Stock market analysts use all kinds of math all day, says Ming Lam, a stock market analyst. His job is to evaluate the potential success of a stock based on its financial statements and its current performance on the stock exchange.

Each analyst and the company they work for has a style or philosophy of investing. This depends largely on the clients they have. If an analyst is working for a mutual fund company that specializes in retirement investing for young adults, the analyst may look for higher-risk stocks. If the client base is older and closer to retirement, the analyst will look for more secure investments.

There are hundreds of ratios and formulas that a stock market analyst uses to estimate a stock's future performance and risk. "From valuations of financial statements involving ratios to determining market positions of stocks, many of the calculations involve university-level math and an in-depth understanding of stock market terms and mechanisms," says Lam.

With your classmates, discuss the importance of equations and formulas. Pose the following questions:

• What formulas or equations have you used to this point? (List them on the board.)
• Why did you use those formulas or equations? (Did they make it easier?)
• What is the purpose of using equations? (What do they do for you?)

Discuss how formulas combine 2 or more variables to form a single new unit. For example, distance and time can be joined to form a third unit called velocity. The relationship between the variables is therefore much easier to see. Just as a graph makes patterns in data easier to see, an equation ties together a number of variables to show the combined effect in the form of the new unit.

To better understand the function of equations, let's take a closer look at one that everyone should be familiar with: the equation for volume.

In small groups, measure the length, width and height of 5 or 6 small pieces of wood supplied by the teacher. Record the dimensions in chart form.

(Note to teachers: Try 2 or 3 short pieces of two-by-four measured at 6, 8 and 10 inches in length; a 7-inch square piece of 3/4-inch plywood; a large piece of 1/8-inch paneling measuring 3 feet by 3 feet; and a 3-inch piece of four-by-four.)

Use the formula:

Calculate the volume of the pieces of wood. Make sure you use consistent units. Express the answer in cubic units.

An equation can be used to calculate more than one variable, however.

Using the data from the volume calculations, the teacher will demonstrate how the formula can be manipulated so that it is possible to calculate the length of a piece of wood given its volume, width and height. Note how any one of the dimensions may be calculated with the other three values.

Now, it's your turn. Use sample numbers for other pieces of wood provided by the teacher. Manipulate the equation to find whatever variable is left as the unknown.

Now that you can manipulate equations, let's see what kind of math Lam uses in his work as a market analyst.

Using any newspaper with comprehensive stock market coverage, familiarize yourself with the terms and layout of the page.

Create a spreadsheet listing the name, symbol, closing price and share profit for at least 10 stocks with a bullish trend and 10 stocks with a bearish trend. If possible, include 5 local companies.

Lam often uses the Capital Asset Pricing Model (CAPM) and the Price/Earnings Ratio formulas. The CAPM is used to assess the price of a stock in relation to general movements in the stock market. The Price/Earnings Ratio is used to compare the price of a stock to others in the same industry.

You work as a stock market analyst. The fund you advise has a very conservative investment strategy. The managers want fairly secure, solid investments because they cater to an older, lower-risk-oriented client.

You've been watching the stock of an established resource company -- Domtar (symbol DTC). Domtar produces paper, pulp products and packaging. It's a fairly volatile industry, but you think it may have some potential for your fund.

Currently Domtar stock is trading at $10.50. You want to assess the stock's price in relation to the market.

The formula for CAPM is:
stock price = A (stock's variance) + B (how the stock fluctuates in relation to the market) M (market level)

Determining stock variance (A) and its fluctuation (B) involves the use of university-level math. These values often require hours of work and research to determine. Market level is the composite index for the stock market in which the stock is traded.

You've already calculated the stock's variance and how DTC fluctuates in relation to the market. The stock's variance is 3 and that stock fluctuates at a 0.01244. Domtar stock is trading at $10.50 and the stock exchange composite index (market level) is 843.64.

Is the price of the stock overvalued? Or, is it undervalued?

The formula for Price/Earnings Ratio (P/E) is:
stock price/earnings per share

Stock price is the cost of buying 1 share on the market. Earnings per share is the annual per share earnings reported in the company's financial reports. If the P/E for the company is lower than that for the industry, an analyst would investigate further to discover the reasons for its low price. Depending on those reasons, an analyst might recommend investing in it.

Check the Price/Earnings Ratio for Domtar. According to a past quarterly report, its net earnings per share is $-0.69.

You do some research and find the P/E for similar companies in the same industry:

MacMillan Bloedel Limited = -0.76
Repap Enterprises Inc.= -0.67
Fletcher Challenge Canada Limited = -0.38
Abitibi Price Inc = 1.17
Ainsworth Lumber = -1.10

(Note that the P/E for these companies may be quite different today.)

Put this data into a table format. Determine the P/E for this group of stocks from the forest industry. How does Domtar's P/E compare to it? Should you suggest investing in it?

Optional Extra Activities

1. Divide the class into groups. Have each group select 5 or 6 stocks from a particular industry, such as mining, manufacturing, auto or communications. Have each group select a different industry. Calculate the P/E for these stocks. How do the P/E ratios compare for the different groups? Which sector would your class recommend investing in? Present findings to the class.
2. Discuss P/E ratios. Which is better, a low P/E or a high P/E? What does a negative P/E mean? Could a stock with a negative P/E be a good investment?
3. In small groups, discuss this statement: "The fund you advise has a very conservative investment strategy. They want only fairly secure, solid investments because they cater to an older, lower-risk-oriented client." Why does age make a difference in investment strategy?

Published in Partnership by the Center for Applied Academics, Bridges Transitions Inc., a Xap Corporation company and The B.C. Ministry of Education, Skills and Training. Copyright © 2002 Center for Applied Academics