In: Statistics and Probability
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% and a standard deviation of 8.3%. For the same period, T-bills had an average return of 3.5% and a standard deviation of 2.5%. 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.) Probability of return greater than 10 percent % Probability of return less than 0 percent % 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.) Probability of T-bill return greater than 10 percent % Probability of T-bill return less than 0 percent % c. In one year, the return on long-term corporate bonds was −3.7 percent. How likely is it that such a low return will recur at some point in the future? T-bills had a return of 10.11 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.) Probability of return on long-term corporate bonds less than –3.7 percent % Probability of T-bill return greater than 10.11 percent %
LOng term corporate bonds mean return = 5%
standard deviation = 8.3%
T- bills average return = 3.5%
standard deviation = 2.5%
Q What is the probability that in any given year, the return on long-term corporate bonds will be greater than 10 percent?
Answer : Pr(x > 10%) = 1 - NORMDIST(x < 10% ; 5% ; 8.3% ; true) = 1 - 0.7265 = 0.27345 = 27.35%
Less than 0 percent?
Pr(x < 0%) = NORMDIST(x < 0% ; 5% ; 8.3% ; true) = 0.2735 = 27.35%
Q 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?
Answer :
Pr(y > 10%) = 1 - NORMDIST(y < 10% ; 3.5% ; 2.5% ; true) = 1 - 0.9953= 0.0047 = 0.47%
Less than 0 percent?
Pr(x < 0%) = NORMDIST(y < 0% ;3.5% ; 2.5% ; true) = 0.0807 = 8.07%
c. In one year, the return on long-term corporate bonds was −3.7 percent. How likely is it that such a low return will recur at some point in the future? T-bills had a return of 10.11 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?
Answer :
Here for corporate bonds
Pr(x < -3.7%) = NORMDIST(x < -3.7% ; 5% ; 8.3%; true) = 0.1473 = 14.73%
Now for T- bill
Pr(y > 10.11%) = 1 - NORMDIST(y < 10.11% ; 3.5% ; 2.5% ; true) = 1 - 0.9959 = 0.0041 = 0.41%