Question

an investment had an average return of 15% and a standard deviation of 20% over the last 100 years. Assuming the investment had a normal distribution, how many of the 100 years did the investment lose more than 5%?

Answer 1

Answer:

Average return = mean = 15%

Standard deviation = 20%

Approximately 68% of the returns fall within one standard deviation of mean:

That implies 68% of times return will be between (15% + 20% = ) 35% and (15% - 20% = ) - 5%.

Hence number of time return will be less than - 5% is = (100% - 68%) / 2 = 16%

Hence in 100 years expected number of years the investment will lose more than 5% = 16