Hey! Did you read my post on investment strategies for saving for college? Well you’re in good company because my friend *Beginner MD* did too! And when Beginner MD contacted me for some guidance on contribution amounts I was pleased to help out.

# College Investment Strategies

*Please read the important notes, they describe the conditions of this blog*.

Beginner MD has a 2 year old and has already put away $4,500 in a 529 account. So I’m going to award an A+ for starting early, since we know that the success of any kind of saving strategy is dramatically improved by letting time do its work.

Beginner MD wants to target having the full 4 years of college costs in the bank and therefore provide the full capital amount to fund college. Again, A+ for intention and vision, this is one lucky child!

*But the key question is what annual contribution is required to make this happen?*

## Setting the Scene

As before we are going to use historical equity and bond returns from 1802 to 2015, and given the age of the child we will restrict ourselves to a 16 year time horizon only. Again we will use real returns (adjusted for inflation) but make no allowance for the fact that college expenses have historically risen faster than prices in general. We also won’t make any deduction for investment management expenses. So you should therefore view these results as under-stating the contribution required.

In the last post I described amounts in terms of the annual cost of college. So a contribution of 0.2 per year is a saving rate of 20% of the annual college cost. For example, if you are targeting a college with annual costs of $75,000 then a saving rate of 0.2 is equivalent to saving $15,000 a year.

Beginner MD’s goal is to save up a value of “4” in the next 16 years. i.e. to save four years of college costs.

## Projecting the Minimum Contribution Requirement

For every past projection period we find the minimum contribution rate (MCR) required to fund a value of 4 at the end, and we will test different investment strategies. The chart below shows the MCR for all the different starting years.

You can see that the MCR varies wildly depending on which cohort you are in. You may be lucky and start saving in 1984 and enjoy the go-go years of the 80’s and only have to save 0.08. For a college cost of $75k this equates to annually saving $6k per year – not too bad!

But if you were unlucky to start saving in the 1959 cohort you would be battling the inflationary decade of the seventies that provided a huge headwind resulting in an MCR of 0.36. This translates to $27k a year to fund a $75k a year college fee – pretty ugly!

Let’s look at the median MCR and also the 95th percentile amounts.

The median MCR is 0.145 and the 95th percentile is 0.260. So half the scenarios resulted in an MCR in excess of 0.145, and 1 in 20 of the scenarios were in excess of 0.260.

In other words:

- If Beginner MD wants to have a 50% chance of meeting a goal of saving four years of college then a contribution of 14.5% per year for 16 years is required
- If Beginner MD wants to have a 95% chance of meeting a goal of saving four years of college then a contribution of 26% per year for 16 years is required.

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## Let’s Talk About Risk

You might be thinking that there are some parallels here with the Safe Withdrawal Rate (SWR) used to determine how much you can safely spend in retirement. But the risk of failing to meet a college saving goal is not the same as the risk of running out of money in retirement. If you spend more than the SWR then the downside is a life spent in penury on the streets scrounging in dumpsters; the downside of failing to save sufficiently for your child’s college is benign in comparison! If you under-save for college the shortfall can be met from salary, student loan, attending a cheaper school, or student jobs.

So we need to think a little differently about risk in this context when compared to retirement saving.

The measure I’m going to choose is **cost uncertainty**, and in particular the uncertainty that might force Beginner MD to massively increase the annual contributions to meet the goal.

I’m going to define this as the difference between the 95th percentile MCR and the median MCR. The median MCR is the expected cost. In the example above it was 0.145 however there is a risk that this could escalate to 0.26 in a 1 in 20 event. So the additional uncertainty is 0.115. This is the additional contribution over and above the expected amount I might need to cover.

Does the diagram below help you understand this concept? The risk is the gap between the expected cost and the potential 1 in 20 cost.

## Investment Strategies

Let’s now look at how things look when we change the investment strategy. We can look at three simple investment strategies:

- 100% Equity
- 50% Equities, 50% Bonds
- 100% Bonds

The chart above shows the historical MCR for the three different investment strategies. It’s a bit difficult to take away any firm conclusions from this, but it seems that the MCR looks like it increases as the allocation to stocks decreases. Here’s a groovy interactive chart!

