*This course is no longer eligible for CE credits. Go to cecorner.ca to find eligible courses.*

A Registered Education Saving Plan (RESP) is an effective way of saving for the cost of a child’s post-secondary education. The maximum contribution allowed for each child within an RESP is $50,000. The government matches contributions with Canada Education Savings Grants up to a maximum of $7,200 per child. The growth on the savings is tax deferred and the accumulated assets are withdrawn during the period the child attends post-secondary education.

We examine the potential of the RESP to meet the future costs of higher education given the recent history of tuition fees increasing above the general rate of inflation.

## Start with the end in mind

Our focus is to assess the future cost of post-secondary education and whether savings through an RESP is likely, with current expected capital market returns, to cover these costs. We examine different investment strategies, different savings periods and the impact of investment management fees. This is an area that has not received much attention because the amounts are small compared to many investors’ total investment capital. In addition, it is more challenging to design a portfolio to meet a specific liability over a fixed time period than to seek long-term capital growth.

Clear thinking about objectives drives the investment strategy. Investors who attach a high importance to maximizing the potential final value must shoulder the risk of a shortfall. Investors who want to avoid downside risk must be prepared to invest more to achieve the same outcome to compensate for the lower return. Understanding these trade-offs is the motivation for constructing our analysis.

## Cost of post-secondary education

What is a reasonable estimate of the future cost of a university degree? A 2013 BMO study estimated the total current cost to be $60,000, including tuition, residence, meals and books. A frequently cited report from TD Canada Trust suggests that the annual increase to a student budget over an 18-year period is in the 2.9% to 3.5% range – well above the current rate of inflation. If we apply the mid-range of the TD estimate over the next 20 years, this would suggest a total cost of $112,653 in 2034. The BMO report estimates a cost in excess of $140,000 over the next 18 years. All these estimates are in future dollars.

These figures have attracted criticism. Some commentators feel that the banks are not impartial sources of advice and may be inclined to inflate savings requirements. Others point out that while it is true that tuition costs have outpaced the rate of inflation in the past, this is not sustainable indefinitely. Yet the most recent data on tuition costs from Statistics Canada shows a 3.3% increase in 2013-2014, following a 4.2% rise in 2012-2013. In comparison, inflation (as measured by the Consumer Price Index) was 1.3% between July 2012 and July 2013. Our approach is to take the average of the latest Statistics Canada data of 3.3% and PWL’s own estimate of general inflation of 2% to yield 2.65% as our estimate of the increase in total educational costs, recognizing that it is a blend of tuition costs and general student living costs.

Starting with the BMO estimate of current education costs of $60,000 and inflating it for 20 years at 2.65% yields a cost in 2034 dollars of $101,234. To enable comparisons over different time horizons, it is convenient to convert 2034 dollars into 2014 dollars, which is $68,127, a 13.5% real increase.

## Asset allocation decision

Having established a reasonable funding target, how successful are different asset allocation strategies?

We first discuss a 100% fixed-income strategy; then we’ll consider a 100% equity strategy and finally, intermediate asset allocations.

### 100% fixed income

If we could invest all the funds in the first year we could simply buy a bond that matures in 20 years. In the first year the initial deposit would be $50,000, which would attract a single government grant of $500, giving a total investment of $50,500. No further grants would be paid but this strategy maximizes the benefit of the tax-free compounding.

In our model we assume a single payment representing the total cost of a 4-year degree rather than staged payments over a 4-year period. We assume a maximum investment period of 20 years but also look at a 10-year period.

Currently, a Canadian investment-grade 20-year bond yields 4.0%. The total maturity value after 20 years of an initial investment of $50,500 is $74,225 (in 2014 dollars), which exceeds our target of $68,127. The main risk to this strategy is unexpectedly high inflation that erodes the spending power at maturity.

In practice, most young families are unable to make a $50,000 lump sum investment when their child is born. This leads us to construct a more realistic regular payment schedule. In Table 1 we construct a series of deposits that maximizes the government grant over both a 20-year and 10-year period. We assume the 10-year schedule starts 10 years later than the 20-year schedule and finishes on the same date.

