6.1 Calculate the return and the return relative for the following assets: A preferred stock bought for $70 per share, held one year during which $5 per share dividends are collected, and sold for $63. A warrant bought for $11 and sold three months later for $13. A 12 percent bond bought for $870, held two years during which interest is collected annually, and sold for $930. 6.2 Calculate the arithmetic and geometric mean return for the S&P 500 (Table 6.1) for the years 20002002. How does this change when 2003 is included? 6.3 Calculate the index value for the S&P 500 (Table 6.1) assuming a $1 investment at the beginning of 1980 and extending through the end of 1989. Using only these index values, calculate the geometric mean for these years. 6.4 Assume that one of your relatives, on your behalf, invested $100,000 in a trust holding S&P 500 stocks at the beginning of 1926. Using the data in Table 6.6, determine the value of this trust at the end of 2018. 6.5 Now assume that your relative had invested $100,000 in a trust holding small stocks at the beginning of 1926. Determine the value of this trust at the end of 2018. 6.6 What if your relative had invested $100,000 in a trust holding long-term Treasury bonds at the beginning of 1926. Determine the value of this trust at the end of 2018. 6.7 Finally, what if this relative had invested $100,000 in a trust holding Treasury bills at the beginning of 1926. Determine the value of this trust by the end of 2018. 6.8 Calculate cumulative wealth for corporate bonds for the period 19262018, using a geometric mean of 5.9 percent. 6.9 Given a cumulative wealth index for Treasury bills of $20.48 for the period 19262018, calculate the geometric mean. 6.10 Given an inflation rate of 3 percent over the period 19262018 (geometric mean annual average), calculate the inflation-adjusted cumulative wealth index for corporate bonds as of year-end 2018. 6.11 Given a geometric mean inflation rate of 3 percent, determine how long it would take to cut the purchasing power of money in half using the rule of 72. 6.12 If a basket of consumer goods cost $1 at the beginning of 1926 and $15.63 at the end of 2018, calculate the geometric mean rate of inflation over this period. 6.13 Assume that Treasury bonds continued to have a geometric mean as shown in Table 6.6 until 100 years have elapsed. Calculate the cumulative ending wealth per $1 invested for this 100-year period. 6.14 Assume that over the period 19262018 the geometric mean rate of return for Treasury bonds was 5.5 percent. The corresponding number for the rate of inflation was 3 percent. Calculate, two different ways, the cumulative wealth index for government bonds for the period, on an inflation-adjusted basis. 6.15 Using the returns for the years 19261931 (years during the Great Depression) from Table 6.1, determine the geometric mean for this period. Show how the same result can be obtained from the ending wealth index value for 1931 of 0.7405. 6.16 Using data for three periods, construct a set of returns that will produce a geometric mean equal to the arithmetic mean. 6.17 According to Table 6.6, the standard deviation for common stocks for the period 19262018 was 19.8 percent. Using data from Table 6.1, calculate the standard deviation for the years 19811991 and compare your results. 6.18 Someone offers you a choice between $50,000 to be received 10 years from now, or a $20,000 portfolio of stocks guaranteed to earn a compound annual average return of 10.4 percent per year for the next 10 years. Determine the better alternative based solely on this information.