This is another hairy question in investment planning that defies easy answers. To say that “it depends” seems to be a cop-out, but is actually an accurate answer, qualitatively speaking. Yet I think many investors would like quantitative answers, even if this requires making certain assumptions. This is what I plan to do in this blog.

The reason why there isn’t a single right answer to the “how long” question is because many factors determine investment wealth. The careful reader of my last blog would have picked up some of these factors, but here is a recap:

- Investment goal
- Rate(s) of return
- Portfolio risk
- Your risk tolerance
- Initial investment
- Subsequent investments

My last blog employs simulations in Excel to project retirement shortfall risk. The example assumes that a 30-year investor (John) is investing to build a retirement fund that is sufficient to last him 25 years (from age 65 to 90). For that application, I fixed the investment time horizon to 35 years (age 30 to 65) to focus on the asset allocation problem, i.e, what mix of stocks and bonds John should invest to have a good chance of achieving his goal. It turns out that with an assumed 6% return for stocks and 3% for bonds and a suitable investment glide path, John could safely meet his retirement needs with relatively low shortfall risk at any age. In that sense, 35 years is a long enough investment horizon for John.

We can also define long-term as the time needed for wealth to reach a specific **wealth** **target, **expressed as a dollar figure. For example, you may want to have $4 million by year X in the future for whatever purpose not restricted to funding retirement. Due to risk, your *actual* wealth may differ from your desired wealth. Hence, we have to re-frame your goal in terms of average wealth or median wealth. I will frame your goal using the median since the median is the mid-point of the wealth distribution while the average is biased (upwards).

If you are a “kia su” or loss-averse investor, you might also want to specify a secondary goal such as having a 75% chance of accumulating a terminal wealth of at least $3.5 million (i.e., a shortfall probability of only 25%). These two conditions -median wealth of $4 million and shortfall probability of 25% define your overall investment goal.

As in my previous blog, you are assumed to invest an initial sum of $100,000. After that, you will put in regular capital injections, starting with $24,000 at the end of the first year and increasing this sum by 5% each year until the end of your investment horizon.

Since the appropriate investment horizon also depends on how much risk one is prepared to take, I will simulate wealth based on two contrasting asset allocations. The first asset allocation is a play safe one – invest all monies in bonds (average annual return of 3% and risk of 2%). The second asset allocation is to invest according to a glide path similar to the one discussed in my previous blog. This glide path involves investing the following percentage of your portfolio in stocks at different life stages:

70% between 30 and 39

60% between 40 and 49

50% between 50 and 59

40% from 60

Here are the simulation results summarized by a wealth bar chart.

The green bars show terminal wealth statistics assuming that you invested only in bonds The red bars show terminal wealth statistics assuming you invested using the glide path. All simulation results are for a time horizon of **37 years**.

The red bars show that 37 years is long enough to meet both conditions that define your goal, namely a median wealth of $4 million (the simulated median is actually higher at $4.43 million) and a 25th percentile wealth of at least $3.5 million (the simulated 25th percentile is $3.67 million). For those who are rusty with statistics, the 25th percentile is the value such that 25% of values are below it. The tallest red bar is the 75th percentile. This is the value such that 25% of values are above it (the awesome zone!). The 75th percentile for the red bar is $5.6 million.

All the green bars are shorter than the red bars. This is expected. Since you did not take much risk, you shouldn’t expect high returns. Here are the summary statistics for the green bars

- Median wealth: $3.67 million, lower than what you desire
- 25th percentile: $3.51 million, just meeting your threshold
- 75th percentile: $3.84 million, still lower than your desired median wealth)

So, how long is the long-term? In the context of this example, 37 years, provided you invest in a mix of stocks and bonds instead of playing safe.

Playing safe can be a risky choice when one has demanding goals.