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Problem 10-28 Using Probability Distributions [LO 3] Suppose the returns on long-term corporate bonds and T-bills...

Problem 10-28 Using Probability Distributions [LO 3] Suppose the returns on long-term corporate bonds and T-bills are normally distributed. Assume for a certain time period, long-term corporate bonds had an average return of 5.8% and a standard deviation of 8.9%. For the same period, T-bills had an average return of 4.3% and a standard deviation of 3.1%. Use the NORMDIST function in Excel® to answer the following questions: a. What is the probability that in any given year, the return on long-term corporate bonds will be greater than 10 percent? Less than 0 percent? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) b. What is the probability that in any given year, the return on T-bills will be greater than 10 percent? Less than 0 percent? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) c. In one year, the return on long-term corporate bonds was −4.7 percent. How likely is it that such a low return will recur at some point in the future? T-bills had a return of 10.62 percent in this same year. How likely is it that such a high return on T-bills will recur at some point in the future? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Solutions

Expert Solution

Answer -

The Excel NORMDIST function calculates the Cumulative Normal Distribution by specifying TRUE as the type of distribution to be used.

The syntax of the function is:

NORMDIST(x, mean, standard_dev, cumulative)

Where-

x is the value at which distribution function is evaluated

mean is the average of the distribution

standard_dev is the standard deviation of the distribution

cumulative is the logical argument specifying TRUE as the type of distribution to be used

In the question following information is given:

Long-term corporate bonds T-bills
Average Return (mean) 0.058 0.043
Standard Deviation (standard_dev) 0.089 0.031

Answer - a

Using Excel NORMDIST function -

Probability of Long-term corporate bonds return less than 10% = NORMDIST(0.10, 0.058, 0.089, TRUE) = 0.6815

Probability of Long-term corporate bonds return greater than 10% = 1 - 0.6815 = 0.3185 or 31.85%

Probability of Long-term corporate bonds return less than 0% = NORMDIST(0, 0.058, 0.089, TRUE)

Probability of Long-term corporate bonds return less than 0% = 0.2573 or 25.73%

Answer - b

Using Excel NORMDIST function -

Probability of T-bills return less than 10% = NORMDIST(0.10, 0.043, 0.031, TRUE) = 0.9670

Probability of T-bills return greater than 10% = 1 - 0.9670 = 0.0330 or 3.30%

Probability of T-bills return less than 0% = NORMDIST(0, 0.043, 0.031, TRUE)

Probability of T-bills return less than 0% = 0.0827 or 8.27%

Answer - c

Using Excel NORMDIST function -

Probability of Long-term corporate bonds return less than -4.7% = NORMDIST(-0.047, 0.058, 0.089, TRUE)

Probability of Long-term corporate bonds return less than -4.7% = 0.1190 or 11.90%

Using Excel NORMDIST function -

Probability of T-bills return less than 10.62% = NORMDIST(0.1062, 0.043, 0.031, TRUE) = 0.9793

Probability of T-bills return greater than 10.62% = 1 - 0.9793 = 0.0207 or 2.07%


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