| Public College Goal = | Annual Cost Growth = 2.14% | % Higher Ed Financed = 75% | |||
| $35,479 | $37,017 | $39,450 | $41,160 | $43,865 | |
| Annual Contribution: | 5 yrs | 7 yrs | 10 yrs | 12 yrs | 15 yrs |
| $1,000 | 110.5% | 55.7% | 28.9% | 21.0% | 14.3% |
| $2,000 | 69.6% | 33.4% | 15.4% | 10.2% | 5.8% |
| $3,000 | 48.5% | 21.0% | 7.5% | 3.6% | 0.6% |
| $4,000 | 34.6% | 12.5% | 1.8% | -1.1% | -3.3% |
| $5,000 | 24.3% | 6.0% | -2.6% | -4.9% | -6.5% |
| $6,000 | 16.3% | 0.8% | -6.4% | -8.1% | -9.2% |
| $7,000 | 9.7% | -3.6% | -9.5% | -10.9% | -11.6% |
| $8,000 | 4.2% | -7.4% | -12.3% | -13.4% | -13.7% |
| $9,000 | -0.6% | -10.7% | -14.9% | -15.6% | -15.7% |
| $10,000 | -4.7% | -13.7% | -17.1% | -17.6% | -17.5% |
| $11,000 | -8.4% | -16.3% | -19.2% | -19.5% | -19.2% |
| $12,000 | -11.7% | -18.8% | -21.2% | -21.3% | -20.8% |
| $13,000 | -14.7% | -21.0% | -23.0% | -23.0% | -22.3% |
| $14,000 | -17.4% | -23.1% | -24.6% | -24.5% | -23.8% |
| $15,000 | -19.9% | -25.0% | -26.2% | -26.0% | -25.2% |
| $16,000 | -22.2% | -26.8% | -27.7% | -27.4% | -26.5% |
| $17,000 | -24.4% | -28.5% | -29.2% | -28.7% | -27.7% |
| $18,000 | -26.4% | -30.0% | -30.5% | -30.0% | -28.9% |
| $19,000 | -28.2% | -31.5% | -31.8% | -31.2% | -30.1% |
| $20,000 | -30.0% | -32.9% | -33.0% | -32.4% | -31.2% |
| $21,000 | -31.6% | -34.3% | -34.2% | -33.5% | -32.3% |
| $22,000 | -33.2% | -35.6% | -35.3% | -34.6% | -33.3% |
| Public College Goal = | Annual Cost Growth = 2.14% | % Higher Ed Financed = 50% | |||
| $23,653 | $24,678 | $26,300 | $27,440 | $29,243 | |
| Annual Contribution: | 5 yrs | 7 yrs | 10 yrs | 12 yrs | 15 yrs |
| $1,000 | 85.8% | 42.4% | 21.0% | 14.7% | 9.4% |
| $2,000 | 48.5% | 21.0% | 7.5% | 3.6% | 0.6% |
| $3,000 | 29.1% | 9.1% | -0.5% | -3.1% | -5.0% |
| $4,000 | 16.3% | 0.8% | -6.4% | -8.1% | -9.2% |
| $5,000 | 6.8% | -5.6% | -11.0% | -12.2% | -12.7% |
| $6,000 | -0.6% | -10.7% | -14.9% | -15.6% | -15.7% |
| $7,000 | -6.6% | -15.0% | -18.2% | -18.6% | -18.4% |
| $8,000 | -11.7% | -18.8% | -21.2% | -21.3% | -20.8% |
| $9,000 | -16.1% | -22.1% | -23.8% | -23.7% | -23.1% |
| $10,000 | -19.9% | -25.0% | -26.2% | -26.0% | -25.2% |
| $11,000 | -23.3% | -27.6% | -28.5% | -28.1% | -27.1% |
| $12,000 | -26.4% | -30.0% | -30.5% | -30.0% | -28.9% |
| $13,000 | -29.1% | -32.2% | -32.4% | -31.8% | -30.6% |
| $14,000 | -31.6% | -34.3% | -34.2% | -33.5% | -32.3% |
| $15,000 | -33.9% | -36.2% | -35.9% | -35.1% | -33.8% |
| $16,000 | -36.0% | -37.9% | -37.5% | -36.7% | -35.3% |
| $17,000 | -38.0% | -39.6% | -39.0% | -38.1% | -36.7% |
| $18,000 | -39.8% | -41.1% | -40.4% | -39.5% | -38.1% |
| $19,000 | -41.5% | -42.6% | -41.8% | -40.8% | -39.4% |
| $20,000 | -43.1% | -44.0% | -43.0% | -42.1% | -40.6% |
| $21,000 | -44.6% | -45.3% | -44.3% | -43.3% | -41.8% |
| $22,000 | -46.0% | -46.5% | -45.4% | -44.5% | -42.9% |
Having determined the target rate of compound annual real return you need to earn over your 529 investment horizon, the next challenge is deciding on your Plan's asset allocation. A key issue here is the limited number of asset classes offered by most 529 Plans. Consider, for example, the Vanguard 529 Plan offered by the State of Nevada. Based on our definition of an asset class, it offers only four: real return bonds, domestic bonds, domestic equity and foreign developed market equity (though it also offers a large number of tilts within these, which we'll shortly discuss). Unfortunately, it does not offer three asset classes that, in our asset allocation studies, we have found to provide substantial diversification benefits: foreign currency bonds, commercial property, and commodities, as well as emerging markets equity, which can be used to increase a portfolio's expected return.
