Savings rate

Savings rate is the amount set aside from income towards retirement. How much to save every year for retirement, starting perhaps 30 or even 40 years in advance, is a very difficult question to answer. So far ahead, there are probably too many variables to make detailed individual projections. Faced with complex decisions, people tend to use to rules of thumb like “save 10% of your income” (e.g., ), or “save as much as possible”, or “max out your Registered Retirement Savings Plan (RRSP)”, and hope for a good outcome. But depending on a number of factors, using such rules of thumb could result in saving too much, or more worryingly, not saving enough, to maintain one’s standard of living during retirement.

In this article, we explore two different approaches to determine "optimal" savings rates that aim, implicitly or explicitly, to maintain the standard of living of the retiree.

The first approach applies the traditional concept of an income replacement rate, which is used to determine the level of income needed during retirement. It is assumed that replacing a certain percentage of pre-retirement income will maintain the standard of living. A savings rate is calculated that allows this replacement rate to be reached.

In second the approach, the replacement rate is not predetermined. Instead, the aim is to explicitly maintain, or smooth out, the standard of living from year to year, including the retirement transition. The savings rate and the income replacement rate are both outputs of the calculations. This second approach relies on life-cycle models, or has similar goals.

Savings rate

We define the savings rate as the proportion of gross income that is saved and invested for retirement, for example in a RRSP, employer pension plan or Tax-Free Savings Account (TFSA), but not counting Canada Pension Plan (CPP) or Québec Pension Plan (QPP) deductions, because those are inevitable.

The required savings rate is controlled by factors such as:

• the length of the saving period (the longer the accumulation phase, the lower the rate);
• the pre-retirement income to be replaced (higher incomes require higher savings rates);
• the desired income replacement rate (the higher the desired replacement rate, the higher the required savings rate);
• the expected real return during accumulation and retirement (itself a function of asset allocation and investment costs);
• the life expectancy at the beginning of retirement (a longer retirement means saving more during accumulation);
• the withdrawal method during retirement.

The income replacement rate that will actually smooth out consumption is itself influenced by factors such as:

• income levels;
• family size (single or couple, with or without children);
• home ownership.

The multitude of factors influencing the required savings rate make it clear that universal guidelines such as "save 10% of your income" are not very useful.

Calculating your current savings rate

Calculating your current savings rate

Find your latest Notice of assessment from the Canada Revenue Agency (CRA) and look at the RRSP/PRPP deduction limit statement. 1. Add the following: Your "employer's PRPP contributions for 20xx"1 Your "allowable RRSP/PRPP contributions deducted for 20xx"1 Your "20xx pension adjustment"1 Also add any net TFSA contributions, and any net additions to non-registered investment accounts2, that you made during year 20xx and that are aimed at providing retirement income. (These do not appear on your Notice of assessment.)

2. Divide the sum of step (1) by your "20xx earned income":3 this is your savings rate for year 20xx.

Notes: 1. These three amounts are what you and your employer contributed to your RRSP and, if applicable, pension plan, for year 20xx. 2. Pension and RRSP contributions create tax breaks (taxes will be paid later), whereas TFSA and non-registered contributions are made with after-tax dollars. The calculation presented in this table does not account for this. 3. The details of how the CRA calculates "earned income" are given at Calculating your 2015 earned income.

Because an individual's savings rate can very greatly from year to year, you may want to do this for the previous 3 to 5 years and produce an average value. This average can then be compared with the required savings rates indicated in the following sections.

The traditional income replacement rate approach

The traditional approach relies on another rule of thumb, the concept of replacing a percentage of the final pre-retirement income during retirement, typically 70%. Some retirees may need less than 70% replacement while others may need more (see the article on income replacement rates for a full discussion), depending on lifestyle choices and other factors, so some required savings rates for replacement rates of 50% and 100% will also be mentioned as end-members.

The following two C.D. Howe Institute reports are used to illustrate the traditional approach to calculate savings rates. The authors start from a certain income replacement rate as the target (commonly 70%); they then make assumptions on factors such as the real rates of returns on investments; real wage growth; inflation; government transfers; income taxes, etc. and arrive at the required savings rates.

The proposed savings rates are typically constant over the accumulation period. Saving the same proportion of one’s income every year could be difficult to achieve in early years, when incomes are lower and expenses are many, so one report also suggests savings rates that increase over time.

