Kids… Kids are a blessing in your financial planning for long-term independence.

Said no FIRE enthusiast ever.

I think we can all agree that (most of the time) kids are a blessing, but they sit firmly on the “loss” side of the “profit and loss” ledger. And college fees! Man! You need to prepare for those – am I right?

Perhaps like me you’ve created a little spreadsheet to calculate how much you should be saving in your kids’ 529 accounts assuming a certain rate of return. But that is literally only an hour of fun. At most.

*C’mon Team Actuary!* We can extract lots more fun from research into 529 investing. There are a ton of questions that need answering and data that needs mangling, and in all honesty I need a break from thinking about retirement issues. So let’s get into this.

## Fungibility of Investments

Fungibility of investments sounds like a nasty case of something like athlete’s foot – right? We might need to take our investments out and give them a good airing and perhaps sit them down and have a firm discussion around personal hygiene. But no!

What I mean is that I believe that your investments shouldn’t necessarily sit in different “pots” with different goals. You should instead view your investments as one totality meeting a number of different obligations, and you should optimize one single investment strategy.

But you know what screws it all up? Taxes. If it weren’t for taxes then I think we would all have one big pot of money and one investment strategy. We’re not going to get into that here, and there is plenty of information out there about the tax implications of investing, see here for example.

As you know a 529 account provides tax advantages and in return the money has restricted uses. So essentially the money is ring-fenced for the paying college fees and that is what I’m going to assume here.

## Assumptions

I’ve been modeling the minimum annual contribution I need to make to my 529 accounts, and I’m defining my measure of success as having sufficient funds at the start of the college to pay for 4 years. I know you don’t need the full amount on day one, but let’s make things a bit simpler for the modeling.

I’m going to pull two levers:

- The period of the investment, and
- The investment strategy.

I’m going to keep the investment strategy simple with just static allocations to equities and bonds and keep that constant throughout the period of the investment.

## Let’s Quickly Talk About Utility

My success measure above might not necessarily be what you judge to be the right success measure. For example you might not be that bothered if you fall short of saving the complete college cost and are happy to take any shortfall from taxable savings or a student loan. Conversely you might not be too worried about any surplus and have plans for mopping up excess funds. There was a debate around these issues recently on the White Coat Investor forums.

We’re starting to get into “utility functions” here. These define how happy or sad you are under certain outcomes. I’ve shown three potential utility functions above.

Under ‘A’ a dollar of shortfall or surplus impacts you the same. Under ‘B’, if you are below target this can have a big impact on your utility, and being over-target only has a marginal impact on increasing your utility. Utility ‘C’ says that you get no increase in happiness from a surplus and you see it as wasted funds.

I don’t explicitly use Utility functions in my analysis as such, but there is an implicit utility of ‘B’ I would say. And this probably best represents how I see things with college savings.

## Get To The Numbers!

I’m going to take historical investment returns of equities and bonds from 1802 to 2015 and consider periods of investment from 1 year to 18 years. You can make all sorts of arguments that the equity markets from the turn of the 19th Century only had a few railroad companies in, but I have this data lying around, and if you don’t like it then start your own goddam blog.

Note also that my returns are net of inflation, or real returns. It’s worth noting that college costs have generally increased faster than CPI, but I do not take that into account here.

Instead of dollars I am going to work in units of annual college cost. So 1 unit is one year’s worth of college cost. If your child has their eye on a college costing $50k a year, then 1 unit is $50k, and saving 0.1 per year, is equivalent to saving $5k per year in this example. My success measure was saving four years of college costs and so this is equivalent to saving 4 units. *Get it?*

## Impact on Terminal Value

Before we look at the minimum contribution rate required to save up 4 units let’s look at what factors might impact on the terminal value. The terminal value is the value at the end of the period of investment.

The above chart shows the terminal value for a 10 year period of investment and an annual contribution 0.15. You can see it falls quite a bit short of our target of 4. (Remember 4 units is equivalent to four years’ of college costs). In addition you can see there is quite a bit of variability over the different periods.

