A stock's valuation is the final factor of the Fama-French three-factor model of investment returns. A stock's valuation is measured on a continuum from "value" to "growth." In broad strokes, value stocks are cheap and growth stocks are expensive. But there are compelling reasons why an investor might be willing to pay more for a growth stock than a value stock.

Consider a local utility company whose stock is selling for $10 a share. The price has not changed much in the past 20 years. The company only services a specific geographic area that is not experiencing population growth. It has also had consistent earnings each year and paid the entire amount to shareholders at $1 per share.

This company has a price per earnings (P/E) ratio of 10. If you were to buy a share of this company, it would take 10 years to get paid back in earnings. After a decade you would have been paid back the price of your purchase and still own your share of stock. This type of stock is considered a value stock.

In contrast, consider a technology startup company that has shown meteoric growth in the past three years. Annual company earnings were $0.25. Then they doubled to $0.50, and now they are $1 per share. The business has just entered into several synergistic deals with other companies that should vastly increase its market penetration. Expectations are for the earnings to continue to double for the next three years.

Investors might rightly decide that the growing technology company is worth more than the static regional utility. If earnings grow to $2, then $4 and then $8, this technology company might be worth $80 a share instead of just $10. If so, the current P/E ratio of this stock would be 80. This type of stock is considered a growth stock.

The P/E ratio is one common measurement used to place stocks on the value to growth continuum. Low P/E ratios are value and high P/E ratios are growth. When computing P/E ratios, the price (NYSE:P) is easy to compute. Price is the share price on the stock market exchange throughout the day. Calculating earnings, however, is a little more difficult.

Some measurements use the past four quarters of earnings, which is often called the trailing P/E ratio. A projected or forward P/E uses the analyst consensus of the next four quarters' worth of earnings. For companies whose earnings are in flux, these two numbers can be very different.

Additionally, during hard economic times a company's earnings can decrease significantly or even disappear entirely. When earnings go to zero or turn negative, the P/E ratio ceases to make sense.

For these reasons a more common way to place a stock on the value-to-growth scale is the price-to-book ratio. Book value is the value shareholders would theoretically receive if a company was liquidated and all of its assets sold. Using book value ensures that you have some positive number and you won't be dividing by zero.

Many other metrics are used to analyze the value or growth attributes of a stock. These include price per cash flow, cash flow growth, price per sales, sales growth, book value growth and dividend yield. Each metric is simply trying to measure a future return on your investment.

Value and growth stocks react differently to new information. If the local utility company has some additional capital projects one year and only manages to pay $0.80 in dividends, it might not even change the stock's price. Value stocks are more resilient in flat or down markets. Not so with growth stocks.

If the technology startup's earnings grow from $1.00 to $1.80 the next year, the stock's price might tumble 27% from $80 per share down to $58 a share. The company's phenomenal track record of growth would be broken, and a more realistic valuation would be given to the company on account of lowered expectations.

Investors would wonder if instead of doubling earnings from $1 to $2 to $4 to $8, the company might only experience an 80% growth each year. That would mean earnings would grow from $1 to $1.80 to $3.24 to $5.83. As a result the stock might immediately drop 27% from $80 per share down to $58 per share.

Many investors find it baffling that a company could grow their earnings by 80% and the stock would drop 27% as a result. But everything is based on the expectation that the company would grow by 100% each year for the next three years. That expectation was already factored into the share price.

On average, value beats growth. The analysis that Eugene Fama presented during our conference last fall analyzed returns of the U.S. markets from 1927 through 2010. Rather than the price-to-book ratio, he used the book-to-price ratio. Because price is the market price, this is commonly called the book-to-market (BtM) ratio. When the BtM is high, a stock is a value stock. And when it is low, a stock is a growth stock.

Fama analyzed each decile from the lowest 10% of the BtM growth stocks through the highest 10% of the value stocks. The results were remarkable.

The average return of the lowest BtM decile was 10.99%, and the highest decile was 17.32%. There was a continuum such that except for a few, each more valuable decile showed a higher average return. The average return for the top 30% value was 16.30%, a full 4.80% higher than the bottom 30% growth's 11.50%. The neutral 40% in the middle averaged 12.91%.

Most major indexes are split between the value half and the growth half. The S&P 500 has an S&P 500 value and an S&P 500 growth. Similarly, the Russell 1000 Large Cap and the Russell 2000 Small Cap have subindexes for the value and growth side of each.

In my own analysis I measured the returns of the Russell 1000 Value against the Russell 1000 Growth from 1979 through the end of February 2012. During that period, large-cap value returned 13.27% versus growth's 12.47%, a premium of 0.80%.

The difference in small cap was much greater. The Russell 2000 Small Cap Value returned 15.07% versus Small Cap Growth's 12.44% for a premium of 2.63%.

In future articles we will explore how the value premium is higher for small cap than it is for large cap. The landscape of investment returns gets more complex with just the two dimensions of size and value. We begin to see that expected returns do not fit our simple linear formula. Rather they follow a curve.

Adding size and value as factors in our capital asset pricing model shows us certain truths about the markets. Many people follow the Dow and invest like the S&P 500, but tilting small and value provides a better return on average. And while large-cap growth technology companies got all the headlines and captured everyone's attention during the last half of the 1990s, there is quiet money to be made by growing rich slowly with value stocks.

E(R_{i}) = R_{f}+ ß_{i}(E(R_{m}) - R_{f}) + s_{i}SMB_{p}+ v_{i}HML_{p}

Where:

E(R_{i}) is the expected return on an investment

R_{f}is the risk-free rate of interest (about 3.67%)

For example, what you could get in short-term Treasuries

E(R_{m}) is the expected return of the market (about 11.71%)

E(R_{m}) - R_{f}) is sometimes called the market premium (about 8.04%)

ß_{i}= Cov(R_{i}, R_{m}) / Var(R_{m})

The sensitivity of the expected excess asset returns to the expected excess market returns.

S_{i}is the size measurement of the investment

SMB_{p}is the Small Minus Big premium (about 3.92%)

V_{i}is the value measurement of the investment

HBL_{p}is the High Minus Low premium (about 5.04%)