Continuing from Part 1 and Part 2 in this series, we will now explore what happens when we change our long term expectations of return on our investment portfolios. I looked at increasing the ROR from 8% to 10% (1% interest, 2% dividends, 2% realized capital gains, 5% unrealized capital growth) and I also looked at decreasing the ROR to 6% (1% interest, 2% dividends, 1% realized capital gains, 2% unrealized capital growth).

Here are the annual after-tax incomes, in today’s dollars for the lower ROR of 6%, the base ROR of 8% and the higher ROR of 10%:

**Scenario A** – Surplus funds go to the RRSP first, tax refunds not used productively, once mortgage is paid off that money is re-directed to the RRSP

6% ROR = $31,250 8% ROR = $40,000 10% ROR = $54,800

**Scenario B** – Surplus funds go to the mortgage first, tax refunds not used productively, once the mortgage is paid off the RRSP is started

6% ROR = $31,500 8% ROR = $38,000 10% ROR = $48,000

**Scenario C** – Surplus funds go to RRSP first, tax refunds go to paying down the mortgage, once the mortgage is paid off, all extra money goes to the RRSP, and the tax refunds go to a non-registered account to augment retirement savings

6% ROR = $35,500 8% ROR = $46,300 10% ROR = $62,200

**Scenario D** – Surplus funds go to the mortgage first, once the mortgage is paid off the RRSP is started and tax refunds go to a non-registered account to augment retirement savings

6% ROR = $38,000 8% ROR = $48,000 10% ROR = $60,750

**There are a couple of items of note from looking at the results:**

1. Using your tax refund productively is a really good thing (duh).

2. Lower investment returns make paying the mortgage off quickly more attractive

3. Higher investment returns make contributing to your RRSP earlier more attractive

4. Paying the mortgage off quickly is LESS sensitive to changes in investment returns

5. Contributing to your RRSP earlier is MORE sensitive to changes in investment returns

Point 1 is pretty intuitive.

Points number 2 and 3 can be explained by the relative rates between the mortgage interest rate and the rate of return on your investments. Is there a magic number? *Not really *– it’s more complicated than that. While early contributions to the RRSP are more attractive when the long term rate of return on your portfolio increases, you have to take that with a grain of salt since the risk in the portfolio increases exponentially with increased expected portfolio returns. By aggressively paying down the mortgage there is relatively no risk involved since you know what you will end up with (almost) no matter what (as measured by variance in net worth patterns).

With respect to risk and return, most people mistakenly assume that just because they are taking more risk with their portfolios that it automatically means you will have more money down the road so long as you can stomach increased volatility. It is not a given. It is very much a possibility that someone with a balanced portfolio will have more money at the end of the day than someone who was more aggressive. By taking on a more volatile portfolio, you can only assume that the "potential" is higher that you will have more money at the end of the day.

**Let me demonstrate by running Scenarios C and D through Monte Carlo Sensitivity Analyses.**

Actually, first let me talk a bit about Monte Carlo Sensitivity Analyses. A Monte Carlo Sensitivity Analysis will allow you to incorporate standard deviations of portfolios into your financial plan and randomize life expectancies. It shows you the effects of taking on more risk by showing you the probability of the success of your plans based on return patterns that are not static. In other words most financial plans that use an 8% rate of return assume your portfolio will earn 8% each and every year. That’s okay-at-best for a lump sum investment – since the sequence of returns don’t matter, but not okay since you may not actually achieve 8% – it could be higher or lower. It’s horrible for regular contributions, and worse still for the withdrawal phase since, for example, if we look at the beginning of retirement: if the first few years of retirement are good years on the markets – you will substantially increase your average annual income. If they first few years are bad – the exact opposite is true. A static model will never show the true danger of this phenomenon. So the Monte Carlo simulations will model different life expectancies, different average rates of returns, and different sequences of returns all extrapolated from a model of risk/return that incorporates a parabolic relation between the risk and return. It will then spit out what amounts to a probability of success – where success is defined by certain variables (like dipping into a line of credit for more than $10,000 in any one year for example).

**Having said that, here is the Monte Carlo Graph of Scenario C** – it has a probability of success of 71% using an 8% ROR of attaining $46,300/year in retirement. Recall that this scenario calls for the saving to the RRSP from the get go.

