Suppose the returns on long-term government bonds are normally distributed. Assu

Question

Suppose the returns on long-term government bonds are normally distributed. Assume long-term government bonds have a mean return of 5.2 percent and a standard deviation of 8.7 percent.

What is the approximate probability that your return on these bonds will be less than 3.5 percent in a given year? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).)

What range of returns would you expect to see 95 percent of the time? (Do not include the percent signs (%). Negative amount should be indicated by a minus sign. Input your answers from lowest to highest to receive credit for your answers. Round your answers to 2 decimal places (e.g., 32.16).)

What range would you expect to see 99 percent of the time? (Do not include the percent signs (%).Negative amount should be indicated by a minus sign. Input your answers from lowest to highest to receive credit for your answers. Round your answers to 2 decimal places (e.g., 32.16).)

Suppose the returns on long-term government bonds are normally distributed. Assume long-term government bonds have a mean return of 5.2 percent and a standard deviation of 8.7 percent.

Explanation / Answer

Requirement 1: In the normal probability distribution, approximately 3/5 of the observations are within one standard deviation of the mean. This means that 2/5 of the observations are outside one standard deviation away from the mean. Pr(R< –3.5 or R>14) = 2/5 one tail = Returns less than –3.5 percent =Pr(R< –3.5) = 4/5 80.00% Requirement 2: 95% level: Mean plus or minus 2 x standard deviations Lower Range = 5.2% - 2 x 8.7% -12.20% Lower Range = 5.2% + 2 x 8.7% 22.60% Expected range of returns = -12.20% to 22.60% Requirement 3: 99% level: Mean plus or minus 3 x standard deviations Lower Range = 5.2% - 3 x 8.7% -20.90% Lower Range = 5.2% + 3 x 8.7% 31.30% Expected range of returns = -20.90% to 31.30%

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