The impact of this lack of diversification opportunities is significant. For example, we used our simulation optimization model to develop a model portfolio that maximized the probability of achieving a compound annual real growth rate of six percent after ten years, subject to the requirement that 95% of the time the actual compound rate of return produced would be greater than zero. We first included only the four asset classes available in the Vanguard 529 Plan (for the full list of assumptions we used, see below). We found that the probability of meeting the target is 41%. When we added foreign currency bonds, commercial property, commodities, and emerging markets equity to the mix (with the first limited to a maximum weight of 35%, and the last three to a maximum weight of 20% each), the probability of achieving the target return rose to 68%.
We should also note the range of optimization solutions produced by different asset allocation methodologies. A traditional mean/variance optimization model either minimizes risk (defined as standard deviation) for a given level of expected return, or maximizes return for given level of risk. For a target return of 6%, it produces an allocation of 30% to domestic bonds, 65% to domestic equities, and 5% to foreign equities. The probability that this asset mix would achieve the compound real return target in year ten was 44 percent. The probability that it would produce a compound real return of zero or greater in year ten was 93 percent. Over 10,000 different simulations, the lowest compound annual ten year return it produced was (7.7%). A variation of the traditional mean/variance approach maximizes the ratio of portfolio return less target return to the portfolio standard deviation of returns (this is also known as the "safety first model"). This methodology results in a 100% allocation to domestic equities. The probability that this asset mix would achieve the compound real return target in year ten was 48 percent. The probability that it would produce a compound real return of zero or greater in year ten was 87 percent. Over 10,000 different simulations, the lowest compound annual ten year return it produced was (16.5%). Finally, our simulation optimization approach (for details, see the blue button labeled "methodology summary" on our home page) produces an allocation of 5% to real return bonds, 30% to domestic bonds, 50% to domestic equities, and 15% to foreign equities. The probability that this asset mix would achieve the compound real return target in year ten was 41 percent. The probability that it would produce a compound real return of zero or greater in year ten was 95 percent. Over 10,000 different simulations, the lowest compound annual ten year return it produced was (5.8%).
For now, however, investors in the Vanguard 529 Plan are limited to four asset classes, so that is what we've used to develop our model 529 portfolios. Each of these portfolios is intended to maximize the probability of achieving the specified target real compound annual return over an investment horizon of ten years. We further assume that the investor setting up a 529 Plan wants to be 95% confident that the actual compound annual real rate of return over ten years will be at least 0% (i.e., he or she wants to be 95% confident they won't lose the money they have contributed, except for fees charged by the Plan's manager). We used the four asset classes available in the Vanguard 529 Plan: real return bonds, domestic investment grade bonds, domestic equity and foreign developed market equity. We limited the latter to a maximum of 35% of the model portfolio. Our expected real returns for each asset class were a weighted combination of 67% times the average historical return between 1971 and 2002, and 33% times our estimate of future returns (for more on these assumptions see our May through August, 2003 issues). We also used historical standard deviations (again for 1971-2002), and return correlations from 1994 to 2003. To calculate our model portfolios' asset allocations, we used our simulation optimization model. Possible asset allocations were adjusted in 5% increments to reduce the time required to run the optimization. More details about this approach can be found by clicking the blue button on our home page labeled "Methodology Summary."
