abstract
The Arithmetic of Reading and Writing
The Paradox of the College Savings Account
Tuition at American universities, both private and public, has been increasing at an average annual rate of 7.6% (private) and 7.87% (public) over the period 1976–2005. For 1976–2008, these averages declined slightly to 7.47% for private universities and 7.72% for public universities.
High tuition rate increases create financial hardship for many attempting to save for college. But college savings plans that invest solely in government bonds are unlikely to generate the necessary amounts. And as investors have recently and painfully experienced, investing solely in stocks is a risky proposition because equities may not outperform government bonds over any given period. Nor is a combination of stocks and government bonds a viable, risk-managed college tuition saving strategy.
The reason for the college savings dilemma is the fundamental mismatch between the risk–return characteristics of tuition increases and those of the usual alternative savings vehicles, such as stocks and government bonds. Prepaid college savings plans offer one solution; and, for those who are not financially able or willing to participate in such prepaid plans, 529 college savings plans will provide some tax relief.
The Data
The historical record presented in Table 1 compares average annual tuition increases at public and private universities to the arithmetic, average annual rates of return of several fundamental benchmarks in the US economy, including US inflation rates, the HEPI (Higher Education Price Index; an index of the costs of running a higher educational institute), long-term government bonds (both yields and returns), intermediate-term government bond yields, the S&P 500, US small stocks, the US equity risk premium, and faculty salary increases. The annual volatility (σ) of these series is also given in order to assess risk–return profiles.
Table 1: Tuition Increases vs. Fundamental Benchmarks
Investors make their investment decisions partially on the basis of expected returns that are unobservable quantities. They should use the longest available historical data sets to estimate these expected returns via arithmetic means of actual returns (see Bodie, Kane, and Marcus 2009; also see Goldenberg and Schmidt 1996).
The Dilemma
The disconnect between the tuition data and the other series is evident—particularly when one considers the volatility as measured by the standard deviation (σ). Tuition has roughly the same volatility as long-term government bond yields but provides an expected return that is 231 basis points higher for private tuition and 258 points higher for public tuition.
With college tuition rising at an average annual rate of 7.6%–7.87% and long-term government bonds yielding just 5.29% on average, it is not possible to save for college tuition just by using long-term government bonds, even if one were to put the entire present value of four years of college tuition into an account, pay no annual taxes, and leave it there for 10–20 years. That, of course, is an unlikely scenario. Most people pay some form of taxes and are on an installment savings plan. Those who save by putting installments into an account are much more sensitive to reinvestment rate risk as interest rates change.
Both intuition and experience teach savers that they cannot expect long-term, taxable government bonds to cover tuition increases. Therefore, they often look at the stock market as a “money machine.” In doing so, they sometimes forget that the college savings problem (like many investment problems at the household level) is a fixed-horizon investment problem. That fixed horizon is highly problematic in light of the fact that, although stocks tend to outperform bonds on average, they will not necessarily do so over any given period.
Using a riskier investment like equity markets as a savings vehicle raises the horrifying specter that ex post returns will generally deviate from expected returns. There is a volatility mismatch between college tuition (a more or less deterministically increasing series) and equity investments (which have a highly random component to their increase over the long run) (see Table 1: S&P 500, US Small Stocks, and the US Equity Risk Premium).
Equity markets are usually touted as the cure-all savings vehicle. They are not. The magnitude of the US Equity Risk Premium is a hotly debated topic, but the consensus seems to be that it is much lower than generally perceived (see Song 2008). Investors in New York State college savings plans experienced the downside of equity markets over relatively short time periods in the early 2000s, when guaranteed investments offered by TIAA-CREF outperformed their equity investments.
For example, as of December 2005, the previous five-year geometric average annual rate of return on long-term government bonds was 7.72%, while the corresponding return for the S&P 500 was 0.54%. The recent events of 2008 require no description. Suffice it to say that the massive losses in non-prepaid 529 plans are initially estimated to be in the 20%–30% range or higher, depending on the allocation to equities in those funds.
Asset Allocation to the Rescue?
Could some portfolio of stocks and bonds match both the expected return of tuition and its risk? To analyze this question, investing in bonds can at first be equated with investing in long-term government bond funds—risky portfolios that fluctuate in price according to their interest rate volatilities. Drawing statistics from Table 1, the mean (expected) return of long-term government bonds is 5.85% and the standard deviation is 9.24%. For the market (S&P 500), the mean (expected) return is 12.3% with a standard deviation of 20.2%.