### Table 1(a) 20-Year Deposit Schedule

Year | Deposit | Grant | Cumulative Total Deposits |
---|---|---|---|

1 | $2,500 | $500 | $3,000 |

2 | $2,500 | $500 | $6,000 |

3 | $2,500 | $500 | $9,000 |

4 | $2,500 | $500 | $12,000 |

5 | $2,500 | $500 | $15,000 |

6 | $2,500 | $500 | $18,000 |

7 | $2,500 | $500 | $21,000 |

8 | $2,500 | $500 | $24,000 |

9 | $2,500 | $500 | $27,000 |

10 | $2,500 | $500 | $30,000 |

11 | $2,500 | $500 | $33,000 |

12 | $2,500 | $500 | $36,000 |

13 | $2,500 | $500 | $39,000 |

14 | $2,500 | $500 | $42,000 |

15 | $2,500 | $200 | $44,700 |

16 | $2,500 | $47,200 | |

17 | $2,500 | $49,700 | |

18 | $2,500 | $52,200 | |

19 | $2,500 | $54,700 | |

20 | $2,500 | $57,200 |

### Table 1(b) 10-Year Deposit Schedule

Year | Deposit | Grant | Cumulative Total Deposits |
---|---|---|---|

11 | $5,000 | $1,000 | $6,000 |

12 | $5,000 | $1,000 | $12,000 |

13 | $5,000 | $1,000 | $18,000 |

14 | $5,000 | $1,000 | $24,000 |

15 | $5,000 | $1,000 | $30,000 |

16 | $5,000 | $1,000 | $36,000 |

17 | $5,000 | $1,000 | $42,000 |

18 | $5,000 | $200 | $47,200 |

19 | $5,000 | $52,200 | |

20 | $5,000 | $57,200 |

A fundamental principle of investing is to avoid risks that you do not get paid for. With this in mind, the best fixed-income strategy is to buy a bond every year that matures at the target date of the RESP. Thus, considering the 20-year investment schedule, in the beginning of Year 2 we would purchase a bond maturing in 19 years, and so on. Buying bonds that mature before the 20 years exposes the investor to reinvestment risk; buying bonds that have a maturity longer than 20 years exposes the investor to interest rate risk. Matching the maturity of the bonds with maturity of the RESP makes us indifferent to what interest rates might do over the intervening period.

Since we do not know future bond yields, we use the simplest model of taking the current yield curve and construct a straight line between the cash yield and the 20-year bond yield. Expected returns and standard deviations are based on PWL estimates using an equally weighted blend of historical performance and current market conditions. We use a Monte-Carlo model to simulate the volatility in returns and assess the downside risk. The model uses a normal distribution, which underestimates tail risk in equity market returns. So, consider our estimates of downside risk to be understated. See Appendix A for further details of the simulation model.

The model predicts a range of outcomes rather than a single value, reflecting the uncertainty around future bonds prices. The average value, as represented by the median or 50th percentile, is $56,406 with less than 1% probability of reaching the desired outcome of $68,127.

Under present market conditions we conclude a 100% fixed-income strategy is not going to achieve our target outcome and, since the total deposits in the RESP amount to $57,200 (including the grant portion), there is a more than 50% chance the 100% fixed-income strategy does not keep pace with inflation. We should note that thus far we have only considered gross market returns and ignored investment fees, which would further reduce returns.

### 100% equity option

We repeat our analysis with a well-diversified global equity portfolio. Equities have higher expected returns but also higher volatility. The median outcome rises to $91,234, but there is a 1 in 20 chance that the outcome is less than $52,331, which is less than initial contributions (including the Government grant). Whether this is an acceptable trade-off depends on the risk tolerance and circumstances of the investor. Clients who expect to have sufficient savings when the RESP funds are withdrawn to top up any shortfalls might be more tolerant of both the possibility of a poor outcome and the annual volatility along the way.

### Range of scenarios

Having established the basic model we explore:

- Impact of varying the mix of bond and equities
- Impact of investing over a shorter time horizon (10 years).

In each scenario we note the median outcome (50th percentile) and the 5th percentile (i.e. the portfolio value below which 1 in 20 of the outcomes fall).

