Understanding and Calculating the Value Line Index Using Excel

The Value Line Index is a stock market index that measures the performance of about 1,700 companies from the major North American markets1. It has two forms: the Value Line Geometric Composite Index and the Value Line Arithmetic Composite Index. These indexes are based on the analysis and ratings of Value Line, a respected investment research firm.

The Value Line Geometric Composite Index is the original index, launched in 1961. It is an equally weighted index that uses a geometric average to calculate the daily price change. This means that the index reflects the median stock price change, rather than the average. The geometric index is more representative of the broad market performance, as it is less influenced by extreme price movements of individual stocks.

The Value Line Arithmetic Composite Index is a newer index, introduced in 1988. It is also an equally weighted index, but it uses an arithmetic average to calculate the daily price change. This means that the index mirrors the performance of a portfolio that holds equal amounts of each stock. The arithmetic index is more sensitive to the price movements of individual stocks, and it tends to be higher than the geometric index.

The Value Line Index is widely used as a benchmark for investors who want to track the performance of the U.S. stock market or compare the returns of their own portfolio. The index covers various sectors, such as technology, health care, consumer services, and financials, but it is especially known for its high concentration of technology stocks. The index has experienced several periods of growth and decline over its history, reflecting the changes in the U.S. economy and business cycle1. As of December 28, 2023, the Value Line Geometric Composite Index reached a new high of 1,027.02 points, while the Value Line Arithmetic Composite Index reached a new high of 9,433.55 points.

Basic Theory:

The Value Line Index is a capitalization-weighted index, meaning that the stocks with higher market capitalizations have a greater impact on the index value. The formula for calculating the Value Line Index is as follows:

$VLI = \frac{\sum (P_i \times Q_i)}{D}$

Where:

$P_i$ is the price of the $i^{th}$ stock,
$Q_i$ is the number of shares outstanding for the $i^{th}$ stock,
$D$ is the divisor.

The divisor is adjusted periodically to maintain the continuity of the index over time.

Procedures:

Gather Data: Collect the stock prices ( $P_i$ ) and the corresponding shares outstanding ( $Q_i$ ) for the selected stocks.
Calculate Market Cap: Multiply the stock price ( $P_i$ ) by the shares outstanding ( $Q_i$ ) for each stock to determine its market capitalization.
Calculate VLI: Sum up the market capitalizations of all selected stocks and divide by the divisor ( $D$ ).
Adjust Divisor: Periodically adjust the divisor to account for events such as stock splits or other corporate actions.

Explanation:

Let’s consider a scenario with three stocks in the Value Line Index: Stock A, Stock B, and Stock C. The stock prices and shares outstanding are as follows:

Stock	Price ($)	Shares Outstanding
A	50	1,000,000
B	75	800,000
C	60	1,200,000

Scenario Calculation:

$VLI = \frac{(50 \times 1,000,000) + (75 \times 800,000) + (60 \times 1,200,000)}{D}$

Assuming the initial divisor is 1, the calculated VLI is the sum of the market capitalizations divided by 1.

$VLI = \frac{50,000,000 + 60,000,000 + 72,000,000}{1}$

$VLI = \frac{182,000,000}{1}$

$VLI = 182,000,000$

Excel Calculation:

In Excel, you can use the SUMPRODUCT function to calculate the sum of the products and then divide by the divisor. Assuming the stock data is in cells B2:D4, and the divisor is in cell F2, the formula would be:

$\text{=SUMPRODUCT(B2:B4, C2:C4) / F2}$

Other Approaches:

Using SUMPRODUCT and INDEX/MATCH: You can use INDEX/MATCH to dynamically reference stock prices and shares outstanding based on the stock symbol.
Automating Divisor Adjustment: Implement a formula or VBA macro to automate the divisor adjustment process based on events like stock splits.
Creating a Dashboard: Enhance your Excel sheet by creating a dashboard that visualizes the Value Line Index trend over time.