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When you start your career in the financial/investment industry there are a few tenants you learn quickly and never question.

- Compliance runs the show–resistance is futile.
- 8% is the return we assume people will earn on their investments because…

Finishing tenant #2 often involves reference to a vague statistic that's very tricky to track down exactly. The 8% assumption on investments became so sacrosanct that I estimate many gave up on trying to prove its legitimacy and decided instead it must be true because everyone else uses it.

I've spent a good deal of time over the years trying to locate the source that validates this assumption (8% average return on investments).

Surely there is an air-tight academic paper somewhere that gives credence to this ubiquitous assumption?

After hours of research, on separate occasions, I'm NOT here to tell you that the supporting stats don't exist. I am, however, going to tell you that I have yet to find them.

So, I set out on my own number crunching endeavor to validate the 8% assumption and what I discovered is quite interesting. What you read below may cause you to re-think “reasonable assumptions.”

While I have, I promise, spent a good amount of time trying to locate the research mentioned above that validates an 8% compound annual growth in stock market investments I did not come to the research/number crunching that I'm going to discuss today because of the lack of locatable evidence to support the practice. Instead, I got here mostly by accident.

I was on the phone with Brantley. I don't remember the details of the day or the conversation all that well. If I did I could detail the story with a tad more dramatic pizzaz–regretfully that won't be the case.

He was going off on a point that I was admittedly only half listening to at the time, but then he made a point that set off a sequence of thought processes that turned on my unrelenting research mind. His point was simply that to accomplish some goal (again, I can't remember exactly the topic of conversation) one would need to achieve a 9-ish percent rate of return.

And then he said something that set my mind into hyperdrive. His comment was something to the effect of “and we know how much more practically impossible that would be to accomplish.”

That comment immediately made me wonder. Has anyone ever attempted to calculate the probability of various returns in the market as targeted rates of return increase? Let me clarify because I know this is a bit obtuse and loaded with semantics.

We know that there are several possible results of your investment portfolio over the course of several years. We even suspect that the probability of getting a return no worse than say 4% is much higher than a return no worse than 10%. But how do these probabilities stack up as we move up the line for the rate of return? In other words, how much less likely is that 9% effective return versus an 8% rate of return?

And I suppose it's also fair to address the question: why do I care?

I'd argue it's a vital consideration because it establishes an understanding of the task you undertake should you attempt to achieve higher returns to reach various financial goals. One of the resulting recommendations financial advisors, et al. give clients who are falling short of accumulation goals is to take on additional risk in hopes to capitalize on the risk/reward assumption that goes along with general investing.

We have long argued that this is a foolish approach to wealth management and retirement planning

Alas, the “powers that be” have yet to come around to our way of thinking.

So, I set out to gather data and estimate probabilities of various returns for general stock market investing.

Harvesting data and preparing models for such a question requires some legwork. I needed sufficient data points to arrive at any reasonable conclusion, and unfortunately, the S&P 500 simply hasn't been around long enough to make any reasonable inferences about multi-year investment returns using annualized returns data.

So I used the trick many analysts have used before me to generate more data points and make meaningful inferences–rolling monthly data.

This exploded my data points into many multiples of what I had originally when taking the S&P500 annualized returns from 1928 through 2017 which permitted me to generate over 60 observable tranches each for a 10, 20, and 30-year investment scenario.

Using the rolling monthly data allowed me to observe market returns over a plethora of economic events.

Using this data, I was able to generate (as I mentioned) over 60 observations each for three different tranches. Specifically 10 years, 20 years, and 30 years. I then calculated the effective compound annual growth rate of each observation and from there used the results to estimate probabilities of achieving various rates of return.

When I set out, I hypothesized that the probability of an 8% return in each of the three tranches would come in somewhere around 50%.

To fully understand this hypothesis, you'd need to have a good grasp on some advanced aspects of probability theory that I'm not going to get into here. Simply understand that assuming the 8% assumption is correct, a resulting 50% or better probability would be a solid indicator of the assumptions viability.

I also hypothesized that that probability of a 6% or better return would likely come in well over 90%. This turned out to be way wrong.

**10 Year Scenario**

CAGR 10 Years | Probability of CAGR |

0 | 89% |

1 | 85% |

2 | 78% |

3 | 72% |

4 | 63% |

5 | 60% |

6 | 55% |

7 | 49% |

8 | 43% |

9 | 32% |

10 | 29% |

11 | 18% |

12 | 14% |

The probability of an 8% return over the 10-year scenario (i.e., investment for 10 years made once per year for 10 years) is 43%. This isn't terrible. It's short of the 50% I needed to have faith in the 8% average and sheds new light on the fragility of the traditional 8% assumption.

What's more troubling is how far below expectations 6% comes in.

At 55% this causes extreme pause on my end to believe assumptions as low as 6% per year over a 10 year period would be a reasonable assumption for modeling. Notice also that 0 comes in at 89%. Keep in mind that these results reflect a result no worse than the number you see on the table. This means there were years (11% of the data points to be exact) where the resulting return over 10 years was **negative**.

**20 Year Scenario**

CAGR 20 Years | Probability of CAGR |

0 | 100% |

1 | 98% |

2 | 97% |

3 | 88% |

4 | 83% |

5 | 71% |

6 | 65% |

7 | 54% |

8 | 48% |

9 | 38% |

10 | 28% |

11 | 12% |

12 | 8% |

The 20-year scenarios show a probability of 8% (over 20 years in this case) of 48%. This is closer to the 50% mark in my hypothesis but still short.

Again more troubling is that 6% falls well short of my hypothesized 90% plus result.

The good news is that no data points showed negative returns.

**30 Years**

30 Year CAGR | Probability of CAGR |

4 | 100% |

5 | 89% |

6 | 76% |

7 | 59% |

8 | 30% |

9 | 17% |

10 | 8% |

11 | 5% |

12 | 2% |

The probability of an 8% return or better drops significantly in the 30-year scenario. This seems incredibly counter-intuitive. Time is supposed to eliminate or substantially reduce risk and at the same time bring us closer to the magical targeted investment rate of return. Or so the amateur investment advisor would have you believe.

The probability of 6% significantly improved still but continues to fall well short of the 90% or more hypothesis.

No data points fell below 4%

We often think that time's relationship to investing helps us accomplish two things.

- It reduces the risk of loss, and
- it helps us draw closer to our desired result. This belief comes largely from a misunderstanding of conditional probabilities.

In truth, it's no surprise to true finance industry experts (or just someone with a basic understanding of conditional probabilities) that time brings just as much risk as it does insulation from risk. If this weren't true options pricing would make no sense at all.

But an even more critical take away here is that time doesn't increase the probability of great prosperity. A longer investment time horizon will not increase the likelihood that you achieve remarkable investment returns. Time **can only** diminish the probability that you realize extraordinary losses.

8% is a lofty assumption with a lower than anticipated probability in all scenarios. It's advisable to adjust assumptions downwards for wealth accumulation planning. The exact adjustment requires significantly more analysis than provided with this exercise, but somewhere between 5% and 7% seems reasonable given the data.

Brandon launched the Insurance Pro Blog in July of 2011 as a project to de-mystify the life insurance industry. Brandon was born in Northern New England, and he currently calls VT home. He attended Syracuse University and graduated with a triple major in Economics, Public Administration, and Political Science.

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