Saving for 30 years (Guay & Jean, 2013)

Guay & Jean (2013) calculate that on a balanced (50-50) portfolio, the expected long-term real return is only 2.7% (0.5% on long bonds and 4.8% on stocks), before taxes (if applicable) and investment costs (fees). Based on this they construct scenarios for two income profiles: a final salary of $50k and a final salary of $100k. The investor is currently 35 years old and wants to retire at age 65, i.e. in 30 years. The authors generate results for income replacement levels of 50%, 70% and 100% at retirement, taking OAS/GIS as well as CPP/QPP into account. They assume 2% real growth in income during accumulation and a 20 year life expectancy at age 65. Investment costs (fees) and taxes are not taken into account. The results are in the following table:

	Savings rate (%)
Start/final income: $27,600/$50,000
50% replacement	6.5
70% replacement	14
100% replacement	25.3
Start/final income: $55,200/$100,000
50% replacement	12.1
70% replacement	19.6
100% replacement	32.8

Note that some of the savings rate in this table surpass the 18% of earned income maximum for RRSP contributions. The 18% of earned income rule -- the current limit on RRSP contributions -- was established at a time when interest rates where much higher, but the rules have yet to change to reflect lower interest rates and higher required savings rates to reach the 70% income replacement ratio at age 65.

If your life expectancy is longer, or your final salary will be higher, or the real returns are lower, or your costs are not zero, the required savings rates would be even higher with this approach. For example, if we add 1% investment costs (which is still much lower than the average management expense ratio on Canadian mutual funds), the required savings rate become:

	Savings rate (%)
Start/final income: $27,600/$50,000
50% replacement	8.1
70% replacement	17.6
100% replacement	31.7
Start/final income: $55,200/$100,000
50% replacement	15.1
70% replacement	24.6
100% replacement	41.0

Saving for 33-37 years (Dodge et al., 2010)

Dodge et al. (2010) assume 33 to 37 years of saving, by setting the beginning age at 30 and the retirement age at 63, 65 or 67. A 4% real return is assumed for a "prudent portfolio" (by which they mean something like 60% Canadian equities, 20% long bonds and 20% T-bills) during the accumulation stage but they reduce the real return to 3% "to be prudent and to compensate for other potential sources of bias". This 3% real return is only slightly more than in the 2013 study presented above. Dodge et al. assume 2% inflation and real wage growth of 1% (in other words, the income during the accumulation stage grows at 1% a year over the rate of inflation). During retirement, government benefits are accounted for in the income replacement rates, and the investor purchases an indexed annuity to provide a stable income. Investment costs and taxes on savings (if applicable) are not taken into account.

The following table shows the constant saving rates to replace 70% of income at retirement, with retirement taking place at age 63, 65 or 67.

	Age 63	Age 65	Age 67
Annual earnings, age 30-55	Savings rate (%)	Savings rate (%)	Savings rate (%)
1st Decile – $12,451	0	0	0
2nd Decile – $21,056	0	0	0
3rd Decile – $28,530	11	7	5
4th Decile – $35,782	15	10	8
5th Decile – $42,803	16	11	9
6th Decile – $51,381	17	13	10
7th Decile – $61,270	19	14	12
8th Decile – $73,958	20	16	13
9th Decile – $95,627	22	17	15
High Income – $150,000	25	21	17

Dodge et al. recognize that a constant savings rate may not be practical (perhaps one focusses on paying down the mortgage first for example), so they examine a scenario in which the investor saves for retirement "normally" between the ages of 42 and 53; at half this rate between the ages of 30 and 41; and at 1.5 times the "normal" rate between the ages of 54 and retirement. This yields the following table for a 70% replacement rate and a 35 years savings period (retirement at 65):

	Age 30-41	Age 42-53	Age 54-64
Annual earnings, age 30-55	Savings rate (%)	Savings rate (%)	Savings rate (%)
1st Decile – $12,451	0	0	0
2nd Decile – $21,056	0	0	0
3rd Decile – $28,530	4	8	11
4th Decile – $35,782	6	11	17
5th Decile – $42,803	6	12	19
6th Decile – $51,381	7	14	21
7th Decile – $61,270	8	16	24
8th Decile – $73,958	9	17	26
9th Decile – $95,627	10	19	29
High Income – $150,000	11	23	34

Reducing the assumed real return to account for investment costs would produce even higher savings rates.

Safe savings rates

Instead of making explicit assumptions about future returns, Pfau (2011) looks at what has worked in the past for US retirees. He takes historical returns for US stocks, and six-month commercial paper (very short term fixed income) between 1871 and 2009 and looks at the experiences of retirees based on portfolios with constant asset allocations (such as 60% stocks and 40% 'bonds') over the full period of saving and retirement. He assumes a constant savings rate, and a salary that growths along with inflation (0% real wage growth). The worker wishes to replace 50% of her final salary, adjusted every year for inflation, based on withdrawals from her portfolio. Taxes and investment costs are ignored. Pfau computes the savings rates actually required to achieve this for every retirement year in the studied time period. For a 30 year savings period and a 30 year retirement, with a balanced 60/40 portfolio, the required savings rates were historically between 9.3% and 16.6%. Therefore, 16.6% is considered the "safe savings rate" in this particular example: this is the savings rate that has always been enough to achieve the 50% income replacement rate in the past. Someone who believes that the future will look the same could therefore save 17% every year over 30 years, and fingers crossed, the nest egg will last 30 years (again assuming no taxes and no investment fees). Note that this approach allows withdrawal rates that may be well above 4%, the assumption being that if investment returns are low during the saving period, they have a tendency to be higher during the retirement period. While this worked during the study period, there are of course no guarantees about the future.