**Compare that to the Monte Carlo Graph of Scenario D** – it has a probability of success of 84% using an 8% ROR of attaining $48,000/year. Recall that this scenario calls for an aggressive paying down of the mortgage.

You can look at the grids at the top of this post that shows the annual incomes for each scenario at the three different rates of return. From there you will see that you can eye-ball the sensitivity if you keep in mind that the probability of success decreases (RELATIVE TO THE STATED INCOME AMOUNTS) as the ROR increases.

For example, if you look from left to right, you will see that the **range** between income levels for each scenario are bigger or smaller depending on what strategy you are using. Look at Scenario C from left to right. The range is from $35,500 to $62,200. Scenario D ranges from $38,000 to $60,750. This can be accounted for by the difference in variance between the two plans, especially during the time the mortgage is still outstanding.

While paying to an RRSP becomes more attractive as the rate of return on your portfolio increases, you have to keep in mind that the probability of having that *higher* annual income in retirement decreases. So the next logical step would be to instead model the Monte Carlo Sensitivity Analysis on Scenarios C and D for the same level of income, at different rates of return to really have a solid understanding as to which strategy is better.

**But I’m not going to do that.** I’ve already made a TONNE of assumptions. I’m predicting things 60 years into the future, and not to mention, I haven’t looked at the variability in home equity, nor dipping into that equity. But I do think I’ve given a clearer pe

rspective to the debate. Normally, I’ve seen commentary that will indicate that one way is better than the other based on some principles – but without delving into actual numbers, and ultimately conceding that their theory does not always hold true. We never see soft numbers and fairly in-depth assumptions being made, so I decided to do that. Not to prove one strategy better than the other, but rather to help you make up your own mind based on your own "money personality".

Not everyone has the stomach for investing aggressively, and as such this analysis would suggest that paying the mortgage down aggressively is very attractive. For those who believe they can manage double digit returns long term – they will find the early RRSP savings strategy to be more attractive.

But beyond the quantitative aspects, there are the more qualitative aspects to consider as well.

1. Not everyone uses their full RRSP refund productively.

2. Some people are happy to downsize their homes in retirement – this then frees up capital for retirement income.

3. Aggressively paying down your mortgage may lead to a string of ever more expensive houses, which may negatively impact your RRSP savings plans in the future.

4. Flexibility. This is a big one. By aggressively paying down your mortgage first you are sacrificing flexibility. If you had some sort of emergency that required you to access cash, chances are the reason that you have the emergency will also hinder your application for an extension of credit. For example, if you lost your job, or were fired – your ability to get money back from the bank is reduced as they will look at your new income level. Certainly setting up a HELOC ahead of time would help you out, as would proper insurance, etc. But you get the idea.

5. Will you indeed pump as much money into the RRSP as you did to your mortgage payment once it is paid off?

My personal point of view is that there is no "one size fits all" answer to this debate. You need to understand your own risk profile, personal values, and financial plans to determine which strategy is best for your own personal situation. Sorry to disappoint those who were waiting for my verdict! :) Nonetheless, I hope I provided some insights and analysis techniques that will help you to better decide the debate as it applies to your own situation.

If you found this article of interest, please consider subscribing to my RSS Feed. If you want to learn more about what an RSS Feed is, click here.

For special deals for readers of WhereDoesAllMyMoneyGo.com (that’s you!), please visit the "Deals For Readers" section.

Fernando

Hi. I’m a relatively recent reader of your blog, and I must say I’m quite impressed with your analysis. This is by far the most thorough one I’ve seen on this whole debate. Thank you!

Adeem Zafar

Very helpful series you have written. I did have a question though…this is about mortgage vs. RRSP…what about credit card debt versus RRSP?

Preet

Fernando: thanks for the kind words. :)

Adeem: due to the high interest rates associated with credit cards – it is much better to pay that (and any other high interest debt) off first.

rm

In your assumptions of our subject being able to increase RRSP contributions after the mortgage is paid off early in D, does this assume that ALL of that mortgage payment money would fit into RRSP contribution room? Someone making 60k/year (in today’s dollars) can’t put 24k into RRSPs/year. Was this factored in?

Preet

@ rm – good question – the unused RRSP contribution room carries forward and more than allows for future contributions over and above the annual contribution room generation. I generated a table of it somewhere. I’ll see if I still have it and then post it as a follow up comment.

Cheers