Archive for the 'calculations' Category

Global TV Says Vancouver Housing Bubble Has Burst

Just over 4 months ago, I wrote that the Vancouver housing bubble had finally burst. The mainstream media has finally come on board and is supporting the idea that housing prices will fall over the next few years, based on a report from Central 1 Credit Union. Take a look at this report from Global TV:

Global TV is now saying that the “air is now officially out of the real estate balloon.” My only complaint with the piece is that there is no mention of the complete lack of affordability being any factor in the price drop. They are attributing the drop to “the global financial crisis and a big drop in consumer confidence” which have “combined to drive the housing market into recession.” Helmut Pastrick mentioned the “uncertain and volatile times we’re living in.” They say “how many times have we heard that somehow Greater Vancouver’s real market was insulated from what was happening in virtually everywhere else in the western world….that prices were falling?” They talk as if there are only two possible outcomes: either Vancouver is insulated from the rest of the world in which case our prices won’t fall along with the rest of the world, or Vancouver is not insulated in which case our housing prices will fall because prices are falling elsewhere. Even if Vancouver were completely insulated from the rest of the world (no trade, no communication, an island in the middle of the ocean) our housing prices would have to fall in order for affordability return to normal levels. Yet the piece leaves us with an overwhelming feeling that Vancouver’s real estate market woes are the fault of others, the fault of a US/world credit crisis and of a US/Canadian recession, the fault of some mysterious outside, external force. There is some mention that speculators and investors, who up until recently were lining up to pre-buy condos are likely to be the hardest hit, but no mention of their part in causing this mess. No mention of the fact that housing prices were just too damn high and affordability too damn low.

The real estate agent near the end says that we are now (or are soon to be) in a “classic move-up market.” What he is saying is that when housing prices are low, it is easier to move up from a small townhouse/condo to a house, for example. It’s funny because this is what a lot of people were doing when market prices were high; taking the equity out of their home and buying a second home or moving into a bigger house, while taking on more debt. Obviously when market prices are on the low-side it is a better time for a “move-up”, just like it is a better time to buy, or to enter the market for the first time. When market prices were high it is a better time to “down-grade”, or to leave the market entirely and become a renter.

The piece also got some of the math wrong. A drop of 12%, 13%, and 5% is an overall drop of 27.2%, not 30%:


The above is just a complicated way of saying that you had something that was reduced by 12%, then 13%, the 5%, the result would be a reduction of 27% from the original, not 30%.

Hmm, my guess is that no banks will be offering 0% down mortgages any time soon… at least not unless you have some other really expensive assets that they think they can repossess..

Popularity: 64% [?]

Buy vs. Rent Calculators (for a Home)

I just discovered a great buy vs. rent calculator at the New York Times website. Check it out:

New York Times buy vs. rent calculator (don’t forget to check out the advanced settings on the right-hand side!)

Don’t forget about the VanCity buy vs. rent calculator, which I blogged about previously: Vancity buy vs. rent calculator.

The Canadian government also has their own rent vs. buy calculator.

Popularity: 9% [?]

Fidelity Says You Need 80% Pre-Retirement Income in Retirement (just don’t use them to get you there)

According to Fidelity, we need 80% of our current income to retire (see Canadian Capitalist’s “Fidelity’s ‘Scary’ Retirement Findings“, where I found this story). Canadians on average have 50% of their pre-retirement income in retirement, but this is no different from other countries; United States: 58%, Britain: 50%, Germany; 56%, Japan: 47% (see “Want to play in retirement? Test your future income“). If those numbers are not adequate, it implies that the average senior in the United States, Britain, Germany, and Japan are all in dire need. I doubt that is the case. (My opinion is that people should save as much as they want. You might need only 50% but if you want to spend a lot in retirement and travel instead of just tinkering in your garden then maybe you need 80% of your pre-retirement income, or maybe 150%, just in case.)

The funny part is that even if you wanted to get to 80%, the hardest way to get there would be to use Fidelity’s products. All their MERs are above 2% (click on Facts & codes). It’s too bad their retirement calculator doesn’t have a slider bar for the MER or rate of return, then you would be able to see just how badly these management expense fees can affect the final value of your portfolio, and in turn, your annual income in retirement.

I just did a calculation and if you invest $8,500 annually starting from the age of 30 you end up with $2 million at the age of 65 if the contributions are indexed to inflation and the rate of return is 8% (the return you might get if you buy a low-MER (0.25%) investment, like an index ETF). Decrease that return to 5.75% (the return you’ll get if you pay a 2.5% MER on Fidelity mutual funds or their managed portfolios) and you’ll have only $1.32 million at age 65. Assuming $2.64 million is what one would need to keep the same income one enjoyed pre-retirement:

In the 2.5% MER case: $1.32 million is 50% of $2.64 million

In the 0.25% MER case: $2 million is 76% of $2.64 million.