At the moment this doesn’t really help Beginner MD and we need a more rigorous analysis.

## So What’s Our Measure of Success Here?

Now that we have defined our measure of risk we need to quantify success.

I think the ideal investment strategy is one that provides a low expected cost and a small risk. So we want a small MCR and a small gap between the median and 95th percentile MCR.

So… let’s check all the portfolios from 0% equities to 100% equities in 10% increments and measure these key values.

The above chart crystalizes everything into one chart. Each dot is a portfolio, so for example the “20%” dot refers to the portfolio that has 20% equities, and 80% bonds. The horizontal axis is the *Risk*. This is the additional contribution that might be required in a 1 in 20 event, over and above the expected amount.

The vertical axis is the *Cost*. This is the expected, or median, minimum contribution rate.

But look! I reversed the vertical axis!

You weren’t expecting that were you? That’s a life-lesson for you. Just when you think you have actuaries down pat, with their sober suits and smart shoes, they suddenly veer off-piste and reverse axes! I know – crazy cats!

The reason I did this was because I wanted to have a lower cost going up the page. Risk / Return charts usually have lower risk and higher return portfolio in the top left. That’s what I am aiming for here. Those portfolios that represent the lowest cost and lowest risk are in the top left.

If you move right then you are increasing risk, and if you move down you are increasing cost.

I’ve drawn by hand a (sort of) efficient frontier. This is more as a guide for the eye and helps you to quickly make sense of those portfolios that are optimal and those that are sub-optimal.

## Finally, Some Results!

So what does the above chart tell us? Well, the most top-lefterly point is the 90% and 100% equity portfolio. These provide the lowest expected cost with a good balance of risk. For the 90% portfolio you can see that the cost is 0.15 and the risk is 0.11

The lowest risk portfolio is 30% Equity / 70% Bonds. But with this greater cost certainty come higher cost expectation.

In the chart below I’ve grouped the portfolios into three main buckets. This should help to make sense of it all.

So if Beginner MD targets an annual college cost of $75,000, then with a 90% equity portfolio the minimum contribution is expected to be 0.15×75000=$11,250. The risk is 0.11×75,000 = $8,250. In other words there is a 1 in 20 chance that the actual contribution rate could require an additional $8,250 per year on top of the $11,250.

This is all for a 16 year time horizon.

## Final Comments

So what’s my advice to Beginner MD? (Which of course is not advice – have you not read the Important Notes?)

It certainly seems that based on the last two centuries a very equity heavy portfolio performs best. Stocks for the Long Run wins again! A portfolio of 90% looks ideal. The expected minimum contribution rate would be 15% a year and this would give a 50/50 chance of meeting the goal of funding all four years of school. However there is a 1 in 20 chance that the minimum contribution could escalate to 26% a year, depending on market conditions and inflation.

So far I have just looked at static investment strategies. It’s very common in 529 accounts to have an investment option that grades down the equity allocation at the end of the investment period. This is supposed to reduce sequence of return risk. Testing this will be a whole new barrel of fun – so stay tuned for another post on this topic!

*Did you find that a useful analysis? Were you cursing me when I reversed that axis? What did you make of the efficient frontier, was that a useful way to think about things? Leave me a note below, and if you want to be featured as case study then drop me a line!*

**Technical Notes:** I didn’t love how the results came out with the risk-return chart. It’s all correct and I did some cross checks but it looked a bit weird to me. I was expecting a neater efficient frontier with the portfolios lined up with higher equity as higher risk, and higher bonds as lower risk. It didn’t turn out that neat. I guess the lesson is that real life (and past performance data) does not conveniently coincide with the theory, I also think that inflationary regimes play a big part in this randomness. I wonder whether if I re-ran this with nominal returns the results would be more like the theory.

DocBVery well put together. Could you do an article on a 53 year old with a 16 year investment horizon? I am interested in putting together a indexed fund (Vanguard, Fidelity or Schwab) outside my 401k at around 85% small/large caps and rest in bonds, foreign stocks. I could invest about $1-2K per month.

Thanks for your detailed analyses.

actuary on FIREDocB – thanks for dropping by, I can’t promise I’ll be quick, but I’ll try to look at that. Thanks!

