We now know that a correct returns measure must incorporate the two components of return, yield and price change, keeping in mind that either component could be zero. TheTotal Return (TR)for a given holding period is a decimal or percentage number relating all the cash flows received by an investor during any designated time period to the purchase price of the asset calculated as
TR¼CFtþ ðPEPBÞ
PB ¼CFtþPC PB
(6-2) where
CFt¼cash flows during the measurement periodt PE ¼price at the end of periodtor sale price
PB ¼purchase price of the asset or price at the beginning of the period PC ¼change in price during the period, or PEminus PB
The periodic cashflows from a bond consists of the interest payments received, and for a stock, the dividends received. For some assets, such as a warrant or a stock that pays no dividends, there is only a price change. Part A of Exhibit 6-1 illustrates the calculation of TR for a bond, a common stock, and a warrant. Although one year is often used for convenience, the TR calculation can be applied to periods of any length.
Total Return (TR) Percentage measure relating all cashflows on a security for a given time period to its purchase price
E X H I B I T 6 - 1
Examples of Total Return and Price Relative Calculations A. Total Return (TR) Calculations
I. Bond TR
Bond TR¼ltþ ðPEPBÞ PB
¼ltþPC PB
lt ¼ the interest payment sð Þreceived during the period:
PB and PE ¼ the beginning and ending prices,respectively PC ¼ the change in price during the period
Example: Assume the purchase of a 10-percent-coupon Treasury bond at a price of $960, held one year, and sold for $1,020.
The TR is
Bond TR¼100þð1,020960Þ
960 ¼100þ60
960 ¼0:1667 or 16:67%
II. Stock TR
Stock TR¼Dtþ ðPEPBÞ
PB ¼DtþPC PB
Dt¼the dividend sð Þpaid during the period
Calculating Total Returns for the S&P 500 Index Table 6-1 shows the Standard & Poor’s (S&P) 500 Stock Composite Index for the years 1926 through 2011 (a total of 86 years because the data start on January 1, 1926). Included in the table areend-of-year values for the index, from which capital gains and losses can be computed, and dividends on the index, which constitute the income component.
Example: 100 shares of DataShield are purchased at $30 per share and sold one year later at $26 per share. A dividend of
$2 per share is paid.
Stock TR¼2þ ð2630Þ
30 ¼2þ ð4Þ
30 ¼ :0667 or 6:67%
III. Warrant TR
Warrant TR¼Ctþ ðPEPBÞ
PB ¼CtþPC PB ¼PC
PB
where,Ct¼any cash payment received by the warrant holder during the period. Because warrants pay no dividends, the only return to an investor from owning a warrant is the change in price during the period.
Example: Assume the purchase of warrants of DataShield at $3 per share, a holding period of six months, and the sale at
$3.75 per share.
Warrant TR¼0þ ð3:753:00Þ
3:00 ¼0:75
3:00¼0:25 or 25%
B. Return Relative Calculations
The return relative for the preceding bond example shown is
Bond return relative¼100þ1020
960 ¼1:1667 The return relative for the stock example is
Stock return relative¼2þ26
30 ¼0:9333 The return relative for the warrant example is
Warrant return relative¼3:75 3:00¼1:25
To convert from a return relative to a total return, subtract 1.0 from the return relative.
Table 6-1 Historical Composite Stock Price Index, Based on Standard & Poor’s 500 Index, Dividends in Index Form, and Total Returns (TRs), 19262011. Values are End-of-Year. (No monthly compounding.)
