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 5.8 percent and the standard deviation of those bonds for that period was 8.2 percent.

Based on this historical record, what is the approximate probability that your return on these bonds will be less than -3.5 percent in a given year? (Do not round intermediate calculations.) What range of returns would you expect to see 95 percent of the time? (Do not round intermediate calculations.) What range would you expect to see 99 percent of the time? (Do not round intermediate calculations.)

Answer 1

Anuxi iun 'nfamation, Expeuted Petun= 5.8 standayd Deviationco) = g.2. aThe Proba bifty that Teturn uwilt be less than-3-5 meanstandard Deviation PCx-.) P(2 (-3.5-5./3.3 8.a P(z-1.13446 PCt -13)0.1aqa xioo = ia.9a neastfom-tabk value) Pz-1.13) = 12.7aq The Expertel Ren-la vahue iso). tums At25. Prcdi tion level, Value 2

LowtY volue , hies vadue -10.64.) he Yang yetun-1064,aa.a YetesEpeced ietun- 1+ ( vedue) (sD) The At 9 Poudiction keveb, val = 3 S0 ( lowt1yalue , hur value 58-(3)(a), 58+(2) (3.a)) 18.91. 30.141 Yatarns=1,e js0.4) .Thi