Beginner MDThank you so much for your thorough analysis! It looks like I need to start cranking up the contributions, although at least I have the allocation set correctly for now! Look forward to seeing your future post about equity allocation that grades down.

actuary on FIREGreat – thanks for swinging by!

GasemMasterpiece!! Thank you for introducing the “efficient frontier” to blog land. Took an actuary to do it! Many blogs consist of boilerplate posts that are click bait. Some, like this one push the envelop of understanding.

The way people learn is in small chunks, mostly by exposure. First the word efficient frontier. Then someone looks it up on investopedia. Then maybe a tinker toy scaffold stick man brain picture develops. Nothing that requires Matlab but just the ability to understand the notion. Then maybe a few sentences in another post expanding on the notion.

I’m going to describe the “risk free asset” (another term in efficient frontier lingo) but I think an important contrast.

My college choice for my kids was a State sponsored pre-paid college education. I bought 120 hours (not 4 years but 120 hours) of education at any state run institution tuition and fees. It was a fixed cost, in my case $22K. It is guaranteed and inflation protected. I bought it when they were 2 and my oldest is going into her last semester of senior year. My intangible cost is that their universe of choices are limited. My goal was to have them graduate debt free, and guaranteed in case of my death, which lowered the cost of my life insurance because I could justify a smaller policy. I didn’t need $500K of “college cost” factored into that equation, and again my cost WAS AND IS FIXED, and already paid for. This is why it is the risk free asset.

For variable costs (the cost related to keeping a kid alive during college) I plowed another $15K into some stocks only Vanguard funds, in a UGTM gift trust. Over 20 years those funds grew to about $55K. I use that $55k to pay various expenses of theirs like travel computers cameras clothes monthly allowance, even a car. In 1996 when I started looking into this problem, 529b’s had terrible track records and terrible funding options. I have friends who’s 529b’s are under water because of the drag and poor fund choice. I see virtually zero advantage to “the pre tax” marketing gimmick if your money goes into crap funds. So once again I’m challenging the echo chamber.

Your analysis of the risk is spot on! College is a virtually fixed number of months, NOT decades. The money also is disbursed over time. I just left my kids money invested and sliced off little hunks of dough to pay for a year or half year. This is why I count the investment as 20 years as opposed to 16. It comes off as a glide path. I never had any problem saying yes to the “Daddy can I…” request, even after I fully retired, because the UGTM had that cash flow covered.

To better expand the idea of what you need to save somehow “real” inflation needs to be included into the analysis, not just CPI or something. And maybe something about borrowing costs and leverage.

Were I to do it again, I would choose an all stock portfolio of individual stocks plus a bond fund using an efficient frontier calculator as opposed to VTI or something. I would start with $4K and add $2K per year into the UGTM. Mine are housed at Fido, and my investment choices are whatever Fido has to offer..

Super interesting discussion

actuary on FIREThanks, I had never thought about pre-paid college as the risk free asset, but you are exactly right. That’s the right way to look at it.

The treatment of inflation does trouble me. I really need to examine the failure scenarios a bit more closely, because I wonder whether erosion of purchasing power is what’s making some of the scenarios really high cost. If that was the case then I’m really under-stating the problem by not incorporating a decent attempt as “college inflation”. Glad you enjoyed the post.

AlanInteresting analysis, can you expand on the market returns data selection risks ? is this US only ? how relevant is it to include results from 2 centuries ago before a more globalized world and democratized investing, 401k, indexing, etc …

Then for this particular example, it doesn’t make sense to save a lot when inflation is high, more recent dollars are more valuable. In this case should the savings be dynamic ? For example shift to short term bonds for college cost and move college funds to the retirement bucket (longer term). Does it significantly change the approach that should be adopted ?

actuary on FIREHi , yes the equity returns are US only. Mainly to keep things simple for me. Is the last two centuries of data useful as any kind of guide to the future? I don’t know, but the alternative is to come up with my own forward-looking assumptions (or borrow someone’s assumptions) and do a Monte Carlo analysis. That introduces a whole load of new subjectivity about the future. So IMO using back-testing provides quite a nice transparency that Monte Carlo simulations do not.

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