Question

Over a particular period, an asset had an average return of 10.9 percent and a standard deviation of 21.2 percent. What range of returns would you expect to see 68 percent of the time for this asset? (A negative answer should be indicated by a minus sign. Input your answers from lowest to highest to receive credit for your answers. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Expected range of returns % to 1% What about 95 percent of the time? (A negative answer should be indicated by a minus sign. Input your answers from lowest to highest to receive credit for your answers. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Expected range of returns | % to

Answer 1

Based on 68-95-99 rule

68% 95% 99% -30 +10 -20 -10 +20 +30

a) So for 68%, the range would be +/-1 Standard deviation

Lower value = Average - (1 * Standard deviation) = 10.9% - 21.2% = -10.30%

Higher value = Average + (1 * Standard deviation) = 10.9% + 21.2% = 32.10%

b) For 95%, the range would be +/-2 Standard deviation

Lower value = Average - (1 * Standard deviation) = 10.9% - (2 * 21.2%) = -31.50%

Higher value = Average + (1 * Standard deviation) = 10.9% + (2 * 21.2%) = 53.30%