1 A stock has an annual return of 11 percent and a standard

1. A stock has an annual return of 11 percent and a standard deviation of 44 percent. What is the smallest expected loss over the next year with a probability of 1 percent? (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the \"%\" sign in your response.)

  Smallest expected loss _________%

2. A stock has an annual return of 11.6 percent and a standard deviation of 47 percent. What is the smallest expected gain over the next year with a probability of 1 percent? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the \"%\" sign in your response.)

Solution

1.

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.01      
          
Then, using table or technology,          
          
z =    -2.326347874      
          
As x = u + z * s,          
          
where          
          
u = mean =    11      
z = the critical z score =    -2.326347874      
s = standard deviation =    44      
          
Then          
          
x = critical value =    -91.35930646% = -91.36% [ANSWER]

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2.

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.99      
          
Then, using table or technology,          
          
z =    2.326347874      
          
As x = u + z * s,          
          
where          
          
u = mean =    11.6      
z = the critical z score =    2.326347874      
s = standard deviation =    47      
          
Then          
          
x = critical value =    120.9383501 = 120.94% [ANSWER]