| 2% Target | 3% Target | 4% Target | 5% Target | 6% Target | 7% Target | |
| Real Return Bonds | 35% | 5% | 0% | 10% | 5% | 0% |
| Domestic Bonds | 45% | 65% | 55% | 30% | 30% | 30% |
| Domestic Equity | 20% | 20% | 35% | 50% | 50% | 40% |
| Foreign Equity | 0% | 10% | 10% | 10% | 15% | 30% |
| Total | 100% | 100% | 100% | 100% | 100% | 100% |
| Expected Annual Return | 3.96% | 4.67% | 5.21% | 5.52% | 5.73% | 5.89% |
| Expected Standard Deviation | 4.15% | 5.68% | 7.53% | 9.575 | 10.31% | 11.04% |
| Return per unit of risk (Std. Dev,) | .95 | .82 | .69 | .58 | .56 | .53 |
| Probability of Achieving Target in 10 years | 92% | 81% | 66% | 51% | 41% | 32% |
The table below shows the target real rate of return each model 529 portfolio is designed to achieve, the weights given to each asset class, the expected annual return and standard deviation (note that, where standard deviation is greater than zero, the expected annual return is always greater than the compound annual return over a longer period), and the estimated probability of achieving the target compound annual real return in year ten. Over shorter periods, this probability will be lower, while over longer periods it will be higher.
As the table shows, as with all our other model portfolios, these are also subject to the limitations that beset all quantitative approaches to asset allocation. For example, the inputs used in asset allocation processes are themselves only statistical estimates of the "true" values for these variables. As important, the underlying economic processes that generate the return distributions are not stable (or, as they say in statistics, it isn’t "stationary"). This is why every mutual fund prospectus notes (though too often in the small print) that "past results are no guarantee of future results." In sum, asset allocation is at best an imperfect science, if not an art. Despite the apparent precision of the models that are used, they can only increase the probability of achieving your goals -- they cannot guarantee it. When it comes to investing, a certain degree of uncertainty is inescapable.
In addition to index funds covering broad asset classes, the Vanguard 529 Plan offers a number of index funds that allow an investor to take tilts within them. These include tilts toward growth, value, midcap and small cap within domestic equities, and long versus short term maturity in domestic bonds. Should one take these tilts? The answer to this question depends on your view of market efficiency. Broadly speaking, there are two schools of thought. The first believes that markets are generally efficient, and that one takes tilts to gain exposure to a different mix of risk factors than that contained in the broad market index. In a reasonably efficient market, these tilts are logically expected to produce either higher returns than the broad index, but with higher risk, or lower returns with lower risk. The second school of thought believes that the presence of irrational investors, uneven flows of information, and obstacles to immediate arbitrage together creates long term market inefficiencies, which logically lead to the possibility of a tilt delivering higher returns with lower risk than the broad asset class index. Of course, this view also requires that the opposite also be possible: that there exists a group of investors on the other side of these trades, who will be stuck with lower returns and higher risk than the broad index. In our writing in The Index Investor, we have repeatedly examined this issue; on balance, we come down on the side of generally efficient markets, and believe that the most logical basis for taking a tilt is to achieve either higher returns than the broad asset class index with higher risk, or lower returns with lower risk. Hence, based on historical results, a tilt toward value, midcap, or small cap equities should produce somewhat higher returns than the broad index, though with a higher degree of risk, while a tilt toward growth should have the opposite effect.
With respect to bond funds, the tilts on offer are towards longer and shorter maturities than the broad market index fund, which has an intermediate average maturity. Unlike the case of equities, taking these tilts only makes sense if you are confident in your ability to time changes in interest rates. Logically, you would shift to the long maturity fund when you expected rates to fall, and to the short maturity fund when you expected them to rise. As a general principle, we believe that most investors lack the skills to succeed at market timing over the long term. That being said, we aren't ideologues on the issue; we also believe that there are some situations where it makes sense. With nominal U.S. interest rates currently at their lowest levels in decades, it would be a brave investor indeed who decided today to put a substantial portion of his or her portfolio into a long maturity bond fund. Then again, if you expected a sharp all in the price level (that is, rising deflation), then this would be a smart move. As we said, market timing is a very, very difficult game to play well, and most people would be better advised to avoid it, and invest in the broad bond market index fund.
Finally, what about those 529 funds which are based on the beneficiary's year of birth? The key selling point of these funds is their promise to automatically adjust their underlying asset allocation (to make it more conservative) as the start of college grows closer. How do they compare with the asset allocations in our model 529 target return portfolios? That is a subject we'll address in next month's issue. Stay tuned...