The portfolio value plots show the accumulation of both risk and return in the investment account. The bottom line on the graph below shows two standard deviations below the mean return. The probability of the portfolio being above this value is 97.7%. This line hits zero at age 78, therefore the probability of not running out of money through age 78 is 97.7%. The second line from the bottom shows one standard deviation below the mean. The probability of the portfolio bein
Using the monthly return and standard deviation, of the S&P 500, 0.94% and 4.38% respectively, since monthly return is not random, the expected return after 12 months is (1.0094)^12, or 11.88%. The variability in the monthly data is random and therefore the volatility, or standard deviation, accumulates as the square root of the sum of squares. The annual standard deviation is SQRT(12) times the monthly standard deviation or 15.17%. The expected return after 30 years is (1.
For an investment portfolio, we care about the probability the portfolio is above or below a desired value. For the S&P 500, which is normally distributed, there is a 15.9% probability the monthly return will be lower than -3.4% (which is 0.94% - 4.38%, or one standard deviation below the mean). There also would be a 2.3% probability the monthly return would be lower than -7.8% (which is 0.94% - 2*(4.38%), or two standard deviations below the mean). Disclosure: The informati
Assets with a lower standard deviation, or volatility, have less variation in their return than assets with higher volatility. Below is a plot of the asset values over time of two assets with equal return and different volatility. The asset with lower volatility has less variability in performance. Disclosure: The information presented here is the opinion of the author and may quickly become outdated and is subject to change without notice. All material presented in this art