*So what has the biggest impact on the terminal value?*

With a set investment horizon I think there is an understandable fear of a market crash the same year that you need to access the funds. You really don’t want to experience another 2008 directly before you have to write the check to the college. But is this fear justifiable, or is it an example of psychological bias?

I looked at the terminal value after 10 years along with the last year’s return.

The blue line is as before and shows the terminal value of the account after ten years. I have overlaid in red the last year’s investment return. It’s like actuarial spaghetti thrown at the wall! I guess if you squint a bit you might see a pattern, but I don’t think there is a strong connection.

Instead of the last year’s return let’s look at the last ten years’ of annualized return.

That’s a nice correlation! This is telling us that the return over the whole period plays a big part in determining the value of the account at the end of the period. You don’t necessarily need to fear a poor return in the final year, it’s a whole decade of crappy returns that will kill you.

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## Gimme The Big Picture!

That’s enough noodling, we need to look at the bigger picture.

I’m now going to find the minimum contribution rate (MCR) to meet a terminal value of 4. We’re going to look over all time periods from 1 to 18 years.

The above chart shows the MCR for a 90% equity strategy. Here’s a few observations:

- The MCR gets lower the longer the period of investment. No surprise! It’s a cliché in personal finance, but I’ll say it. S
*tart saving early! Compound interest is your friend!* - The start year makes a difference, and so market returns matter. Those lighter areas in the blue are big market downturns. This could impact your MCR by 10-20%, which is a lot.

We can break things into broad regions.

In broad terms you can see that for a period of investment north of 13 years then a contribution of 0.1 per year is sufficient in all but the worst sequences. But if your investment period is only 5 years (bad parents!) then a contribution of 0.5-0.6 is required.

What is not smacking you in the face is the speed of the exponential growth over the time periods. It’s really difficult to appreciate the power of this effect (without a logarithmic scale). But let’s quickly put on our 3-D glasses.

Key takeaway – if you don’t give yourself a long enough runway you have to rely on contributions and not investment returns.

Let’s now look at how things change when you flex the investment strategy. First with 60% equities and then 30% equities.

It’s difficult to compare easily (and I’ll work on that in a later post) but you can see that as we reduce the equity allocation two things happen. The colors bleed out more, a higher MCR is required, and the colors get less “spiky”. What this means is that as you have a more balanced portfolio you see less volatility year to year. Part of the reason is sequence of returns. More on this in a later post.

## Wrap Up

Did you think I was going to wrap this up in one post? Nope, there is too much fun to be had here. So I’m going to leave things on a cliff-hanger for this week and come back to this analysis soon with some firm recommendations. Hopefully I’ve whetted your appetite for some more investigation and you’ll return for another installment.

*What did you think? Do you think this kind of analysis will help you plan for investing for college education? Did you disagree with my target of fully funding all four years on day one? Do you not care if you build up a surplus? Comment below on any further aspects of this you would like to see. *

GasemInteresting post! I have 2 kids I adopted from China ateach at age 1. At age 3 I bought them 120 hours of education at any state university. My goal was to give each kid a credible education and have them graduate debt free. The cost for 120 hours at a 15 year horizon was $22K it included all tuition and fees, but not housing. My second investment was a UGTM with $15K invested in a typical Vanguard portfolio. That portfolio grew unmolested over the course of maybe 13 years and essentially doubled. As college happened I sliced off some and used the dough to pay for things like summer abroad, laptops cameras cell phones plane tickets trips clothes a monthly allowance etc all of the typical stuff needed by a 20 year old in college. The housing I paid out of pocket which was maybe $800/month which included a food plan. After 4 years there is still about $10K in my oldests account with 1 semester to go.

