## Holding Period Returns

A famous set of studies dealing with rates of return on common stocks, bonds, and Treasury bills was conducted by Roger Ibbotson and Rex Sinquefield.5 They present year-by-year historical rates of return for the following five important types of financial instruments in the United States:

1. Large-Company Common Stocks. The common-stock portfolio is based on the Standard & Poor's (S&P) composite index. At present, the S&P composite includes 500 of the largest (in terms of market value) stocks in the United States.

2. Small-Company Common Stocks. This is a portfolio composed of the bottom fifth of stocks traded on the New York Stock Exchange in which stocks are ranked by market value (i.e., the price of the stock multiplied by the number of shares outstanding).

3. Long-Term Corporate Bonds. This is a portfolio of high-quality corporate bonds with a 20-year maturity.

4. Long-Term U.S. Government Bonds. This is a portfolio of U.S. government bonds with a maturity of 20 years.

5. U.S. Treasury Bills. This is a portfolio of Treasury bills of three-month maturity.

None of the returns are adjusted for taxes or transactions costs. In addition to the year-by-year returns on financial instruments, the year-to-year change in the consumer price index is computed. This is a basic measure of inflation. Year-by-year real returns can be calculated by subtracting annual inflation.

Before looking closely at the different portfolio returns, we graphically present the returns and risks available from U.S. capital markets in the 74-year period from 1926 to 1999. Figure 9.4 shows the growth of \$1 invested at the beginning of 1926. Notice that the vertical axis is logarithmic, so that equal distances measure the same number of percentage changes. The figure shows that if \$1 were invested in common stocks and all dividends were reinvested, the dollar would have grown to \$2,845.63 by the end of 1999. The biggest growth was in the small-stock portfolio. If \$1 were invested in small stocks in 1926, the investment would have grown to \$6,640.79. However, when you look carefully at Figure 9.4, you can see great variability in the returns on small stocks, especially in the earlier part of the period. A dollar in long-term government bonds was very stable as compared with a dollar in common stocks. Figures 9.5 to 9.8 plot each year-to-year percentage return as a vertical bar drawn from the horizontal axis for common stocks, for small-company stocks, for long-term bonds and Treasury bills, and for inflation, respectively.

Figure 9.4 gives the growth of a dollar investment in the stock market from 1926 through 1999. In other words, it shows what the worth of the investment would have been if the dollar had been left in the stock market and if each year the dividends from the previous year had been reinvested in more stock. If Rt is the return in year t (expressed in decimals), the value you would have at the end of year T is the product of 1 plus the return in each of the years:

(1 + R1) X (1 + R2) X ... X (1 + R) X ... X (1 + Rt)

5The most recent update of this work is Stocks, Bonds, Bills and Inflation: 2000 Yearbook™ (Chicago: Ibbotson Associates). All rights reserved.

Ross-Westerfield-Jaffe: I III. Risk I 9. Capital Market Theory: I I © The McGraw-Hill

Corporate Finance, Sixth An Overview Companies, 2002

Edition

Part III Risk

■ Figure 9.4 A \$1 Investment in Different Types of Portfolios, 1926-1999 (Year-end 1925 = \$1.00)

Index

\$10,000

\$100

\$100

\$0 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I 11 I I I I I I I I I I I I I I I I I I I I I I I I I I I 11 I I I I 1925 1935 1945 1955 1965 1975 1985 1999

### Year-End

Redrawn from Stocks, Bonds, Bills and Inflation: 2000 Yearbook,™ annual updates work by Roger G. Ibbotson and Rex A. Sinquefield (Chicago: Ibbotson Associates). All rights reserved.

■ Figure 9.5 Year-by-Year Total Returns on Common Stocks

Total annual returns in percent

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