Pfau then expands the approach to savings periods between 20 and 40 years, and retirement periods between 20 and 40 years. He also varies the asset allocations. This yields the following table:

Safe savings rates

		40% stocks/ 60% 'bonds'			60% stocks/ 40% 'bonds'			80% stocks/ 20% 'bonds'
Retirement phase → Accumulation phase ↓	20 years	30 years	40 years	20 years	30 years	40 years	20 years	30 years	40 years
20 years	32.0	39.5	47.0	30.9	35.9	38.9	30.5	34.5	35.9
30 years	15.6	19.3	22.2	13.9	16.6	18.6	12.9	15.1	16.6
40 years	10.3	12.4	13.8	7.6	8.8	9.2	6.3	7.4	8.1

Even if the savings rates in the table above should not be taken too literally, the table is still very useful to visualize the effect of changing the saving (accumulation) or retirement duration, as well as the asset allocation. The length the accumulation phase, in particular, has a dramatic effect on savings rates.

A follow-up study showed that conducting a similar exercise in other developed countries leads to higher 'safe' savings rates than in the US.

Lifecycle models

Horner (2009)

The models in the previous section assume a target income replacement rate (typically 70%), and calculate the savings rate required to reach this, using a number of assumptions. The idea is that a 70% replacement rate is needed to allow the retiree to maintain the same level of consumption. However, this premise is not tested explicitly. Is a 70% replacement rate necessary for everyone? Shouldn’t factors such as the income level, renting or owning, and family size (single or couple, with or without children), be taken into account?

Horner (2009) does exactly this in a report prepared for the Research Working Group on Retirement Income Adequacy (see for a summary of the working group’s findings). This is a long report that cannot be entirely summarized here, but it is well worth reading (especially part 3, “Benchmarks for savings adequacy”). Retirement is assumed to take place at age 65, after 35 years of saving.

The approach is to calculate the savings rate that will allow household consumption at age 64 (pre-retirement) to equal consumption at age 65 (after retirement), using a stylized two-period lifecycle model (rather than a more general multi-period lifecycle finance model). Importantly, there are no a priori ideas on the income replacement rates necessary, instead, the income replacement rates are calculated by the model. Assumptions include 2% inflation; a real rate of return on savings of 3.5% (higher than in the previous two studies, and based on "an assessment of pension plan returns over a long period"); 1% real wage growth; 20 year life expectancy at retirement (a 20-year annuity is purchased); limits on RRSP contributions are ignored; work-related expenses are $300 a year plus 3% of earnings; and certain other assumptions about the Canadian tax system, the effect of children on consumption and taxes, and the costs & benefits of home ownership.

Graphs in the report show the savings rate, and the replacement rate, as a function of earnings, for:

• Single renter and single homeowner
• Single-parent renter with two children
• One-earner and two-earner homeowner couples
• One-earner and two-earner two-parent homeowner couples

The following table gives some savings rate (during accumulation), and income replacement rates (during retirement), for a $80k pre-retirement income, the middle of the range shown in the graphs. Except were otherwise noted, the real return on savings is 3.5%:

	Savings rate (%)	Income replacement rate (%)
Single renter	15	75
Single homeowner	13	69
Single parent (renter, 2 children)	6	45
Homeowner couple, one earner	10	65
Homeowner couple, two earners	8	67
Idem but 2.5% real return	9.5	?
Homeowner parents, one earner	7	53
Homeowner parents, two earners	4	53

(Note: the numbers were eyeballed from the graphs, and should be accurate to +/-1% on the savings rates and +/-3% on the replacement rates)

In summary:

• home ownership reduces savings rates by 2% and earnings replacement rates by about 7%
• having children is expensive, but greatly reduces the necessary savings rate (after retirement, only the parents’ consumption is maintained, the children are assumed to have left the household)
• the savings rates are lower than those proposed in the previous section, because the replacement rates are lower, the assumed real returns are higher, and children/home ownership are taken into account
• decreasing the assumed real return by 1% rises the required savings rate, but not as much as could be expected because saving more money reduces consumption during asset accumulation, which means that the income to be replaced during retirement becomes less. The C.D. Howe reports ignore such effects.

