Hey folks, how you doing? I feel like its been aaaaaaaages since we had a good content-rich exploration of some investment issue. But come to think of it, it was only the beginning of January I wrote an article analyzing the difference between lump sum and dollar-cost averaging strategies. That got a Rockstar Finance feature that now takes pride of place on the AoF mantelpiece. So if you are a new reader, or a returning reader, then welcome!

Have you read the important notes before proceeding?

College Saving Investment Strategies

We’re going to look at college investment strategies and I have to say I really reveled in this analysis. Actuaries love a good revel so let’s get to work!

Do you know who cares about college savings? Yep, Moms.

And who is the Chief Mom of college savings? Yep, Chief Mom Officer (CMO).

Chief Mom Officer

Did you see CMO’s article on her decade plus journey to save for her three boys’ college education? It provides a testament to the power of consistency of savings and starting early. No gimmicks, no fluff, just getting the basics right year on year.

So I was delighted to provide her, and her boys, with some analysis that I thought would be helpful.

She has three boys of varying ages and levels of college saving, and I summarize the data below.

Her target is to provide full funding for four years at their in-state College which amounts to a total cost of $110k. So you can see that the eldest child has a substantial chunk saved, amounting to 2.6 years’ worth. That’s a great result from CMO; with 3.5 years to go, my sense is that this is a readily achievable target.

Previous Analysis

If you have seen my previous analysis and case study you will recall that I prefer to convert the dollar amounts to fees for one year, where ‘1 unit’ represents a year of college fees, and ‘4 units’ is the cost of providing four years of school. I’m just going to concentrate on the eldest son in this article, and in those terms we have;

Method

To perform the analysis I simulated portfolio returns using historical data going back to 1802. I also made sure I used ‘real’ returns that take account of the loss in purchasing power from inflation.

I regularly get the comment along the lines of “how relevant is the last two centuries of investment data, given we are in a totally different epoch of human development”? Honestly, I dunno. Basically, you take it or leave it. I really don’t want to come up with my own subjective assumptions on the future, or borrow some assumptions from elsewhere, and then have to engage in tedious and interminable discussion of those. At least this method is transparent – you know what it is, and can make your own judgement of relevance.

OMG! Give us the Results!

I know, I know! We’re 500 words in and not a single chart! This is not why you visited, I get it, but hang tight wannabe actuary buddies, we’re getting there.

Let’s first look at running-out the projections with the assumptions above and see what the final amount saved up would be. To recap for the eldest child, we will assume a starting balance of 2.57 units, an annual contribution rate of 0.24 units and a target of 4 units. Let’s also start off with a good-old 60/40 portfolio. i.e. 60% equities and 40% bonds.

The above chart shows all the different simulations with the starting year on the horizontal axis, and the vertical axis shows the final amount saved up. Remember each unit is one year of college costs. You can see that almost all the simulations exceeded 4, and so this means there is a very high probability that CMO can meet her target with this annual contribution. In fact, you can see that in many scenarios the amount substantially exceeded the target of 4, and she could have diverted some contributions to the other two kids. If you wanna get all actuarial about it (and who doesn’t right?) then 83% of the scenarios were a success.

Look at those two dips below the red line. These are the periods where the market did not cooperate and CMO did not meet her target of providing four years’ of college costs. In these periods the minimum balance was around 2.5; so even the worst period in two centuries it would not have been a very bad fail for the eldest. Note that we have seen these two pesky periods in previous posts, and they are the Great Depression and the Stagflation era of the 70’s.

More Results

Let’s show this in a slightly different way. For each scenario I calculated the minimum contribution rate (MCR) that would be required to exactly meet the target of 4 units. A low minimum contribution rate means the market was strong and therefore fewer contributions were required. During periods when the MCR was high the market was poor and so CMO had to plug the gap with additional contributions.

Just for variety I looked at a portfolio with 100% equities. Above you can see the MCR by historical period. It is striking how many scenarios that produced a zero MCR.

Yes, there have been plenty of historical periods where CMO could just sit tight and let the market do its work, without plugging in any more money! Nice work huh?

But look at those periods during the Great Depression and 70’s Stagflation where the MCR soars to over 0.5! That means CMO would have to contribute a half-year college cost each and every year to plug the gap. Urgh!

