homepage

ETF-Index Pricing Relationship
Written by John J. Neumann   
Wednesday, 30 April 2008 09:25
In the more than a decade since the first exchange-traded products were introduced, these securities have become progressively more popular investment vehicles among professional and individual investors alike. As of March 2008, there were more than 600 exchange-traded fund portfolios being actively traded and several hundred more in registration.

Not only has the number of ETF offerings increased, but the size of the individual ETF issues has grown. At year-end 2007, the S&P 500 index-tracking ETF (SPY, or the SPDR) had 25 times more shares outstanding than in 1998, and its average daily trading volume grew at an average annual rate of 40.5 percent over that time. DIA, or ''Diamonds,'' which was introduced in 1998 to track the portfolio of 30 stocks in the Dow Jones Industrial Average (''DJIA'') and is the focus of this article, has seen its daily average volume grow by 41 percent per year on average over that same period.

ETFs in general allow investors to gain from intraday moves of an index since they trade as individual company stocks do, with continuously updated bid/ask quotes. They support investors' pursuit of passive investment strategies with more direct control of tax events (and generally lower expense ratios) than mutual funds. Thus, if investors believe that large, blue-chip-type companies are going to have a good (bad) day on average, but are unable to pinpoint exactly which of the 30 stocks in the DJIA might experience the most significant price increases (declines), Diamonds now provide a vehicle with which they can try to profit from their expectation. This is not possible with a traditional index mutual fund, since these funds calculate their net asset value once a day, after the markets have closed, so buyers and sellers of shares do so at the same price. Additionally, unlike mutual funds, ETFs can be sold short to gain if the index is expected to decline.

If the individual stocks in the DJIA index are all subject to their own buying and selling pressures throughout the day, DIA, as a stand-alone security, must also be subject to buying and selling pressures. One can envision a piece of news being released which motivates investors to transact in the ETF¡X but not the individual companies¡Xperhaps because the news is so fundamental a systematic news event, in modern portfolio theory terms, that it is expected to have an on average effect on ''the market.'' Conversely, and perhaps more clearly, news released about individual companies in the index might attract investor attention to these individual stocks more so than to the portfolio as a whole, especially during earnings reporting periods. What, then, is the mechanism that assures that the share price of an independent ETF security does not become disconnected from the underlying portfolio of stocks to which it is tied and consistently fulfills its objective of tracking the underlying index portfolio? In a word, arbitrage.
Arbitrage And The ETFs

Strictly speaking, an arbitrage is a mispricing between two (or more) assets or bundles of assets which are identical in some way and related via a well-defined pricing relationship. The mispricing may exist because one asset (or bundle) is overpriced for a period of time, because the other asset (or bundle) is underpriced for a period of time or because both assets (bundles) are mispriced. An arbitrage strategy attempts to lock in a risk-free profit by exploiting the mispricing with a virtually costless portfolio that calls for short positions in the overpriced asset(s) and long positions in the underpriced asset(s), the latter financed using the short proceeds. Implemented on a large scale, the net selling pressure of the short positions causes the price(s) of the overpriced asset(s) to decline, while the net buying pressure forces the price(s) of underpriced asset(s) to rise. The expectation is that when prices return to levels at which the well-defined relationship once again holds, this portfolio can be unwound to leave a net cash amount as the investor's arbitrage profit.

The Diamonds prospectus reads: ''[T]he Sponsor's aim in designing DIAMONDS was to provide investors with a security whose initial market value would approximate one-hundredth (1/100th) the value of the DJIA.'' Figure 1 reveals that from January 20, 1998, the day the Diamonds ETF started trading, until December 31, 2005, the ratio of the closing values of the Dow Jones Industrial Average to the per-share price of Diamonds ranged from 98.4526 to 102.4855. The mean ratio was 99.8978, with a standard deviation of 0.2204, indicating that roughly 95 percent of the time, this ratio has been between 99.457 and 100.3386. Interestingly, the standard deviation of this ratio was highest in the years immediately after the introduction of this price-weighted ETF, perhaps reflecting a learning curve among the financial markets.