# Variance and standard deviatio

Variance and standard deviation

?(expected).

Bacon and? Associates, a famous Northwest think? tank, has provided probability estimates for the four potential economic states for the coming year in the following? table:

LOADING…. The probability of a boom economy is 22%?, the probability of a stable growth economy is 40?%, the probability of a stagnant economy is 21%? and the probability of a recession is 17?%.

Calculate the variance and the standard deviation of the three? investments: stock, corporate? bond, and government bond. If the estimates for both the probabilities of the economy and the returns in each state of the economy are? correct, which investment would you? choose, considering both risk and? return?

?Hint: Make sure to round all intermediate calculations to at least seven? (7) decimal places.

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# Variance and standard deviatio

Variance and standard deviation. Calculate the variance and the standard deviation of U.S. Treasury? bills, long-term government? bonds, and? small-company stocks for 1950 to? 1959, 1960 to? 1969, 1970 to? 1979, and 1980 to 1989 from Table 8.1. Which had the highest? variance? Which had the lowest? variance? Click on the Spreadsheet Learning Aid to see Table

8.1long dash—?Year-by-Year

?Returns, 1950-1999.

What is the variance of U.S. Treasury bills for 1950 to? 1959, 1960 to? 1969, 1970 to? 1979, and 1980 to? 1989?

The variance of U.S. Treasury bills for 1950 to 1959 is

0.00554______?%.

?(Round to five decimal? places.)

The variance of U.S. Treasury bills for 1960 to 1969 is _____

?%.

?(Round to five decimal? places.)

The variance of U.S. Treasury bills for 1970 to 1979 is

0.03809____?%.

?(Round to five decimal? places.)

The variance of U.S. Treasury bills for 1980 to 1989 is

0.08285_____?%.

?(Round to five decimal? places.)

What is the standard deviation of U.S. Treasury bills for 1950 to? 1959, 1960 to? 1969, 1970 to? 1979, and 1980 to? 1989?

The standard deviation of U.S. Treasury bills for 1950 to 1959 is

0.744____?%.

?(Round to three decimal? places.)

The standard deviation of U.S. Treasury bills for 1960 to 1969 is

____?%.

?(Round to three decimal? places.)

The standard deviation of U.S. Treasury bills for 1970 to 1979 is

1.952?%.

?(Round to three decimal? places.)

The standard deviation of U.S. Treasury bills for 1980 to 1989 is

2.878?%.

?(Round to three decimal? places.)

What is the variance of? long-term government bonds for 1950 to? 1959, 1960 to? 1969, 1970 to? 1979, and 1980 to? 1989?

The variance of ? long-term government bonds for 1950 to 1959 is

0.21066 ?%.

?(Round to five decimal? places.)

The variance of ? long-term government bonds for 1960 to 1969 is

0.39149 ?%.

?(Round to five decimal? places.)

The variance of ? long-term government bonds for 1970 to 1979 is

0.40207 ?%.

?(Round to five decimal? places.)

The variance of ? long-term government bonds for 1980 to 1989 is

?%.

?(Round to five decimal? places.)

What is the standard deviation of? long-term government bonds for 1950 to? 1959, 1960 to? 1969, 1970 to? 1979, and 1980 to? 1989?

The standard deviation of? long-term government bonds for 1950 to 1959 is

?%.

?(Round to three decimal? places.)

The standard deviation of? long-term government bonds for 1960 to 1969 is

6.257 ?%.

?(Round to three decimal? places.)

The standard deviation of? long-term government bonds for 1970 to 1979 is

6.341 %.

?(Round to three decimal? places.)

The standard deviation of? long-term government bonds for 1980 to 1989 is

11.175 ?%.

?(Round to three decimal? places.)

Calculate the variance of? small-company stocks for 1950 to? 1959, 1960 to? 1969, 1970 to? 1979, and 1980 to? 1989?

The variance of? small-company stocks for 1950 to 1959 is

8.67926 ?%.

?(Round to five decimal? places.)

The variance of? small-company stocks for 1960 to 1969 is

15.38544 ?%.

?(Round to five decimal? places.)

The variance of? small-company stocks for 1970 to 1979 is

13.15023 ?%.

?(Round to five decimal? places.)

