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Focusing on investments from the perspectives of both return and risk is important. Although returns are an easy concept for investors to grasp, they are more likely to lack an understanding of the importance of accompanying risk.

Investment risks can be classified in various ways. One of the first issues to consider is asset class. Although other categories such as real estate are available in general, the most common investment assets are traditional investments, including stocks, bonds, or money market assets.

Firm size is another crucial issue. Although different ways are available to measure a company's size, such as its sales, assets, or even the number of employees, the most frequently used method is by market capitalization calculated as the product of the number of shares outstanding and the market value of each share. Consider, for example, that on August 16, 2019, the price of Apple Inc. stock closed at $206.50. At that time, the firm had 4.5 billion shares outstanding in the hands of investors. Combining the two values, on August 16, 2019, the market capitalization of Apple, Inc. was about $928.8 billion ($206.40 per share × 4.5 billion shares outstanding = $928.8 billion of market capitalization).

Different size categories of stock include large-cap (large-capitalization), mid-cap (mid-capitalization), small-cap (small-capitalization), micro-cap (micro-capitalization), or even nano-cap stocks. Nano is a prefix used to represent a one-billionth part of something – here, nano-capitalization stocks.

Although capitalization categories can differ substantially depending on the source, large-cap stocks are usually thought of as those with a capitalization of $10 billion or larger. For mid-cap stock, capitalizations generally lie in the $2 billion to $10 billion range, while small-cap stock capitalization definitions range from $300 million to $2 billion. Alternatively, some small-cap stocks have capitalizations greater than $500 million but less than $2,400 million. Micro- and nano-cap stocks are often defined as those whose market capitalizations are between $50 million and $300 million for micro-caps and less than $50 million for nano-cap stocks.

Collectively, large-cap companies may be considered the backbone of the U.S. economy. For example, the total market capitalization of the S&P 500 Index firms consists of roughly 80 percent of the market capitalization of the entire stock market. By comparison, small-capitalization and micro-capitalization firms are often young and focus on one or two niches of expertise.

Much like market-cap classes, debt issues can also be categorized by class. Bond categorization, however, is more likely to be by the identity of bond issuers and maturity than by size. Commonly used bond segments include classifications such as long-term corporate, long-term government, municipal issues, and short-term issues, which include U.S. Treasury bills.

As Table 3.3 shows, major differences exist in both the returns possible and the risk accepted by investing in different classes of stock and bonds. In general, stocks provide higher average returns than bonds, but they also involve a higher level of risk.

TABLE 3.3 Returns and Risk Between 1926 and 2018

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This table shows the statistics of various classes of financial assets between 1926 and 2018.

Asset Classification	Geometric Mean Returns (%)	Arithmetic Mean Returns (%)	Standard Deviation of Returns (%)
Large-cap stocks	10.0	11.9	19.8
Long-term corporate bonds	5.9	6.3	8.4
Long-term government bonds	5.5	5.9	9.8
U.S. Treasury bills	3.3	3.4	3.1
Inflation	2.9	3.0	4.0

A review of the data shown in Table 3.3 provides good insight into the average returns and risks of basic asset classes over time. Based on their long-term geometric mean rate of return, large-capitalization stock investments provide at least four percentage points more annually on average over the long-term than long-term corporate bonds. This difference might look modest for one or two years, but it makes a big difference after accumulation over the years.

Consider that a $1 investment in large-cap stocks at 10 percent a year grows to $2.59 over 10 years, $45.25 in 40 years, and $2,048.40 in 80 years. Alternatively, investing $1 in long-term corporate bonds at 6 percent a year only returns $1.79 in 10 years, $10.29 in 40 years, and $105.78 in 80 years.

This example is both interesting and important to investors, especially those with long-term investment horizons. The four-percentage-point yearly difference between stocks and bonds may not initially appear large, but with time the difference increases substantially. Consider also the issue of Treasury bills, a short-term debt offered by the U.S. federal government. The long-term return from Treasury bills at only 3.3 percent a year is only slightly higher than the 2.9 percent long-term rate of inflation.

The substantially higher returns available over the long term with stock investments beg an important question: Why do investors hold bonds with lower returns or even Treasury bills with much lower returns? A partial answer may lie in the last column of Table 3.3, which shows the amount of risk quantified as the standard deviation of expected returns for the investment alternatives.

The standard deviations of stock classes are more than twice the standard deviation of bond classes. Note that an easy but often inaccurate way to interpret standard deviation is to consider that it quantifies the amount of a variation from the mean over time. For large stocks, a standard deviation of 19.8 percent suggests that while the average arithmetic return on those stocks was 11.9 percent between 1926 and 2018, that return had a range of returns between −7.9 percent and 31.7 percent, which is a spread of 39.6 percentage points. By comparison, long-term corporate bonds provided an average return of 5.9 percent with a standard deviation of only 8.4 percent over the same period, which equates to a possible range of returns from −2.5 percent to 14.3 percent, or a spread of only 16.8 percentage points, which is about 40 percent of the range of large-company stocks.

Although investors must still bear uncertainty with bond investments, the magnitude of accepted risk is much smaller than that of stock investments. Furthermore, the standard deviation of U.S. Treasury bills is only 3.1 percent, implying that for investors of Treasury bills, returns were much lower, but with an average return of only 3.3 percent, possible losses are low.

A further look into the various classes of equity provides a clear pattern of both returns and risk. The relative performance comparison between large and small companies has attracted interest from both finance scholars and practitioners. For example, Fama and French (1993) find that firm size is a key factor determining stock returns, as small firms outperform large firms in the long-term.

This difference can be explained from a risk perspective. Although large-cap stocks tend to be more stable than smaller stocks, as shown by their relatively lower standard deviation of returns, they also provide lower average returns. At the other end of the spectrum, micro-cap stocks, many of which are risky gambles with the potential for high levels of growth, also have a high potential for failure as evidenced by their long-term arithmetic average returns of 17.7 percent between 1926 and 2018 and their accompanying 38.5 percent standard deviation.

As Figure 3.9 shows, the DJIA, another proxy for the market in general, rose 11.67 percent annually on average between 2009 and 2019. This result suggests that while stock returns vary over time, the market's general long-term trend is up, not down. Although market returns periodically fall, these declines generally occur less frequently and for shorter durations than the rising movements.

In general, as Table 3.3 shows, an important axiom in finance is that an investment's expected return should be commensurate with its risk. The fundamental reason for this tradeoff is that most investors are risk-averse. The risk aversion of investors implies that they prefer less risk and choose the investment with the least risk if returns are comparable across investment options. For risk-averse investors to participate in risky investments, they must be rewarded with higher expected returns.

FIGURE 3.9 Recent Annual Returns on the Dow Jones Industrial Average

This figure shows the Dow Jones Industrial Average between 2010 and 2019.

Note: Daily returns between 2010 and 2019 are unadjusted for any seasonal effect and were last updated on August 28, 2019.

Source: S&P Dow Jones Indices LLC (2019b).