### Figure 1: Impact of asset allocation on terminal RESP values

Source: PWL Capital

Figure 1 summarizes the results of different asset allocations for both the 20-year and 10-year investment horizons. The dashed horizontal line represents the desired outcome of covering 100% of the estimated future cost (in 2014 dollars) of post-secondary education of $68,127.

Over a 10-year period, none of the investment strategies with less than an 80% equity allocation achieve a 50% chance of success. Over 20 years a minimum 40% allocation to equities is required. In either case pursuing a higher equity allocation leads to a higher expected return.

The likelihood of a poor outcome is measured by the 5th percentiles: there is a 1 in 20 chance of outcomes below this value. Over 20 years the 5th percentile is not very sensitive to a rising equity allocation. Although equities over a one year period are more volatile than bonds, their higher expected return means that, over longer periods, the probability of a loss in value decreases while the expected value due to compound growth increases.

The net effect of these two trends is small. Over 10 years, higher equity allocations result in higher downside risk, as the compounding effect of higher equity returns is less over a shorter horizon. As a consequence, the shorter investment period has a higher probability of a bad outcome.

## Shortfall risk

In general, shortfall risk, in dollars, of a bad event is the probability of that event multiplied by its cost. For example, auto insurance premiums are calculated not just on the basis of driving history to assess the probability of an accident, but also the cost of vehicle repair or replacement should an accident occur.

Suppose we wanted to insure our RESP portfolio against loss. What would it cost?

This question has been addressed very succinctly in a paper by Zvi Bodie, using option pricing theory. The details need not concern us, but the conclusions should. We use his analysis to compute the cost of insuring an RESP deposit against loss (for our purposes a loss is a return less than the assumed rate of inflation of 2%). We use the volatility data from the portfolios in our previous analysis. The results are summarised in Figure 2.

### Figure 2: Shortfall risk to RESP contributions

Source: PWL Capital

The first point to note from Figure 2 is that the common view that stocks are safer in the long run is wrong: the cost of insuring against loss increases as the investment period increases. Although the probability of stocks underperforming declines, when stocks lose value they can fall dramatically and the cost of protecting against this risk increases with the investment horizon. To quote Bodie: “Stocks are not a hedge against fixed-income liabilities even in the long run.”

In Figure 2 the cost of insurance is measured as a percentage of the initial deposit. Since our analysis has a series of deposits over time, the curves in Figure 2 only represent the insurance cost of an initial deposit in Year 1. However, taking into account that the RESP is not just a single lump sum would not change the second conclusion from Figure 2: the cost of shortfall risk increases with equity allocation. To take a specific example: over 20 years the cost of a shortfall for an 80% equity portfolio is 18.3% compared with 10.3% for a 40% equity allocation.

In addition, there is a behavioural challenge associated with a high volatility portfolio that these numbers do not address. In the situation of falling portfolio value and a looming liability it can be a challenge to stay the course. Some commentators have suggested a high allocation to equities initially, reducing as the target date approaches. We examined the impact of starting with 100% equities and decreasing the equity allocation every 4 years (20-year investment horizon) or every 2 years (10-year investment horizon). In both cases the terminal value and downside risk was within 1% of a constant 40% equity allocation. Reducing the equity allocation seems attractive if the portfolio is ahead of target (which is likely the outcome most people like to think about when considering this scenario) but is more difficult if it is lagging and there is a desire to catch up.

## Impact of fees

Thus far we have looked at gross market returns, ignoring investment fees, which reduce the portfolio return but leave volatility unchanged. We consider two fee levels, 1.34% and 2.38%, and look at the impact on a portfolio with a 60% equity allocation over 20 years. The lower fee is an estimate for fee-only clients; the higher fee is indicative of a comparable retail mutual fund with a 60% global equity allocation.

### Figure 3: Impact of Fees: 60% equity portfolio

Source: PWL Capital

As seen from Figure 3, the impact of fees is to reduce the probability of a 60% equity portfolio achieving the desired outcome (as represented by the dashed line) to less than 50%. With a 1.34% fee, the median outcome falls from $76,130 to $66,495 and with a 2.38% fee it reduces further to $59,928. The downside risk also increase as 1 in 20 of the outcomes fall below lower values, as indicated by the 5th percentile.

