Over the past four years a stock produced returns of 23 perc

Over the past four years, a stock produced returns of 23 percent,-39 percent, 4 percent, and 16 percent, respectively. Based on these four years, what range of returns would you expect to see 99 percent of the time? O-82.39 percent to 86.41 percent O-82.39 percent to 84.39 percent O -82.39 percent to 88.56 percent O -78.46 percent to 84.39 percent O-78.46 percent to 86.41 percent

Solution

Solution: Answer is 2nd option -82.39 percent to 84.39 percent Working Notes: Average return(Er)= Sum of returns/ No. of returns =(0.23 - 0.39 +0.04+0.16)/4 =0.04/4 =0.01 =1% Standard deviation = Square root of (variance) Variance[(s.d.)^2] =[(r1 -Er)^2+(r2 -Er)^2+(r3 -Er)^2+(r4 -Er)^2]/(n-1) = [(0.23 - 0.01)^2 + (-0.39 - 0.01)^2 +(0.04 - 0.01)^2+(0.16 - 0.01)^2]/(4-1) =0.2318 /3 = 0.07726667 Standard deviation = Square root of (variance) =Square root of (variance) = ( 0.07726667)^(1/2) =0.277968829 =27.7968829 % =27.79688% At 99% of confidence level range of return would be given by Avg. of returns ± 3 times multiple of standard deviation of the returns of the long term government bond. R = µ ± 3 (s.d.) R= Expected range of returns µ = mean of returns or Avg. Of returns = 1% s.d. = Standard deviation of the bond returns = 27.79688% R = µ ± 3 (s.d.) low = 1% - (3 x 27.79688%) = 1% - 83.39064% = -82.39% High =1%+ (3 x 27.79688%) = 1% + 83.39064% = 84.39% R= Expected range of returns = -82.39 % to 84.39 % Please feel free to ask if anything about above solution in comment section of the question.