The variance of? small-company stocks for 1980 to 1989 is

3.40688 ?%.

?(Round to five decimal? places.)

Calculate the standard deviation of? small-company stocks for 1950 to? 1959, 1960 to? 1969, 1970 to? 1979, and 1980 to? 1989?

The standard deviation of? small-company stocks for 1950 to 1959 is

29.461 ?%.

?(Round to three decimal? places.)

The standard deviation of? small-company stocks for 1960 to 1969 is

39.224 ?%.

?(Round to three decimal? places.)

The standard deviation of? small-company stocks for 1970 to 1979 is

36.263 ?%.

?(Round to three decimal? places.)

The standard deviation of? small-company stocks for 1980 to 1989 is

18.458 ?%.

?(Round to three decimal? places.)

Which investment had the highest? variance? ?(Select the best? response.)

*** HERE IS THE DATA NEEDED***

 Table 8.1 Year-by-Year Returns, 1950-1999 Year Three-Month U.S.Treasury Bills Long-Term Government Bonds Large Company Stocks Small Company Stocks 1950 1.20% -0.96% 32.68% 48.45% 1951 1.49% -1.95% 23.47% 9.41% 1952 1.66% 1.93% 18.91% 6.36% 1953 1.82% 3.83% -1.74% -5.66% 1954 0.86% 4.88% 52.55% 65.13% 1955 1.57% -1.34% 31.44% 21.84% 1956 2.46% -5.12% 6.45% 3.82% 1957 3.14% 9.46% -11.14% -15.03% 1958 1.54% -3.71% 43.78% 70.63% 1959 2.95% -3.55% 12.95% 17.82% 1960 2.66% 13.78% 0.19% -5.16% 1961 2.13% 0.19% 27.63% 30.48% 1962 2.72% 6.81% -8.79% -16.41% 1963 3.12% -0.49% 22.63% 12.20% 1964 3.54% 4.51% 16.67% 18.75% 1965 3.94% -0.27% 12.50% 37.67% 1966 4.77% 3.70% -10.25% -8.08% 1967 4.24% -7.41% 24.11% 103.39% 1968 5.24% -1.20% 11.00% 50.61% 1969 6.59% -6.52% -8.33% -32.27% 1970 6.50% 12.69% 4.10% -16.54% 1971 4.34% 17.47% 14.17% 18.44% 1972 3.81% 5.55% 19.14% -0.62% 1973 6.91% 1.40% -14.75% -40.54% 1974 7.93% 5.53% -26.40% -29.74% 1975 5.80% 8.50% 37.26% 69.54% 1976 5.06% 11.07% 23.98% 54.81% 1977 5.10% 0.90% -7.26% 22.02% 1978 7.15% -4.16% 6.50% 22.29% 1979 10.45% 9.02% 18.77% 43.99% 1980 11.57% 13.17% 32.48% 35.34% 1981 14.95% 3.61% -4.98% 7.79% 1982 10.71% 6.52% 22.09% 27.44% 1983 8.85% -0.53% 22.37% 34.49% 1984 10.02% 15.29% 6.46% -14.02% 1985 7.83% 32.68% 32.00% 28.21% 1986 6.18% 23.96% 18.40% 3.40% 1987 5.50% -2.65% 5.34% -13.95% 1988 6.44% 8.40% 16.86% 21.72% 1989 8.32% 19.49% 31.34% 8.37% 1990 7.86% 7.13% -3.20% -27.08% 1991 5.65% 18.39% 30.66% 50.24% 1992 3.54% 7.79% 7.71% 27.84% 1993 2.97% 15.48% 9.87% 20.30% 1994 3.91% -7.18% 1.29% -3.34% 1995 5.58% 31.67% 37.71% 33.21% 1996 5.50% -0.81% 23.07% 16.50% 1997 5.32% 15.08% 33.17% 22.36% 1998 5.11% 13.52% 28.58% -2.55% 1999 4.80% -8.74% 21.04% 21.26% 50-year average 5.226% 5.936% 14.890% 17.103% Standard Deviation 2.980% 9.493% 16.695% 29.043% Note: Sources for annual returns are the Center for Research on Security Prices, Standard &Poor’s 500 index, Russell 2000 index, and Solomon-Smith Barney U.S. Treasury bill index.

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