The only bit of data still missing is the correlation coefficient between the market and long-term government bond returns, which can be computed at a mild 0.12. Then the feasible portfolio set is graphed in Figure 1. Tuition, both public and private, is roughly at the 8% expected return and 2.86%–2.96% standard deviation level.
Figure 1: The Feasible Portfolio Set Generated by the S&P 500 and Long-Term Government Bond Returns
One can clearly target a portfolio expected return level of 8% through a judicious choice of approximately 35% equities and 65% long-term government bonds. However, the standard deviation of such an asset allocation scheme is about 9.8%, more than 300% of the standard deviation of either public or private tuition. Once again, there is a risk mismatch with potentially disastrous consequences for the college tuition saver.
Alternatively, investing in bonds could mean investing in the appropriate maturity bonds to match the savings period (for example, 18 years). In the case of the long-term government bond yields given in Table 1, the parameters are the mean (expected) long-term government bond yield of 5.29%, with a standard deviation of 2.8%. The correlation coefficient between the market and the long-term government bond yield is now 0.005, virtually zero.
As Figure 2 indicates, the expected return of tuition can only be targeted at a much higher risk level—between 7.3% and 8.3%. The required asset allocation between stocks (the S&P 500) and long-term government bonds is roughly 35%–40% market and 60%–65% long-term government bonds. The key point, though, is the volatility mismatch. The asset allocation strategy that matches the expected return of tuition will again be much riskier than tuition, resulting in potentially calamitous consequences to savers.
Figure 2: The Feasible Portfolio Set Generated by the S&P 500 and Long-Term Government Bond Yields
In both the return and the yield scenarios above, the expected return and the volatility of tuition cannot be targeted simultaneously. This problem applies to all investors, including state and private universities, and pertains to the discussion below of state and independent 529 prepaid college savings plans.
Indeed, the college tuition savings problem has to do with the risk–return profile of tuition increases relative to equities and long-term government bond returns and yields. Figure 1 reveals tuition’s dominance over long-term government bond returns. That is, tuition has a higher expected rate of return and a lower standard deviation.
If tuition were a traded financial instrument it would be a dominating financial security, in the language of finance. Everyone would sell their long-term government bond funds and invest in it. This would drive up its price (lower its yield) until an equilibrium with the long-term government bond fund market would be reached. Tuition would not survive at its current price level as a traded financial security.
Similar reasoning applies to long-term government bond yields. However, as Figure 2 demonstrates, tuition dominates all those portfolios of long-term government bond yields and stocks that are directly below it, not above it, in expected return. Again, an arbitrage process would come into effect, bringing the expected rate of return of tuition in line with other traded securities.
Higher and Higher Ed
In financial markets, market-related risk and expected return go together, at least according to most financial theories of capital asset pricing. Higher relative volatility means higher expected return. Tuition has low volatility relative to the market. Over the period 1976–2005, the estimated beta of private tuition relative to the S&P 500 was 0.02—in other words, effectively zero, with a correlation coefficient of only 0.13. The estimated beta of public tuition was very similar: -0.01, with a correlation coefficient of 0.08. These findings suggest that tuition should be priced at the average long-term government bond yield of about 5.29%, not at the current rate of 7.6% for private or 7.87% for public tuition.
What determines tuition increases? Inflation is a factor. Yet the average increase in tuition over the period 1976–2005 was about 175% (private) or 181% (public) of the average inflation rate over that period, 4.35% (see Table 1).
The usual argument for this multiplier effect is that the CPI (Consumer Price Index) does not represent the true cost of providing higher education, that the HEPI is the correct index for understanding the costs facing colleges. The geometric average annual growth rate of the HEPI, 5.03% over the period 1976–2005, exceeds that of the CPI over the same time period, 4.31%, by 72 basis points. Furthermore, over the same period of 1976–2005, the standard deviation of the HEPI was only 2.16% versus the CPI’s 3%.
The HEPI, like tuition, is effectively deterministically increasing. This creates a savings problem. Markets that are free and efficient benefit from volatility in prices. For example, if gasoline prices decline, the consumer gets a break. But tuition changes have little downside or upside volatility.
