Required: Suppose the returns on long-term corporate bonds are normally distribu

Question

  

        
      

       
       

         

Required: 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 6.4 percent and the standard deviation of those bonds for that period was 9.5 percent. Based on this historical record, what is the approximate probability that your return on these bonds will be less than -3.4 percent in a given year? What range of returns would you expect to see 95 percent of the time? What range would you expect to see 99 percent of the time?

Explanation / Answer

(a) P(X<-3.4) = P((X-mean)/s <(-3.4-6.4)/9.5)= P(Z<-1.03) =0.1515 (from standard normal table)

(b) So 95 percent of the time is

xbar +/- 2*s

--> 6.4 +/- 2*9.5

--> (-12.6, 25.4)

(c) So 99 percent of the time is

xbar +/- 3*s

--> 6.4 +/- 3*9.5

--> (-22.1, 34.9)

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