Suppose the returns on long-term corporate bonds are normally distributed. The a

Question

Suppose the returns on long-term corporate bonds are normally distributed. The average annual return for long-term corporate bonds from 1926 to 2007 was 6.2 percent and the standard deviation of those bonds for that period was 8.3 percent. Picture Required:

(a) Based on this historical record, what is the approximate probability that your return on these bonds will be less than -3.3 percent in a given year? (Do not round intermediate calculations.)

(b) What range of returns would you expect to see 95 percent of the time? (Do not round intermediate calculations.)

(c) What range would you expect to see 99 percent of the time? (Do not round intermediate calculations.)

Explanation / Answer

Suppose the returns on long-term corporate bonds are normally distributed. The average annual return for long-term corporate bonds from 1926 to 2007 was 6.2 percent and the standard deviation of those bonds for that period was 8.3 percent. Picture Required:

(a) Based on this historical record, what is the approximate probability that your return on these bonds will be less than -3.3 percent in a given year? (Do not round intermediate calculations.)

Z value for -3.3, z=(-3.3-6.2)/8.3 =-1.14

P( x < -3.3) = P9 z <-1.14)

= 0.1271

(b) What range of returns would you expect to see 95 percent of the time? (Do not round intermediate calculations.)

Z value for 95% is 1.96

Lower value =6.2-1.96*8.3 =-10.068

Upper value =6.2+1.96*8.3 =22.468

(c) What range would you expect to see 99 percent of the time? (Do not round intermediate calculations.)

Z value for 99% is 2.576

Lower value =6.2-2.576*8.3 =-15.1808

Upper value =6.2+2.576*8.3 =27.5808

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