is not perfectly replicated, rebalancing will be required as market prices of stocks in the benchmark change. A partial replication strategy reduces the transaction costs of building the portfolio, but increases tracking error.

Provided the investor knows the benchmark that is being used, tracking error is the fundamental source of uncertainty. Up to this point I have left the definition of tracking error vague; it is related to the difference between the return (value) of the replicating portfolio and the return (value) of the benchmark. I consider two general methods to measure tracking error. One is a simple average of the deviations of the returns (values). This approach gives the same weight to all observations. Thus, two index funds based on the same index will have the same tracking error as long as their average returns are the same over the measurement period--their variability could be very different. However, if a large deviation, regardless of direction, is given a larger weight than a small deviation, tracking error can be measured as the average of the squared values of the deviations. This approach is consistent with the measurement of error in forecasting models. It permits decomposition of the error into a number of identifiable components, one of which is the difference in the average returns (values).

The index fund purchaser should have a way to determine ex ante whether the fund is expected to track well and, after the fact, how well it did track. For funds that have been in existence long enough, assuming the replication philosophy will not change, expected tracking error can be assessed using historical data. However, how does a buyer of a new index fund assess its tracking error? The fund's published replication strategy will give some indication. The fund can provide the tracking error components based on a simulation of the performance of the index fund and the benchmark.

Since all index funds are not the same and can differ in fundamental ways, more information should be provided to the investor. Information on a fund's replication philosophy, the method used to construct the portfolio, and a rating system for index funds based on their observed or simulated tracking error and its components would help investors make informed investment decisions.

Paul Halpern is the Toronto Stock Exchange Chair in Capital Markets and a professor of finance at the Rotman School of Management, University of Toronto.