The Value Line Investment Survey

Comparing the Value Line Averages

We receive many inquiries from our subscribers regarding the differences between the Value Line Arithmetic and the Value Line Geometric Averages. In response, we are partially reprinting and updating an article that first appeared in Selection & Opinion a number of years ago.

On June 30, 1961, we introduced the Value Line Composite Index. This market benchmark 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) Average (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 Averages

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 Hewlett-Packard goes from $43.95 to $47.44 in one day, its ratio is 1.079. Conversely, if Merck goes from $47.02 to $46.13, its ratio is 0.981. 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 average (currently the average includes 1638 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) Average (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 price changes of the stocks in the average.

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, values were computed on a daily basis back five years to the beginning of 1983, thus providing an historical frame of reference. We have used a significant portion of this simulated data in the presentation for the VLA in the chart found below.

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 our universe. 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 average 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 socalled “mid-cap” market because it includes large-cap, mid-cap, and smallcap 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, 2007), the VLG had an annualized price change of 2.9% in comparison with 7.8% 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, although the differences between daily price changes may seem small, the magnitude of the annual differential between the two averages is prodigious. The accompanying bar graph shows that, for the twenty- and ten-year periods ending December 31, 2007, the difference in the average annual price change between the VLA and VLG ranged between 9% and 10%, which generally agrees with the historical the difference between the two averages of about 10%. However, recent data indicates that the gap has narrowed, to some 5% in the three and five years ending December 31, 2007.

We explain this particular discrepancy between the VLG and VLA by noting that despite the wide swings that have taken place in the stock market in the last few months, equities, as an asset class, have been less volatile than usual in recent years. With this in mind, the VLG, which can be thought of representing the median stock in our Universe, is more likely to track nearer the VLA, which represents an average stock. So even though the VLA, by its construction, will tend to capture the upside of the market swings, the difference between the VLG and VLA is narrower than usual in the most recent three- and five-year periods, reflecting a general reduction in market volatility.

It can also be argued that the VLA somewhat overstates returns of the equallyweighted 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 the Average’s 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, which tends to 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 generally 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 the late 1990s were large, high-tech issues. And that investors’ appetite for these shares became more selective after the market burst in early 2000. Meanwhile, 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, generally benefit the VLA over the S&P 500 given the “Effect’s” smallcap nature. Indeed, the outsized performance of the VLA in 2003 and to a certain extent in 2004 can be traced to investor support for a class of small-cap stocks with little or no earnings.

Which one of these two indexes may be more appropriate, depends on one’s goals. The VLA is much more comprehensive, including all of the companies in the S&P 500 along with 1138 other companies of interest to our subscribers.

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. 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.