Hi Say an investment has an annual return of 10%, with a standard deviation of 20% I put in $100 so at year end I have 110 At end of year 2 I have $121 At end of year 3 $133.10 However the Std is 20% so really isn't it true that my final return will lie between an upper and lower amount? If so what would it be and how would you calculate it, just 133.10 +/- 20% or something more complicated? Or is it 133.10 plus/minus the sum of annual variance? Thanks in advance Matt

At the end of three years you have $ 133.10. Initial capital is $ 100.00. One way to calculate return is Cumulative Annual Growth Rate (CAGR) = profit * 100 / years of data / initial capital so ($ 133.10 - $ 100) * 100 / 3 years / $ 100 initial capital = 11.03 % per year with occasional equity fluctuations (positive and negative) of about 20 %.

Try alpha minus sigma squared over two. So: .10 - ( .20^2 ) / 2 = .08 Variance adjusted probable annual growth rate would be eight percent. So three year would be 1.08^3 - 1 = 0.26 or twenty-six percent. Explained in more detail in the attached paper, among others.

I think 20% is too high for investments. Maybe ok for trading. If I recall correctly from statistics -- and please if wrong someone correct me -- it means that with such investment you have: 68.27% of the annual returns lie between $100 +/- $20 95.45% between $100 +/- $40 99.73% between $100 +/- $60 which means that if you invest there is a probability you will lose a significant portion of you money. For such low return I would not accept a standard deviation more than 5%. Alex