Suppose the returns on longterm corporate bonds and Tbills a

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 5.7% and a standard deviation of 8.6%. For the same period, T-bills had an average return of 4.2% and a standard deviation of 2.8%. Use the NORMDIST function in Excel

Solution

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 5.7% and a standard deviation of 8.6%. For the same period, T-bills had an average return of 4.2% and a standard deviation of 2.8%. Use the NORMDIST function in Excel to answer the following questions:

Required:

(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. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)

  Probability of return greater than 10 percent                                               30.85

%

  Probability of return less than 0 percent                                                       25.37

%

(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. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)

  Probability of T-bill return greater than 10 percent                               1.92

%

  Probability of T-bill return less than 0 percent                                       6.68

%

(c)

In one year, the return on long-term corporate bonds was ?4.4 percent. How likely is it that such a low return will recur at some point in the future? T-bills had a return of 10.52 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. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)

  Probability of return on long-term corporate bonds less than 4.40 percent                 12.01

%

  Probability of T-bill return greater than 10.52 percent                                                        1.20