One would expect changes in the HEPI to be highly correlated with changes in tuition if universities determine tuition based on the HEPI’s representation of the costs of doing business. However, the correlation coefficient between changes in the HEPI and changes in tuition is 0.77 (private) or 0.49 (public) from 1976 through 2005, indicating that the HEPI accounts for only about 59% (private) or 24% (public) of the variation in tuition. One might well wonder what accounts for the other 41% (private) or 76% (public) of variation in college tuition.
529 Plans 101
College representatives may point out that, due to financial aid, tuition does not represent the true cost of attendance. From a savings perspective, however, financial aid cannot be relied on. The savings target is college tuition and, as demonstrated, direct investment in long-term government bonds, stocks, or a portfolio of stocks and longterm government bonds cannot match the risk–return characteristics of tuition. Individuals saving for college will therefore need all the help they can get.
Tax-reducing, non-prepaid 529 savings plans will help investors improve the yields on their portfolios. Interestingly, prepaid 529 plans could partially overcome the volatility mismatch problem discussed. They would act like prepaid forward contracts, allowing savers to effectively lock in the cost of tuition at its current level.
Tax-reducing, non-prepaid 529 savings plans will help investors improve the yields on their portfolios. Interestingly, prepaid 529 plans could partially overcome the volatility mismatch problem. They would act like prepaid forward contracts, allowing savers to effectively lock in the cost of tuition at its current level.
But savers lock in current tuition rates only if they purchase enough tuition credits to cover all the tuition costs, and that’s hard to do for people who save for tuition in installments and who thereby end up purchasing tuition credits over time, at higher effective prices that incorporate tuition increases. Another serious problem is the severe penalties inflicted on those who do not use the credits offered by such prepaid plans.
Consortiums of universities are in a much better position than individual households to invest funds in such plans and to absorb the risks of doing so. By paying universities in advance, savers pass on the investment risk and the inability to match the risk–return characteristics of tuition. Such programs are likely to become increasingly popular as investors throw in the towel, frustrated by the near-impossibility of saving for college in a risk-managed manner.
From the savers’ point of view, state and private universities should clearly offer prepaid plans. The plans offer investors tax relief, risk relief, and a wide set of colleges to choose from. Universities, however, are understandably hesitant to embroil themselves in the travails of financial markets. They would be subject to the same volatility mismatch as savers.
However, universities do have two advantages relative to households—they are fully or partially tax-exempt and they are not subject to a fixed horizon. The key question for the universities is one of pricing— how to price the prepaid forward contract implicit in prepaid college savings plans.
But if institutes of higher education are considered candidates for monopolistic pricing, then the solution is clear: make the market more competitive by unfreezing tuition increases. This would allow tuition to vary, like other prices, with the overall economy. It would eliminate the volatility mismatch problem, make prepaid plans a useful but not essential savings vehicle for those who can afford them, and allow the broadest mix of consumers to save for college tuition.
References
Public and Private University Tuition:
College Board. 2003. “Trends in College Pricing 2003–2004.”
College Board. 2005. “Trends in College Pricing 2005.”
HEPI:
Commonfund Institute. 2006. “HEPI 2006 Update.”
US Inflation, Long-Term Government Bond Yields, Long-Term Government Bond Returns, Intermediate-Term Government Bond Yields, S&P 500, US Small Stocks, US Equity Risk Premium:
Morningstar. 2008. EnCorr Analyzer.
Faculty Salary Increases:
American Association of University Professors. March–April 2006 (March 30). “Table A.” Academe / The Devaluing of Higher Education: The Annual Report on the Economic Status of the Profession, 2005–2006. 26.
Expected Rates of Return:
Bodie, Zvi, Alex Kane, and Alan J. Marcus. 2009. Investments. 8th ed. Boston, MA. McGraw-Hill/Irwin. 126–127.
Goldenberg, David H., and Raymond J. Schmidt. December 1996. “On Estimating the Expected Rate of Return in Diffusion Price Models.” Journal of Financial and Quantitative Analysis 31, no. 4. 605–631.
US Equity Risk Premium:
Song, Zhiyi. 2008. “The Equity Risk Premium: An Annotated Bibliography.” The Research Foundation of CFA Institute Literature Review.
David H. Goldenberg is an associate professor of finance in the Lally School of Management and Technology at Rensselaer Polytechnic Institute.
Michael D. Goldenberg’s work on this paper began at RPI, where he earned his BS in chemical engineering and formed a student financial aid lobbying coalition.
Jonathan D. Linton is a professor of the management of technological enterprises in the University of Ottawa School of Management.
