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.