Year Index Val Div TR% Year Index Val Div TR%
1925 10.34 1969 92.06 3.16 28.32
1926 15.03 0.75 8.20 1970 92.15 3.14 3.51
1927 19.15 0.81 32.76 1971 102.09 3.07 14.12
1928 25.61 0.84 38.14 1972 118.05 3.15 18.72
1929 22.05 0.95 210.18 1973 97.55 3.38 214.50
1930 15.31 0.90 226.48 1974 68.56 3.60 226.03
1931 7.89 0.76 243.49 1975 90.19 3.68 36.92
1932 6.80 0.46 28.01 1976 107.46 4.05 23.64
1933 10.19 0.36 55.34 1977 95.10 4.67 27.16
1934 10.10 0.40 3.00 1978 96.11 5.07 6.39
1935 13.91 0.41 41.79 1979 107.94 5.65 18.19
1936 17.60 0.68 31.38 1980 135.76 6.16 31.48
1937 11.14 0.78 32.29 1981 122.55 6.63 24.85
1938 13.60 0.52 26.70 1982 140.64 6.87 20.37
1939 13.19 0.59 1.31 1983 164.93 7.09 22.31
1940 11.51 0.67 27.63 1984 167.24 7.53 5.97
1941 9.59 0.75 210.24 1985 211.28 7.90 31.06
1942 10.45 0.64 15.67 1986 242.17 8.28 18.54
1943 12.59 0.64 26.71 1987 247.08 8.81 5.67
1944 14.33 0.68 19.18 1988 277.72 9.73 16.34
1945 18.87 0.67 36.43 1989 353.40 11.05 31.23
1946 17.08 0.77 25.44 1990 330.22 12.10 23.14
1947 16.74 0.92 3.43 1991 417.09 12.20 30.00
1948 16.11 1.05 2.45 1992 435.71 12.38 7.43
1949 18.11 1.14 19.48 1993 466.45 12.58 9.94
1950 21.94 1.40 28.92 1994 459.27 13.18 1.29
1951 24.98 1.35 19.99 1995 615.93 13.79 37.11
1952 26.94 1.37 13.34 1996 740.74 14.90 22.68
1953 25.85 1.41 1.17 1997 970.43 15.50 33.10
1954 36.73 1.49 47.87 1998 1229.23 16.38 28.36
1955 43.89 1.68 24.06 1999 1469.25 16.48 20.87
1956 46.30 1.82 9.65 2000 1,320.28 15.97 29.05
1957 39.99 1.87 29.59 2001 1,148.08 15.71 211.85
1958 55.21 1.75 42.44 2002 879.82 16.07 222.10
1959 59.89 1.83 11.79 2003 1111.92 17.49 28.37
1960 58.11 1.95 0.28 2004 1,211.92 19.54 10.75
1961 71.55 2.02 26.60 2005 1248.29 22.22 4.83
1962 63.10 2.13 28.83 2006 1,418.30 24.88 15.61
1963 75.02 2.28 22.50 2007 1468.36 27.73 5.48
1964 84.75 2.50 16.3 2008 903.25 28.39 236.55
1965 92.43 2.72 12.27 2009 1115.10 22.31 25.92
1966 80.33 2.87 29.99 2010 1,257.64 23.12 14.86
1967 96.47 2.92 23.73 2011 1257.64 26.41 2.1
1968 103.86 3.07 10.84
Conclusions About Total Return In summary, the TR concept is valuable as a measure of return because it is all-inclusive, measuring the total return per dollar of original investment.
3 TR isthebasic measure of the return earned by investors on any financial asset for any specified period of time. It can be stated on a decimal or percentage basis.
TR facilitates the comparison of asset returns over a specified period, whether the comparison is of different assets, such as stocks versus bonds, or different securities within the same type, such as several common stocks. Remember that using this concept does not mean that the securities have to be sold and the gains or losses actually realized—that is, the cal- culation applies to realized or unrealized gains (see Appendix 2-A).
S o m e P r a c t i c a l A d v i c e
As you analyze and consider common stocks, never forget the important role that dividends have played historically in the TRs shown for large common stocks. For example, for the 85-year period 19262010, for the S&P 500 Index, the compound annual average return was 9.6 percent (rounded).
Dividends averaged 4 percent, and obviously were an important component of the TR. However, in the 1990s the dividend yield on the major stock indexes
continued to decline, and reached levels of about 1.5 percent in 2001 and 2002. Clearly, if all other things remained equal, TRs on the S&P 500 Index would decline relative to the past because of the sig- nificant decreases in the dividend yield. Not surpris- ingly, given the turmoil in the economy, more large companies cut dividends in 2008 than in any year since 2001. At the beginning of 2012, the dividend yield on the S&P 500 Index was approximately 2.1 percent.
What about the importance of dividends for individual stocks? Consider a company with an ordinary product consumed daily around the world, Coca-Cola.
What if a member of your family bought one share in 1919 for $40 when Coca-Cola had its IPO? One share would be worth $322,421 at the end of 2011.3 Coca-Cola also paid dividends. How much impact do you think the reinvested dividends would have on the
Example 6-3
The TRs for each year as shown in Table 6-1 can be calculated as shown in Equation 6-2. As a demonstration of these calculations, the TR for 2010 for the S&P 500 Index was 14.86 percent, calculated as:2TR2010 ¼½1257:641115:10þ23:12=1115:10¼:1486 or 14:86%
In contrast, in 2000 the TR was9.07 percent, calculated as:
TR2000¼½1320:281469:25þ15:69=1469:25¼ :0907¼ 9:07%
2Note carefully that these calculations do not account for the reinvestment of dividends during the year and will differ from the total returns calculated as part of the official series of returns later in the chapter.
3This example is based on“Never Underestimate the Winning Role Dividends Play,”AAII Dividend Investing, Internet mailing, February 25, 2012.
terminal wealth of this one share at the end of 2011? According to one calculation, that one share would have been worth $9.3 million at the end of 2011! Such is the impact of com- pounding reinvested dividends over a very long period of time.