Question

An asset has an average historical rate of return of 12.1 percent and a variance of 0.01089091. What is the upper percentage range of returns would you expect to see approximately two-thirds of the time? (Round your answer to 2 decimal places. Omit the "%" sign in your response.)

Answer 1

Solution:
	The upper percentage range of returns = 22.54
Working Notes:
	two third of times means 2/3 = 0.666666 or 68 % of times
	Range of returns are calculated in 68% , 95% , 99 %
	Our case is of 68% or two third of times
	At 68% of confidence level range of return would be given by Avg. of returns ± 1 times multiple of standard deviation of the returns
	Variance = (Standard deviation )^2
	Standard deviation = (Variance)^(1/2)	=(0.01089091)^(1/2)
		=0.104359523
	R = µ ± 1 (s.d.)
	R= Expected range of returns
	µ = mean of returns or Avg. Of returns = 12.10%=0.121
	s.d. = Standard deviation of the bond returns = 0.104359523
	R = µ ± 1 (s.d.)
low	=0.121 - 0.104359523 = 0.0166404 = 1.66404 %
High	=0.121 + 0.104359523 =0.225359523 = 22.5359523 = 22.54 %
	R= Expected range of returns = 1.66% to 22.54%
	As question requirement is high range = 22.54
Please feel free to ask if anything about above solution in comment section of the question.