I used to day trade stocks and options. My tactic was to buy momentum in 3-5 stocks. Buying 3-5 would dramatically improve volatility. What I would do today I would buy BRK.B $2000/yr for 20 years, which yielded a near $5M account from 1997 to 2017. BRK.B has an expected return of 10% at 16% volatility, OR I would buy 6.5% GOOG 7.5% BRK.B 3% GLD 3% QQQ and the rest VBTLX LT BONDS. This is the efficient frontier tangent portfolio for this quintet and the return for this portfolio is 6.5% and the vol is 4%. 20 years with this portfolio would yield a tax efficient $85K come college time. When college is over, I would let it ride and tell my kids about it when they were 50. Let’s say there was 40K left, at 6.5% that’s $265K 30 years later.

I put VTI as a choice with the others into the efficient frontier analyzer, and the analyzer ignored VTI. It was not included in the best Reward v Risk. Consider what I just said: Total stock market was ignored as a choice in a best diversity calculation. Totally blows the Bogelhead mind doesn’t it.

If you take out Bonds the remaining quartet should yield 14.44% with a 12.7% vol. The 20 year runup at 2K/yr would have yielded $221K at college time, and if you spent $50K of that in the college years and reinvested the remaining 170K for 30 yrs the Christmas present for your kids at age 50 would be $2.5M!

My point is the risk/reward for a college fund is very different from a retirement fund. My scenario basically turned college into a free trade. My cost was fixed, guaranteed, and inflation protected and anything over and above my cost was free money which is why the idea of a pure stock account is not crazy, especially when you understand the efficient frontier. If I give them $1M or $2.5M at 50 it’s still a hell of a deal.

actuary on FIREYou’re braver than me. I hold no single stocks and that would keep me awake at night. Interesting that VTI didn’t improve portfolio efficiency. That’s weird.

GasemThe answer is because of correlations. The correlation between QQQ and VTI is .9. Between QQQ and GOOG is .62, between QQQ and BRK.B is .33, between GLD and QQQ is 0.01, between QQQ and VBTLX is -.03. Sp picking VTI is essentially no different than picking QQQ in terms of diversity.

This is an imperfect analogy but: If you consider your portfolio a circle with a center and the area of the circle the value of the portfolio, what is it that balloons out the circle? Consider the center as the origin and consider each asset as a vector pointing out to the perimeter. Consider the correlations as angles that offset the vectors from each otther. If all the assets have near same correlations your circle will be long and thin and poorly diversified. If your correlations are varied and diverse the area of the circle will be much more circle like. THIS IS IMHO HOW DIVERSITY WORKS in a graphical fashion.

If you look at the 3 etf bogelhead it is much less properly diversified than a stock:bond 2 asset portfolio because that 3 etf portfolio is not on the efficient frontier. The 4 etf bogelhead is even slightly worse. The reason is the 3 etf portfolio has 1.0, 0.72 , 0.07 relative correlation and the %’s of each are just a WRONG guess because the portfolio is way off the efficient frontier. Basically the stock:bond portfilio defines the efficient frontier, so the frontier analyzer chooses the best asset mix. stocks and bonds.

The 4 etf bogelhead has correlations of 1, .88, -.11 and 0.02 So basically this is the same as 1,and -.11 which is stocks and bonds. Again the ratios of the bogelhead are messed up and far off the efficient frontier. If you consider my circle analogy you have 4 assets 2 of which point in one direction and 2 which point in an orthogonal direction. Since the quartet are off the efficient frontier there is way too much volatility v return. Bogelheads tend to be bullies when it comes to their theories, so everyone bows to them. What they actually are are easy to create and balance portfolios which are too risky for their relative rate of return.

There is no reason to assume holding something like BRK.B or QQQ or GOOG is more risky than VTI in a diversified portfolio, if you believe in America, GOOG is not going away. Neither is QQQ or BRK.B or GLD. The point of the efficient frontier is for the portfolio to become greater than the sum of its parts on a risk adjusted or return adjusted basis. In a crash all assets are heading to zero except maybe gold which is a way to leverage fear and reduce volatility. A better way is the VIX but that is way too expensive to own.