So by simply not using a company like Fidelity and going with a competitor like Vanguard or iShares and buying index ETFs (with far lower MERs) instead, you can easily get closer to that 80% figure and increase your nest egg from to $2 million from $1.32 million without even having to save any more money. By the same token, it could probably be argued that one of the main reasons that Canadians do not have 70-80% of their pre-retirement income in retirement (and only have 50% instead) is because of the amount of MERs, fees, and commissions they pay every year to the financial industry.

See also:
Should Retirement Replacement Ratio be 50%, 80% or in between?

Popularity: 24% [?]

Funny Mortgage Math

I was just looking at MLS listings earlier today and I saw this nice little place on Main Street in Vancouver and noticed the following statement by the realtor:

Investor alert, 2 potential suite. Main floor $1200/mo, 2nd floor $1500/mo, total $2700/mo

Investor alert? So he is implying that is an investment and I wanted to see if he was right. He is saying that rent would be $2700 for the whole place per month, and the asking price is $788,000. I am assuming that he his being completely honest on that rent figure or over-estimating it, as he has a vested interest in making this property as appealing as possible. Let’s assume some ideal conditions, that I have a 25% down payment as well, a 35 year mortgage, and a low interest rate of 5.5% (even lower than ING’s lowest rate). Plugging those into MLS’ handy mortgage calculator, even then, the monthly mortgage costs are $3149.80/month. If we rent the place out we are still short $449.80. So this is not an interest-bearing investment of any kind. We have invested $197,000 for the down-payment, and in return we owe at least $449.80/month (most likely more if we include maintenance costs, property taxes, etc…). That’s a -2.7% annualized return. If we put down a $78,800 down payment (or 10%), we owe at least $1100/month. It starts to become profitable with about a $300,000 down payment. I have neglected capital appreciation of the home of course. Historically, however, housing prices have grown with inflation, as shown in the graph below:
A History of Home Values
So one can never expect to make much off of capital appreciation of real estate. Not only that but as prices get higher and higher the probability that they will continue to grow faster than inflation decreases and the chances they will fall increases. Now back to the original MLS listing. How is this an investment?

Popularity: 10% [?]

Ask Dave: Costs of Switching From Stocks to ETFs

Another reader had some questions about how to switch from a mutual fund and/or equity-based portfolio to a passive ETF-based portfolio.

My wife and I have 3 accounts which have about 20 equities in each. As a whole, the accounts are not well balanced, and they are overweighted with Canadian securities from the days that there were restrictions to RRSPs in their foreign content.

I have taken over management of the accounts myself. They have been moved to a discount brokerage that was imposed on us because of some quirks in the accounts that forced us to use a particular broker who was agreeable to accept our holdings. Their trading fee is $29.95/transaction.

After doing extensive reading and research, I have decided to restructure the accounts to resemble a structure similar to your Passive EFT portfolio. I was very impressed with your rationale in formulating your post of April 15, 2007.

We are locked in to some mutual funds and other fixed income vehicles which will restrict our immediate restructuring abilities. I believe it may be best to leave the best of our Canadian equities that are already in place, rather than selling them and purchasing XIC. We will also need to keep the other restricted holdings, as mentioned above. As a result, we will need to take substantial new positions in VTI, VWO and XIN. In essence, we will be paring 50 or more holdings to less than 10. We will basically sell Canadian equities, mostly banks, to purchase diversified content, US and foreign (VTI, VWO, XIN).

First, I want to make a general point. Do not forget that stocks have no MERs. If you have a portfolio of 60 stocks it has no ongoing expense fee. Hold on to them for many years and you may do better than index ETFs which have a small non-negligible MER. So is worth it to sell those 60 equities you have spread out between 3 accounts? Maybe not. 60 equities is plenty of diversification in one market. If a portfolio of 60 Canadian equities was handed down to me I would think twice about selling them and switching to an ETF. The commission to sell those 60 equities is going to be $1200 at least, plus I am going to have to pay around 0.25% commission on the ETF annually. If some of the 60 Canadian equities were going to be sold in order to diversify into international and US investments then some added cost might be worth it. I just wanted remind people that stocks on their own have no commissions but ETFs do and in some cases it might be best to hang on to those stocks if they have already been purchased. In most cases, however, index ETFs are probably a better solution as they provide lots of diversification at a low-cost with little hassle. Another thing to consider is that the commissions to sell the stocks will one day have to be paid anyways; however the commission as a percentage of the investment will decrease because the stocks will surely grow over the long term.