## Implementation considerations

Given the small annual contributions from the investor and the government grant, the lower fees of ETFs compared to mutual funds may more than offset by the higher transaction costs for ETFs. Individual stock or bond portfolios makes no sense within an RESP because of inadequate diversification and high transaction costs.

## Conclusions

The disappointing news is that even under the ideal condition of starting an RESP upon the birth of a child and with modest investment fees, the probability of the RESP final value meeting the future costs of higher education is less than 50%.

The investor who is willing to consider higher (in excess of 60%) equity allocations in search of higher returns must also risk the possibility of a bad outcome, including partial loss of principal. When we account for fees, a 60% equity portfolio would be expected to account for between 71%-98% of the anticipated education cost of $68,127, depending on how confident investors want to be about the outcome (71% is achieved at the 95% confidence level, 98% at the 50% confidence level). Despite these limitations, RESPs should be exploited to the maximum for their tax deferred investment growth and government grants.

Be cautious about equity allocations greater than 60%: the cost of a shortfall rises with the investment period and the portfolio volatility.

Possible mitigation strategies:

- having children go to local universities and reduce residence costs by staying at home;
- higher reliance on student loans;
- student employment income or additional parental support; or
- a combination of all of these.

If RESPs are no longer a one-stop solution to providing for post-secondary education, clients should consider their education savings strategy in the context of their overall financial planning. Our analysis focuses on the key determinants of the final value of the RESP. These are: the investment horizon, asset allocation, fees and the importance investors attach to protecting their initial investment. Compared to retirement, the horizon for post-secondary education is likely to be shorter and the liabilities less flexible. These constraints suggest the asset allocation for investing for educational purposes should be no more aggressive than would be used for retirement planning.

## Appendix A: Monte-Carlo Simulations

To simulate the performance of the RESP under different scenarios we use the Monte-Carlo simulator in Returns 2, a modelling package from Dimensional Fund Advisors (DFA).

To illustrate, we include the model input and results for the case of 40% equity over a 20-year period. The portfolio’s expected return and volatility change over the period because the bond maturity and volatility reduce as the years pass. Returns 2 is primarily designed as a retirement calculator. In our application, ‘retirement’ is at the end of 20 years when the RESP would be withdrawn.

Table 1 is the computed returns and standard deviation. The data are calculated using PWL’s expected bond and equity returns and assuming an average correlation coefficient of 0.14. The bond return and volatility is assumed to reduce linearly to a cash return 1% and 0% volatility in Year 20.

### Table 1: 40% equity

Year | Return | Std.Deviation |
---|---|---|

1 | 5.11% | 5.80% |

2 | 5.02% | 5.75% |

3 | 4.94% | 5.69% |

4 | 4.85% | 5.63% |

5 | 4.77% | 5.58% |

6 | 4.68% | 5.53% |

7 | 4.60% | 5.49% |

8 | 4.51% | 5.44% |

9 | 4.43% | 5.40% |

10 | 4.34% | 5.36% |

11 | 4.26% | 5.32% |

12 | 4.17% | 5.29% |

13 | 4.08% | 5.26% |

14 | 4.00% | 5.23% |

15 | 3.91% | 5.20% |

16 | 3.83% | 5.18% |

17 | 3.74% | 5.16% |

18 | 3.66% | 5.14% |

19 | 3.57% | 5.13% |

20 | 3.49% | 5.12% |

Figures A1 and A2 show summary statistics as a function of time (all the simulations started at age 30 and ended 10 or 20 years later) and the final value grouped by percentile.

### Figure A1: Summary statistics

### Figure A2: Cumulative values at 20 years

## Appendix B: Bodie’s Shortfall Risk Model

The model treats the insurance cost of a stock portfolio underperforming a risk free alternative as a put option which is valued according to the Black-Scholes option pricing model which reduces to:

P/S = N(d1 ) – N (-d1 )

where:

d1 = σ√T∕2

T = the time to maturity

σ = portfolio standard deviation

N(d) = probability that a random draw from a normal distribution will be less than d.

P = Insurance cost

S = Price of investment

*Graham Westmacott is a portfolio manager at PWL Capital in Waterloo, Ont.*