Published March 28, 2003

Comparing the Value Line Indexes

We receive many inquiries from our subscribers regarding the differences between the Value Line Arithmetic Index and the Value Line Geometric Index. In response, we are partially reprinting and updating an article that first appeared in Selection & Opinion on December 10, 1993.

On June 30, 1961, we introduced the Value Line Composite Index. This index assumes equally weighted positions in every stock covered in the Value Line Investment Survey. That is, it is presupposed that an equal dollar amount is invested in each and every stock. The returns from doing so are averaged geometrically every day across all the stocks in the Survey, and consequently, this index is frequently referred to as the Value Line Geometric Index (VLG). The VLG was intended to provide a rough approximation of how the median stock in the Value Line universe performed.

Calculating the Value Line Indexes

The VLG is calculated in the following manner. First, for each stock, compute the ratio of its closing price today to the close on the previous trading day. For instance, if Citigroup goes from $34.20 to $34.05 in one day, its ratio is 0.996. Conversely, if Pfizer goes from $29.70 to $29.86, its ratio is 1.005. The next step is to multiply all of these ratios together, forming a single number. Finally, raise this quantity to the power defined by the reciprocal of the number of stocks in the index (currently the index includes 1675 stocks). The result is the ratio of today's VLG price to the previous trading day's close. To derive the percentage price change, simply subtract 1 from this value and multiply the result by 100.

On February 1, 1988, Value Line began publishing the Value Line Arithmetic Index (VLA) to fill a need that had been conveyed to us by subscribers and investors. Like the VLG, the VLA is equally weighted. The difference is the mathematical technique used to calculate the average price change of stocks in the index.

The VLA is calculated in the following manner. First, compute the ratio of every stock's price change in the same way as described in the first step of the geometric calculation. Next, add all of the ratios together. Finally, divide the total by the number of stocks. The result is the ratio of today's VLA price to the previous trading day's close. Again, to get the percentage price change, subtract 1 from this figure and multiply the result by 100. Upon VLA's introduction in 1988, the index values were computed on a daily basis back five years to the beginning of 1983 to provide an historical frame of reference.

Differentiating the VLA and VLG

The VLA provides an estimate of how an equal-dollar weighted portfolio of stocks will perform. Or, put another way, it tracks the performance of the average, rather than the median, stock in the index. It can be proven mathematically that the maximum daily ratio attainable by the VLG is equal to the daily ratio of the VLA. However, this special case can only occur when every single stock in the index has the exact same percentage price change on a given day—a highly unlikely scenario. For all practical purposes, then, the daily percentage price change of the VLA will always be higher than the VLG. The systematic understatement of returns of VLG is a major reason that the VLA was developed.

The wide-ranging coverage of the Value Line Investment Survey and its equally-weighted nature made the VLG very appealing conceptually as representative of a typical retail investor's portfolio. The VLG also has appeal to institutional investors as a proxy for the so-called "mid-cap" market because it includes large cap, mid cap, and small cap stocks alike. Because of this interest, the Kansas City Board of Trade instituted trading in Value Line Index Futures in 1982. However, the performance of the VLG over time proved to underestimate the portfolio performance by too large a factor. For example, in the latest three-year period (ended December 31, 2002), the VLG had an annualized price change of – 15.1% in comparison with 0.3% for the VLA. Accordingly, it was easy for astute investors to "game" the early Value Line futures with a representative basket of the underlying securities, since the basket would always outperform the VLG. The VLA price changes are much closer to the returns that would be derived by the underlying basket.

Moreover, while the differences between daily price changes may seem small, the magnitude of the annual differential between the two indexes is prodigious. The accompanying bar graph shows that for the ten-year period ending December 31, 2002, the difference in the average annual price change between the VLA and VLG averages is approximately 10%. Although our latest data show that the differences between the two averages is usually about 10%, the gap widened to nearly 15% in the three years ending December 31, 2002.

We explain this particular discrepancy between the VLG and VLA by first noting that the volatility of the stock market has been rising in recent years, with particularly wide swings in 2000 and 2001. In addition, it is important to realize that the VLG will work to filter out market volatility, since it effectively tracks the median of our universe of stocks. Meanwhile, the VLA, by its construction, will tend to capture the upside of the market swings. Taken together, then, these facts account for the wider difference between the VLG and VLA in the most recent three-year period.

It can also be argued that the VLA somewhat overstates returns of the equally-weighted basket of stocks, since it does not assess the transaction costs that would be entailed by following the strict discipline of daily rebalancing to bring the portfolio back to equally-weighted positions. However, our research shows that quarterly rebalancing closely tracks index performance while mitigating transaction costs.

Other Major Indexes

How does the VLA differ from the two most popularly quoted indexes: the Dow Jones Industrial Average (DJIA) and the S&P 500 Index? There are two major differences: the weighting scheme and the number of stocks.

The S&P 500 is weighted by market capitalization. As such, stocks with large market caps account for much of its monthly price fluctuations. And although the S&P 500 tended to "outperform" the VLA in the bull market of the 1990s, reflecting investors' preference for large, easily-traded stocks, the reverse has been the case in the last few years. This situation is probably best explained by noting that a number of the dominant constituents of the S&P 500 in recent years have been large, high-tech issues. And that investors' appetite for technology shares has weakened considerably since the market burst in early 2000. Moreover, there was a pronounced January effect in 2001. We note that the January effect, whether it takes place in January or in an earlier month, will generally benefit the VLA over the S&P 500 given the "effect's" small-cap nature.

The appropriateness of these two indexes depends on one's goals. The VLA is much more comprehensive, including all of the companies in the S&P 500 along with almost 1200 other companies of interest to our subscribers. Nevertheless, more comprehensive indexes, such as the market weighted Russell 3000, also exist, providing even a broader view of market performance.

The Dow Jones Industrial Average is valued mostly for its long history and its simplicity. It consists of only 30 stocks—all of which are included in the VLA—and it was originally designed for easy computation on the back of an envelope. This index is weighted by the price-per-share of each of its component stocks. That is, a 10% gain in a stock that sells at $90 influences its price movements three times as much as a 10% gain in a $30 stock. In truth, there is no rational justification for such a weighting scheme other than that it was simple to calculate before computers were available. Moreover, few investment professionals would consider any basket of 30 stocks to be representative of today's U.S. stock market. Nevertheless, it is useful to understand these differences because the DJIA is still the single most frequently quoted barometer of market performance.

Although fifteen years have past since its inception, we still get many questions on the VLA, and continue to learn more about its behavior. The fact that interest in it continues to be expressed underscores its value as a measurement tool.