Expected value and variance with the S&P 500
One of the most common investments today is an S&P 500 index fund. If you want to know how much an investment in an index fund today will be worth by the time you retire, you can use expected value and variance.
The S&P 500 has produced a 6.5% inflation-adjusted compound annual growth rate since 1928. So, if you have 25 years until you retire, a $5,000 investment today has an expected value of $24,138 in equivalent spending power.
But consider that the S&P 500 has never produced a 6.5% real return on investment in a single calendar year. This is a case where investors are likely to experience variance.
Over a 25-year period, the historical S&P 500 real return has a standard deviation of 2.4 percentage points. That means there’s a 68% chance that the real compound annual returns for an S&P 500 index fund over 25 years is somewhere between 4.1% and 8.9%. That makes a $5,000 investment today likely to fall between $13,653 and 42,137. That’s a wide range of outcomes.
Understanding expected value can help you develop a plan for saving for retirement, but you also need to understand how variance can play a role in skewing your actual results away from the expected value.
