Suppose the returns on an asset are normally distributed. Suppose the historical

Question

Suppose the returns on an asset are normally distributed. Suppose the historical average annual return for the asset was 6.2 percent and the standard deviation was 8.3 percent. Refer to Table A.5.

What is the probability that your return on these bonds will be less than -2.1 percent in a given year? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

What range of returns would you expect to see 95 percent of the time? (Enter your answers for the range from lowest to highest. Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))

What range would you expect to see 99 percent of the time? (Enter your answers for the range from lowest to highest. Negative amounts should be indicated by a minus sign.Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))

What is the probability that your return on these bonds will be less than -2.1 percent in a given year? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Explanation / Answer

The range of returns

Range = Returns + / - z-value x Std. Dev.

a) z-value = 1 for 68.26 percent time, Range = 6.2% +/- 8.3% , i.e. -2.1% or 14.5%

Hence, the probability for returns to be less than -2.1% = (1 - 68.26%) / 2 = 15.87%

b) z-value = 1.96 for 95%

Range of returns = 6.2% + / - 1.96 x 8.3% = -10.07% to 22.47%

c) z-value = 2.576 for 99%

Range of returns = 6.2% + / - 2.576 x 8.3% = -15.18% to 27.58%

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.