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Investment Strategies

These charts are telling me that CMO’s planned annual contribution of 0.24 will be more than enough. In most cases she will probably be able to turn off the tap in the next year or two, it all depends on the markets, but she’s in a good spot.

We now need to optimize the investment strategy and balance risk and return. Let’s look at varying the investment strategy and see what impact that has on these factors.

I re-ran the analysis with varying equity/bond allocations and looked at how many scenarios achieved our savings target. The above chart shows the probability of success for these different portfolios.

You can see that equity-heavy portfolios are more successful and I wouldn’t recommend less than about 40-50% equities for the eldest child. What’s interesting is that the probability reaches a peak at 60% equities and then declines after. The impact of adding additional equities beyond 60% is detrimental. In other words the additional volatility that results from these equities outweighs any benefit in return.

I suspect that with the younger children there will be a different picture with a 100% equity portfolio dominating, but the short time period for the eldest child means that year by year volatility is important.

Efficient Frontier

We need a way of combining the risk and expected cost, and as in previous episodes I am going to create an efficient frontier.

• COST. I will measure this by the median MCR – how much do I have to pay each year to have a 50/50 chance of meeting my goal? A lower median MCR means a high portfolio return and we don’t have to pay in much contributions.
• RISK. I will measure this by the additional MCR to be sure of success in 95% of scenarios. In other words, how much extra do I need to pay to be 95% sure?

I measured these risk and return numbers for all the different portfolios we looked at above.

Let me orient you here – each dot is a different portfolio, and you want dots in the top left corner, since they have a low cost and a low risk. You can see that the 100% equity portfolio has lower cost than the 60% equity portfolio, but comes at a higher risk. That is the trade-off.

The 60% equity portfolio has a cost of 0.12 and a risk of about 0.25. What does this mean?

• A cost of 0.12 means that to have a 50/50 chance of meeting her goal, CMO needs to contribute 0.12 a year.
• However there is a 1 in 20 risk that she has to put in an additional 0.25 a year.

It’s worth noting that you would never invest 0-30% equities, since other portfolios are more optimal (i.e. lower cost, for the same risk).

Pause

Let’s just pause a minute to admire this chart.

Sometimes I go down into the actuary mine to dig out some gems for you and emerge with nothing more than dirty hands and weary limbs. But this is a diamond hewed straight from the data rockface. If you look at any efficient frontier in a textbook or Investopedia you will see an identical curve. What amazes me is that we’re dealing with centuries of investment data applied to CMO’s son, and we have found a sparkling example that looks as if it has jumped straight from a textbook. Don’t you feel a little misty-eyed at such an example of cosmic Platonism?

Advice!

Ok, dry your eyes guys, what have we learned?

Firstly, Eldest son is one lucky guy to have a mom like this. The current balance will be adequate in many scenarios even without further contributions.

I might encourage CMO to contribute the median cost of 0.12 a year ($3,300) and use the remainder for the other kids or taxable savings. Also, I would recommed CMO to adopt a 60/40 investment strategy, or perhaps 70/30 if she wants a bit more octane. I think 60/40 gives a great balance between risk and return for the Eldest child. I suspect the answer will be different for the younger children, but you’ll have to wait for a future episode.

Did you follow the analysis? Anything you would like me to do differently? How do you calculate how much you want to save for your kids’ college costs? Do you think my efficient frontier should have a Twitter account for itself? Comment below.

Technical Notes:

Note that I did not allow for college cost inflation to exceed price inflation. This was just to make the modeling a bit easier but it means my results are under-stated. If we assume that college costs rise 2% a year faster than prices then you should probably inflate my figures by around 10%. I was pretty relaxed for the eldest child, but this will be more important for the younger two.

My equity returns are just US equities. If I had used other asset classes like international equities and real estate than I am sure I could have moved the whole efficient frontier ‘north-west’. That would reduce the costs, and counteract the above point.

I also ignored the small tax break that CMO’s state gives for 529 contributions. That wouldn’t move the needle on this analysis. One misconception of actuaries is that they are uber accurate. Not true; we’re too busy attending wild actuary parties to worry about the small things.