The Standard & Poor's 500 stock index is a commonly used measure of stock market performance in the United States. In the table below, we give the value of the S&P 500 index on the first day of market trading for each year from 2000 to 2005.
YearS&P 500 Index
2000...................................1,455.22
2001...................................1,283.27
2002...................................1,154.67
2003.....................................909.03
2004...................................1,108.48
2005...................................1,211.92
a. Show that the percentage changes (rates of return) for the S&P 500 index for the years from 2000 to 2001 and from 2001 to 2002 are, respectively, - 11.8 percent and -10.0 percent (that is, - .118 and - .100 expressed as decimal fractions),
b. Find the rates of return for the S&P 500 index for each of the years: from 2002 to 2003; from 2003 to 2004; from 2004 to 2005.
c. Calculate the geometric mean return for the S&P 500 index over the period from 2000 to 2005.
d. Suppose that an investment of $ 1,000,000 is made in 2000 and that the portfolio performs with returns equal to those of the S&P 500 index. What is the investment portfolio worth in 2005?