Saving For Retirement

In the post Past Performance Is NOT Indicative Of Future Results we saw that there is great variability in the returns of the S&P 500 over a ten or even a twenty five year period. This has great implications on how much money an investor can expect to have at the end of the day.

One of the key underpinnings of any investment is time. In particular, we only live once and we only have a finite amount of years in our lives. Thus we only have a finite amount of years to grow our investment. If ten or twenty five years have gone by and our investment has not performed as we had hoped, that time is gone forever. We are now 10 or 25 years older and our capital is not where we want it or need it to be.

Given the variability of the stock market returns it is thus mission critical to plan ahead so that we do not come up short in the future. To do so we can once again use statistics to set our expectations and make plans we are comfortable with.

Planning Ahead

Let’s start with an example of a ten year investment. In the post Past Performance Is NOT Indicative Of Future Results we saw that the probability of returns for a 10 year investment in the S&P 500 are as follows:

Probability CAGR
95.43% -1.05%
49.45% 7.18%
5.04% 14.28%

This means that if we make an investment in the S&P 500 and hold it for ten years there is a probability of 95.43% that we will make a CAGR of -1.05% or greater. Similarly there is a 49.45% probability that we will make a CAGR of 7.18% or greater and a probability of only 5.04% that we will make a return of 14.28% or more. Let’s now have a look at what these differences in returns have on the size of our future nest egg.

Using the Financial Calculators on our website we can determine that our nest egg for a $100,000 investment will be as follows:

Probability CAGR Nest Egg
95.43% -1.05% $89,087.48
49.45% 7.18% $219,777.74
5.04% 14.28% $476,609.46

These numbers mean that if you need at least $475,000 in your account so that you can retire, your probability of doing so in ten years is only 5.04%. There is a 49.45% chance that you’ll have at least $219,777.74. Ironically though, you can be very confident, 95.43% confident to be exact, that you’ll have at least $89,087.48.

Looking at the case of a 25 year investment in the S&P 500 the numbers are as follows:

Probability CAGR Nest Egg
96.56% 4.05% $286,115.97
51.28% 6.82% $586,017.88
5.04% 10.87% $1,666,776.07

Similar conclusions can be drawn here as well. If an investor needs about one million and a half dollars to retire, then the probability that they can do so after 25 years invested in the S&P 500 is only 5.04%. There is a 51.28% chance that they will have at least $586,017.68. However, they can say with confidence, 96.56% confidence, that they will have at least $286,115.97.

Dollar Cost Averaging

The above numbers offer a better picture than reality since in most cases investors do not put a big lump sum at the outset. Instead they probably contribute money to their savings on a regular basis as described in the post Dollar Cost Averaging. If we were to utilize this approach for our $100,000 investment over a 10 year period then the numbers would be as follows:

Probability CAGR Nest Egg
95.00% -0.51% $106,993.07
50.25% 3.79% $136,214.23
5.23% 8.69% $183,205.96

The above numbers are for a monthly investment of $833.33 over a 10 year period. Although dollar cost averaging is effective in distributing the investments such that what was previously a loss is now a small gain the picture remains the same. The investor has very low confidence that they can make at least $183,205.96. In addition, this best case scenario is less than half of the $476,609.46 they could potentially make if they invest all the money at the outset.

Investing With Confidence

In conclusion it is worth noting that scientists and mathematicians usually look at the 95% confidence level to determine whether a project or an experiment is worth looking further into. This is a widely accepted level in all areas of practice. Why is it not even considered in conventional investing wisdom? The numbers usually cited in financial media and literature are closer to 6% or more which represent a probability of 50% or less. As mentioned before, this is no better than a coin flip !

Based on the tables above, an investor with holdings in the S&P 500 should use an expected annual return of 4.05% to estimate where his current portfolio will be 25 years from now assuming no further contributions. The expected rates of return for a 10 year investment or for an investment using dollar cost averaging should be even lower.

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