GasemAlso you already limited your risk by buying 120 credit hours inflation protected, so you have 20-50+ years to live through the volatility. If you choose an efficient frontier portfolio you are inherently limiting your risk v return.

I’m not big on single stocks but I reviewed buying BRK.B $2000/year for 20 years compounded and the resulting portfolio ($40,000 basis) was just under 5M dollars. BRK.B is a stock of businesses, QQQ is a ETF of many companies, and GOOG is buying a portfolio of creative destruction. So each is within itself internally diversified. You may as well let the good times roll. I think the chances of this portfolio losing money over 20+ years is zero unless we get hit by an asteroid.

Your kid doesn’t care he just needs enough for an extra $500-$1000 a month for 40 months.

GasemThat last sentence is why planning for college v planning for a 50 year retirement has a very different risk profile

GasemI was thinking more about why VTI wasn’t chosen and I think this is important. The program is an optimizer. It measures combinations of variance co-variance and return and compares the optimal result to a risk free asset (1mo T-Bill). The efficient frontier is a curvilinear set of points that lives on a plane of points which represent various risk/reward values. The program simply optimizes. If you put 10 assets in its hopper it will look at all permutations including sets of less than ten. It may decide 3 assets are most efficient compared to a 1 month T bill and it will tell you the ratio of those 3 assets. This tangent portfolio IS the optimal risk reward point on the plane for the given inputs.

VTI may very well NOT be optimal. Just because it has everything does not mean it’s most optimally diversified. It has its own internal drag and SORR loss because EVERYTHING doesn’t always do well. Some things in “everything” suck, and you can’t control the ratios. So optimal diversity in something like VTI probably doesn’t exist. I figured this out while analyzing the bogelhead stuff. Just heaping more and more on the pile was not optimal in terms of risk reward.BY A LOT.

I compared a 3 stock portfolio “GOOG QQQ BRK.B” v “VTI VEU” The program ignored VEU because it didn’t reduce volatility compared to VTI alone. The result was VTI has 9,79% return v 15.7% risk. The triplet has a 13.21% return v 15.68% risk, ie identical risk but a 3.42% better return, AKA free money. I have nothing against bogelhead philosophy but it is just that, PHILOSOPHY. It creates a credible portfolio that is easy to maintain but it is not optimal in terms of risk reward.

I compared the Bogelhead 3 to GOOG QQQ BRK.B VBMFX VGTSX VTSMX (the vanguard funds are the bogelhead 3 funds). The program chose the optimal of the 6 funds and that was (GOOG QQQ BRK.B VBMFX) reward=5.37% risk=3.7%. The optimal of the 3 bogelhead funds was 2 funds VTSMX and VBMFX reward=4.41% risk=3.36 and the bogelhead 3 was off the efficient frontier. The Bogelhead 3 had reward=6.65% and risk=13.37%. So for an additional 1.3% return you take over 4 times the risk.

Sorry to kind of hijack your work but an additional 3.4% with much less risk, while planning for a 20 year college fund needs consideration.

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Jason@WinningPersonalFinanceFun post. I’d love to see a calculator that shows the missed opportunity cost for over or under funding a 529 with variables including cost of college, rate of return, contributions, time, various tax rates. I feel like planning for this is a total wild card sometimes. My kid could go to Harvard for $$$ or maybe get a free ride to community college. How do you optimize for this? It makes retirement planning look easy.

actuary on FIREJason – apologies this slipped off my radar. The problem I’ve found with under and over funding is that people have different attitudes to it. Some are sanguine about over-funding, others see it as trapped capital. This is what I was getting at with that whole section about utility functions. Everyone’s measure of success in this area can be quite different. So not sure I can ever answer that definitively. But look out for some posts with reader case studies, that will explore this a bit further.

Thanks for dropping by!

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