Chapurat et al. (2012)

There is yet another way to approach the savings rate problem, again using lifecycle finance. Instead of smoothing consumption immediately before and immediately after retirement, like in the Horner (2009) study, a complete lifecycle model would smooth consumption from the beginning of the work life until death. Chapurat et al. (2012) show what such a model could look like in the absence of our complex system of taxes and government benefits. Here is one example for a 25 year old about to start working, planning to retire at 65, and planning to die at 90. There is $3000 in a savings account, and no debt. The initial salary, payable at year end, will be $50,500, and will grow at a real (after-inflation) rate of 1%. All valuation rates are 3% real (return on investment, discount rate for human capital, etc). Yearly consumption is to remain constant in real terms. The following table shows the results of the calculations, with all numbers in today’s dollars:

Age	Salary	Consumption	Savings	Savings rate
25	$50 500	$48 334	$2 156	4.3%
35	$55 783	$48 334	$7 439	13.3%
45	$61 620	$48 334	$13 275	21.5%
55	$68 066	$48 334	$19 722	29.0%
64	$74 443	$48 334	$26 099	35.1%

Note how the savings rate increases from about 4% during the first year of work to over 35% during the last year of work. Yearly consumption, meanwhile, remains constant in real terms (but would increase in nominal terms). A age 65, the financial capital accumulated would be over $800k (in today’s dollars), which would allow consumption to continue at the same constant real level until death. The important message here is that a constant savings rate is not the most rational approach. Consumption smoothing throughout the life cycle requires a variable savings rate.

Discussion

Low income workers

Both types of models, traditional or lifecycle, show that for low income workers, government benefits alone, if maintained at the current levels, should be enough to maintain living standards during retirement. In other words, the required savings rate is zero. Indeed, saving money in a RRSP could be a mistake; the TFSA is a better choice because it does not affect the Guaranteed Income Supplement (GIS), see GIS: maximizing benefits.

Required savings rates

For middle and high income households, some of the savings rates in the two C.D. Howe reports seem nearly impossible to attain, whereas some of the savings rates in the Horner (2009) study can appear dangerously low, leaving no margin of safety. The large differences in savings rates between the various models are caused by the varied assumptions and methodologies. Readers should remember that the models are built mostly for the purposes of government policy discussions, to answer questions such as “are Canadians saving enough?”, not necessarily as savings recommendations for actual living persons.

In the C.D. Howe studies, savings rates are quite high because a unique 70% replacement rate is used. This could result in saving too much for some people: as the Horner study shows, having children or owning a home both depress pre-retirement consumption, so maintaining consumption after retirement may not require 70% replacement rates.

On the other hand, some of the savings rates in the Horner study appear quite low. This is partly a function of a relatively short retirement period that is assumed (only 20 years and then the money is gone, except for government transfers), and an assumed real rate of return that is higher than in the C.D. Howe studies. Consider saving more if:

• you intend to live longer than 20 years after retirement, or
• you think that government transfers might not be maintained at their current levels, or
• you think that tax rates may change, or
• you'd like to have early retirement as a possible option, or
• your investment costs are not zero.

Required savings rate too high?

If you cannot, or are not willing to, reach the required savings rate indicated by the studies presented above, you can:

1. Establish an automated monthly transfer from your chequing account to your RRSP or TFSA ("pay yourself first") -- perhaps the required savings rate will be attainable this way;
2. Lower your investment costs as much as possible, by not paying an advisor and by purchasing low-fee index funds or exchange-traded funds (ETFs);
3. Start saving sooner, or delay retirement, to extend the savings period;
4. Decrease the targeted income replacement percentage, for example only attempt to replace 50% of your final salary during retirement instead of 70%);
5. Take on more risk than with 50% or 60% stocks in your retirement portfolio in the hope of increasing the expected return

See also

• Importance of saving early
• Consumption smoothing

Further reading

• N. Charupat et al. Strategic Financial Planning over the Lifecycle, Chapter #4: Consumption Smoothing, lecture notes: "We are interested in three very important quantities: (1) the optimal savings rate during your working years; (2) the optimal trajectory of financial capital over your lifecycle, and; (3) the optimal retirement spending rate once your wage income is zero."
• M. Hamilton, Do Canadians Save Too Little?, C.D. Howe Institute Commentary 428: "author Malcolm Hamilton takes a fresh look at all the assumptions and finds that Canadians are reasonably well prepared for retirement"

External links

• Bogleheads wiki: Life-cycle finance, tutorial on life-cycle finance.
• Bogleheads wiki: Replacement rate models of retirement spending.
• B. Carlson, When saving trumps investing, A Wealth of Common Sense, May 13, 2014, viewed February 28, 2015