Homework SourseSuppose the returns on longterm government bonds are normall
Suppose the returns on long-term government bonds are normally distributed. Assume long-term government bonds have a mean return of 6.4 percent and a standard deviation of 9.1 percent.
Requirement 1: What is the probability that your return on these bonds will be less than 11.8 percent in a given year? Use the NORMDIST function in Excel ® to answer this question.
Requirement 2: What range of returns would you expect to see 95 percent of the time?
Requirement 3: What range would you expect to see 99 percent of the time?
Solution
1.
Here, we type
=NORMDIST(-11.8, 6.4, 9.1, 1)
Thus,
P(x<-11.8%) = 0.022750132 [ANSWER]
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2.
As the middle area is
Middle Area = P(x1<x<x2) = 0.95
Then the left tailed area of the left endpoint is
P(x<x1) = (1-P(x1<x<x2))/2 = 0.025
Thus, the z score corresponding to the left endpoint, by table/technology, is
z1 = -1.959963985
By symmetry,
z2 = 1.959963985
As
u = mean = 6.4
s = standard deviation = 9.1
Then
x1 = u + z1*s = -11.43567226
x2 = u + z2*s = 24.23567226
Thus, we expect -11.44% to 24.24%. [ANSWER]
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3.
As the middle area is
Middle Area = P(x1<x<x2) = 0.99
Then the left tailed area of the left endpoint is
P(x<x1) = (1-P(x1<x<x2))/2 = 0.005
Thus, the z score corresponding to the left endpoint, by table/technology, is
z1 = -2.575829304
By symmetry,
z2 = 2.575829304
As
u = mean = 6.4
s = standard deviation = 9.1
Then
x1 = u + z1*s = -17.04004666
x2 = u + z2*s = 29.84004666
Thus, we expect -17.04% to 29.84%. [ANSWER]
