# The Accumulation Of Risk and Return

From 12/31/71 through 1/31/17 the monthly return and standard deviation, of the S&P 500 was 0.94% and 4.38%. Monthly return is not random and therefore 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 (1.0094)^360 or 2802.61%. The standard deviation after 30 years is SQRT(360)*4.38% or 83.1%. Since the returns follow a normal distribution, the probability of the actual return being one standard deviation below the expected return (2802.61% - 83.10% = 2719.51%) is 15.9%. The probability of being two standard deviations below the expected return (2802.61% - 2*83.10% = 2636.41%) is 2.3%. The probability of being three standard deviations below the expected return (2802.61% - 3*83.10% = 2553.31%) is 0.14%.

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The information presented here is the opinion of the author and may quickly become outdated and is subject to change without notice.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 article are compiled from sources believed to be reliable, however accuracy cannot be guaranteed. No person should make an investment decision in reliance on the information presented here.

The information presented here is distributed for education purposes only and is not an offer to buy or sell or a solicitation of an offer to buy or sell any security or participate in any particular trading strategy.

Performance data showing past performance results is no guarantee of future returns.