The following information is available concerning the historical risk and return relationships in the U.S. capital markets:

U.S. CAPITAL MARKETS TOTAL ANNUAL RETURNS, 19902015
Investment Category	Arithmetic Mean		Geometric Mean		Standard Deviation of Returna
Common stocks	10.92	%	9.72	%	19.5	%
Treasury bills	4.40		4.36		3.9
Long-term government bonds	5.80		5.69		7.2
Long-term corporate bonds	5.25		5.08		9.8
Real estate	8.72		8.65		4.5
aBased on arithmetic mean.

Explain why the geometric and arithmetic mean returns are not equal and whether one or the other may be more useful for investment decision making.

The arithmetic average assumes -Select-compounding or interest-on-interestthe presence of simple interestItem 1 , while the geometric average assumes -Select-compounding or interest-on-interestthe presence of simple interestItem 2 .

a) For the time period indicated, rank these investments on a relative basis using the coefficient of variation from most to least desirable. Do not round intermediate calculations. Round your answers to two decimal places.

Rank	Investment Category	oefficient of variation, %
1	-Select-Common StocksLong-term corporate bondsLong-term government bondsReal estateTreasury billsItem 3
2	-Select-Common StocksLong-term corporate bondsLong-term government bondsReal estateTreasury billsItem 5
3	-Select-Common StocksLong-term corporate bondsLong-term government bondsReal estateTreasury billsItem 7
4	-Select-Common StocksLong-term corporate bondsLong-term government bondsReal estateTreasury billsItem 9
5	-Select-Common StocksLong-term corporate bondsLong-term government bondsReal estateTreasury billsItem 11

Assume the arithmetic mean returns in these series are normally distributed. Calculate the range of returns that an investor would have expected to achieve 95 percent of the time from holding long-term corporate bonds. Do not round intermediate calculations. Round your answers to two decimal places. Use a minus sign to enter negative values, if any.

b) Arithmetic: from % to %