What value year by year along the way?

A third important way to assess and compare portfolios in dollar-result probabilities for a plan is probebilities for dollar value at end of every year from now to final value at the end of the plan.

For the same plan and Port A represented in red in the graphs just above, the year-by-year value probabilities can be shown on a graph like this:


In this graph, each year’s value probabilities are represented by a symbol shown and labeled in the graph’s upper left.

In line with the probability-percent labeling of that symbol key, the symbols for the years mean the following: Each year there’s 50% probability the value will be at least as high as that year’s horizontal line; each year’s thick vertical line goes from the value you have 80% probability of beating, up to the value you have 20% of beating; and each year’s thin vertical line goes from the value you have 95% probability of beating, up to the value you have only 5% of beating.

For this graph too, Pathfinder offers interactive graphread. Here it is showing the value the portfolio has 50% of beating at the end of final year 30:


With graphread you can move to any year, and in that year move to any of the five proabilities to see the value you have that probability of beating: 95%, 80%, 50%, 20%, 5%.

A principal reason this graph is presented this way, with that symbol for each year, is to enable clearest comparison of two portfolios. Here’s an example comparing two:


When portfolios are compared on this graph, they almost always overlap, and sometimes one is entirely “inside” the other. With these symbols, with the blue for each year slightly to left of the red, the illustrations of both portfolios can be fully seen.

Caution! — This is a good place to warn again that since these analyses are all based on estimates, including those for the asset classes’ “expected returns” and “risks” which have insufficient grounds for precision, this graph along with the others should not be viewed as “precisely right.” In particular, the values shown in this graph’s graphread show much more precision than can be justified considering the uncertainties of the underlying estimates. View those graphread numbers as rough approximations. And to see how far they could be off, due to uncertainties of underlying estimates, try lowering the asset classes’ “expected returns” as the investor did for the Goal Frontier and reproducing this graph with those changes.

However, this graph’s graphread has additional value: building understanding of what the symbols represent, not only individually but all together, as an approximate picture of the value development of this plan with this portfolio over the years of the plan. With this fully understood, the graph can have much more value.

To illustrate, let’s go back to just the red portfolio, without graphread:


From looking at this overall picture, the investor can see a lot:

As the years go by, the spread of possibilities for the result keeps growing.

Most of the growing spread is on the high side of the 50% lines, where as the years go by, the unlikely best possibilities grow very high.

In the last ten years of the plan, which are retirement years with money taken out each year, the value he has 50% probability of beating does not plummet, and even keeps very slowly rising.

It’s comforting to see that through those last ten years, retirement years, even the bottoms of the thin lines that the investor has 95% probability of beating stay well above zero.

But it’s less comforting to note that  toward the end of the plan, the bottoms of the thin 95%-probability lines drop well below the $600,000 or 0.6 million the investor will want at the end for his SPIA.

For those last ten years, look at the bottoms of the thick lines, representing value that has 80% probability of being met-or-beaten. They are just about at 0.6 million or $600,000, the amount the investor plans to use for the SPIA purchase. That means that from this analysis now, it appears that in any of those ten retirement years the investor will have 20% risk of inadequate funds for the SPIA purchase.

For almost any investor, this graph’s view is valuable in showing not only if but whendangers of failure to meet goals may appear. And after the investment is chosen and made, the investor can check actual results against the year-by-year probabilities this graph shows. And for investors who have goals that will require withdrawals along the way, such as financing children’s education, this graph can be especially valuable in seeing effects of those withdrawals on the overall portfolio value development through the years of the plan.


What ups and downs along the way?

The fourth and last graph in this set informs investors about what portfolios may offer and how they compare in short-term ups and downs. For the investor’s dollars. Through the life of the plan. In relation to prospects for the investment purpose, the future dollar goals.

This is important for two major reasons:

Natural fears of investment ups and downs – It’s natural to fear and dislike an investment’s downs, maybe get out of that investment, maybe never get into investments with bigger ups and downs. But among competitive asset-class mixes, those with bigger downs also tend to have bigger ups, and more underlying growth potential that may be essential for best prospects for the investor’s future dollar goals.

University investment education – For two decades now, our universities have flooded the nation with investment education that amplifies and plays on fears of those ups and downs. Investment education labeling a technical measure of those short-term ups and downs with the fear-word “risk”; spreading the notion that investors should focus on the single year; and base their investment selections on comparison for just the single year and their fear of short-term single-year ups and downs, aka “risk tolerance” or “risk aversion” – and do so triple-blind. (1) Without seeing what selections might be best in prospects for the investor’s future needs and goals. (2) Without seeing how financial industry fees can smother multi-year compounded growth and reduce the investor’s longer-term results by half.  (3) Without even seeing what the short-term ups and downs might be for the investor’s dollars.

The best financial advisors take their clients past this diversion. But most investors don’t have enough money to attract or afford that guidance.

Investors should have tools to get past that diversion, to inform themselves for prudent investment choice. So along with the Goal Frontier and the other two graphs illustrated above, all focused on probabilities for future dollar results, there should be another graph showing examples of what a portfolio’s path of ups and downs may be. For an investor’s dollars. Through the life of that investor’s dollar plan. Like this:


This graph shows ten probability-based simulation examples of what the year-by-year path of ups and downs may be with a particular portfolio, in dollar value for a particular plan, through the life of that plan. 

The portfolio used for these examples is the one our investor first looked at, 100% All-stocks. The probabilities are based on the estimated “expected returns” and “risks” of the asset classes in the portfolio, in this case just All-stocks, applied to the dollar plan through the years using Monte Carlo simulation.

Another investor may react that these ups and downs are too big, and the paths end up so far apart that the outcome with this portfolio is too unpredictable.

So he decides to try it with another most-conservative portfolio, 100% T-bills, which the investment textbooks say have least “risk.” On the same graph, for the same dollar plan, ten examples with the T-bills appear in blue like this:


The T-bills examples certainly are smoother paths through the life of the plan, with only tiny ups and downs. And they have far less uncertainty about where they end.

But investments with only tiny ups and downs also have only tiny growth potential. Look where the blue examples end! Down at the bottom.

If an investor’s future dollar goal is any higher than where the blue examples end, for him the T-bills have more real risk – risk of falling short of his future dollar goals. With the stocks, most examples end up much higher, but all the T-bills examples end up below.

It’s more likely that for an investor, there are better choices between these two extremes. The purpose of this graph is to complement the others, which are focused on probabilities for future dollar results, by enabling an investor to also see examples of paths of ups and downs along the way. So the investor is informed to judge portfolios that best meet his dollar plan, future dollar goals, and priorities.

Why only ten examples

Ten simulations is nowhere near enough for assessing results i therms of probabilities. That takes thousands. The reason a click of the button delivers only ten simulation examples is that adding more obscures the individual ups and downs.

But in the Pathfinder software, you can produce these simulation examples only one at a time, or keep adding more and more sets of ten. With these capabilities, this graph is an excellent tool for education and explanation on Monte Carlo simulation.

But that’s another page that is not yet here at this website.



1. Lay out your cash flow plan and goals

2. Define a conservative-to-aggressive range of whole-major-asset-classes- mix portfolios

3. Compare them all in probability of meeting your future dollar goals, on a Goal Frontier graph

4. For the best of those, make further graphic comparisons on:

a. How far above or below the goal the result may be

b. Probabilities for dollar value year by year along the way

c. Examples of ups and downs along the way

5. From these graphic comparisons, select the portfolio you think best for your dollar plan, future dollar goals, and priorities