Suppose the returns on long-term corporate bonds and T-bills are normally distri

Question

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 6.7% and a standard deviation of 10%. For the same period, T-bills had an average return of 5.2% and a standard deviation of 4.2%. 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                     ____%
  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. Enter your answers as a percentage 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 5.3 percent. How likely is it that such a low return will recur at some point in the future? T-bills had a return of 11.72 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 –5.30 percent     _____%

Probability of T-bill return greater than 11.72 percent           _____%

Explanation / Answer

(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

Z = (10%-6.7% )/10%

Z = 0.33

Probability of return = 1- normsdist(z)

Probability of return = 1-normsdist(0.33)

Probability of return = 37.07%

  Probability of return less than 0 percent         

Z = (0%-6.7% )/10%

Z = -0.67                 

Probability of return = normsdist(z)

Probability of return = normsdist(-0.67)

Probability of return = 25.14%

(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

Z = (10%-5.2% )/4.2%

Z = 1.142857143

Probability of return = 1- normsdist(z)

Probability of return = 1-normsdist( 1.142857143)

Probability of return = 12.65%

Probability of T-bill return less than 0 percent

Z = (0%-5.2% )/4.2%

Z = -1.238095238

Probability of return = normsdist(z)

Probability of return = normsdist( -1.238095238)

Probability of return = 10.78%

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