Suppose the average return on Asset A is 6.1 percent and the standard deviation

Question

Suppose the average return on Asset A is 6.1 percent and the standard deviation is 8.1 percent and the average return and standard deviation on Asset B are 3.3 percent and 2.7 percent, respectively. Further assume that the returns are normally distributed. Use the NORMDIST function in Excel® to answer the following questions. (A) What is the probability that in any given year, the return on Assets A will be greater than 9 percent? Less than 0 percent? (B) What is the probability that in any given year, the return on Asset B will be greater than 9 percent? Less than 0 percent? (c-1) In a particular year, the return on Asset A was 4.20 percent. How likely is it that such a low return will recur at some point in the future? (C-2) Asset B had a return of 9.10 percent in this same year. How likely is it that such a high return on Asset B will recur at some point in the future?

Explanation / Answer

ASSET A DATA
Mean ( u ) =6.1
Standard Deviation ( sd )=8.1
Normal Distribution = Z= X- u / sd ~ N(0,1)                  

ASSET B DATA

Mean ( u ) =3.3
Standard Deviation ( sd )=2.7
Normal Distribution = Z= X- u / sd ~ N(0,1)  

a)
                  
P(X > 9) = (9-6.1)/8.1
= 2.9/8.1 = 0.358
= P ( Z >0.358) From Standard Normal Table
= 0.3602                  
P(X < 0) = (0-6.1)/8.1
= -6.1/8.1= -0.7531
= P ( Z <-0.7531) From Standard Normal Table
= 0.2257

b)

P(X > 9) = (9-3.3)/2.7
= 5.7/2.7 = 2.1111
= P ( Z >2.111) From Standard Normal Table
= 0.0174  

P(X < 0) = (0-3.3)/2.7
= -3.3/2.7= -1.2222
= P ( Z <-1.2222) From Standard Normal Table
= 0.1108                  
              

c)
P(X < -4.2) = (-4.2-6.1)/8.1
= -10.3/8.1= -1.2716
= P ( Z <-1.2716) From Standard Normal Table
= 0.1018                  
It is 10% of chace that such a low return will recur at some point in the future

d)
P(X > 9.1) = (9.1-3.3)/2.7
= 5.8/2.7 = 2.1481
= P ( Z >2.148) From Standard Normal Table
= 0.0159                  
It is 1% of chace that such a high return will recur at some point in the future

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