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 6.4 percent and a standard deviation of 9.1 percent. Requirement 1: What is the probability that your return on these bonds will be less than -11.8 percent in a given year? Use the NORMDIST function in Excel to answer this question. (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (eg., 32.16).) Probability % Requirement 2: What range of returns would you expect to see 95 percent of the time? (Negative amount should be indicated by a minus sign. Input your answers from lowest to highest to receive credit for your answers. Do not round intermediate calculations. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).) Expected range of returns % to % Requirement 3: What range would you expect to see 99 percent of the time? (Negative amount should be indicated by a minus sign. Input your answers from lowest to highest to receive credit for your answers. Do not round intermediate calculations. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).) Expected range of returns % to %

Explanation / Answer

1
In excel use NORM.DIST(-11.8%,6.4%,9.1% True)= 2.28%
2.
95% probability Range = 6.4% + 2 x 9.1%
95% probability Range = 6.4% + 18.2% = 24.6% ; 6.4% - 18.2%= -11.8%
Expected Range of Returns = -11.8% to 24.6%
3
99% probability Range = 6.4% + 3 x 9.1%
99% probability Range = 6.4% + 27.3% = 33.7% ; 6.4% - 27.3%= -20.9%
Expected Range of Returns = -20.9% to 33.7%

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