I am guessing you were also thinking about costs when you said you “believe it may be best to leave the best of our Canadian equities that are already in place, rather than selling them and purchasing XIC.” I agree with you that selling all of them and buying XIC seems a bit unnecessary. Assuming you have a good number of stocks (>=30) that would be just as good as XIC, if not better, due to the lowered on-going cost.

For your international investment please consider Vanguard Europe Pacific ETF (VEA) as an alternative to iShares CDN MSCI EAFE Index Fund (XIN) if you can handle the extra foreign currency holdings, as it has a lower MER. Remember that VEA is equivalent to owning the underlying investments in their respective foreign currencies, not US dollars. So you should not be concerned with the US dollar but with Canada’s currency against world currencies. The MER is a lot less in VEA vs. XIN and it is basically the same thing as EFA (which XIN holds underneath but hedged to CAD dollars).

My questions are:

Should I be concerned about the costs of buying and selling the 30 or more holdings?

Well one thing I would be concerned about is if the cost of selling 30 or more holdings was more than, say, 1% of your portfolio (1% figure chosen arbitrarily). If your portfolio is only worth $1000 and you are paying $100 in commissions it doesn’t really make sense. It would take a year at 10% interest to make up the loss and leave you will no gain. That’s like taking one whole year off the investment period. Or another way of thinking about it is that the commission as a percentage of your portfolio is going to affect the final portfolio by that percentage as well, if you consider the commission as affecting the future value of your investments. Here’s the longer explanation. The future value without any commissions is:

FV_0=PV \times (1+i)^n

The final value after paying some one-time commission CC is:

FV_c=(PV-C) \times (1+i)^n

where PV is the present value (on the date you pay commissions), FV_0 and FV_C are final values (of the amount PV, not including any future contributions), i is the interest rate, and n is number of years until retirement (for example). If you find the percentage difference between FV_c and FV_0, or the percentage the final value will be reduced by, you get,

100 \times \frac{FV_c-FV_0}{FV_0} = 100 \times \frac{-C}{PV}

So if you you pay $1000 commissions selling 30 securities and your portfolio is currently worth $100,000 your final value will be reduced by 100 \times \$1000/\$100,000 = -1\% of whatever it ends up being in the future. If it would have grown to $1 million dollars eventually it will be reduced by 1% or $100,000. That was just a long winded way of explaining why I think one should always look at their commissions as a percentage of their portfolio’s present value, and remember that it will affect the final value of their portfolio by the same percentage.

By paring down the portfolios we will end up with a very substantial proportion of our assets in only 2 stocks VTI and XIN. Although I understand that these ETFs are made up of multiple equities, the diversification we presently have with 50-60 holdings will be lost. I am, therefore, concerned that the accounts will largely be influenced by movement in only 2 entities? Doesn’t this increase our risk?

Good question, I had not really though of this before as I have never owned that many individual equities before. Owning two ETFs should be equivalent to owning positions in all the underlying securities. Assuming there were no MER and assuming that tracking error was non-existant, the return would be the same and the risk would be the same, as far as I know.

I am impressed with the incredible power of the internet to stimulate discussion and to disseminate valuable information so easily. I would appreciate your answers to my questions as well as any other thoughts you might have about my portfolios.

I hope my answers made some sense. It looks like you are on the right track and I think you have spotted the main problem with your portfolio (lack of global diversification) and are looking to diversify while minimizing your costs (both one-time commissions and ongoing MERs).

Popularity: 11% [?]

Quicken 2007 XG

I bought Quicken 2007 XG the other day. I wanted it for the detailed investment performance reporting using IRR (internal rate of return). It seems to deliver on that for the most part although I have only loaded in some investment transactions. I actually loaded in my first transactions ever! I still had my transactions from 1996-1999 when I was purchasing the AIC Advantage Fund. I’ll talk more about that investment and what I found out from Quicken’s reports. I looked at the options in the investment performance report and it looks very flexible in terms of showing results for only certain accounts or investments, and for all dates (not just 1,3,5 years). The part that sucks about Quicken is that it’s still a Mickey Mouse program because it doesn’t to double-entry accounting. When I was entering “Bought” transactions there seemed to be an associated cash account that was going negative, but I couldn’t choose the account. Nor do I remember creating this account. I used the BoughtX transaction type instead, and then I could choose an account to fund the purchase. I have been using Gnucash up until now and was very satisfied with it but wanted better investment reporting. I love Gnucash’s double-entry accounting, and it is too bad that Quicken doesn’t have that capability. I thought about getting QuickBooks but it didn’t seem like QuickBooks had any investment support, although I could be wrong. The other annoyance is that Quicken has such a cluttered interface. Gnucash was so simple, just a list of accounts and a ledger. I’ll have to see if I can customize the interface in Quicken at all, but I doubt it. I have made a tentative decision to stop tracking individual transactions in my chequing accounts and just track investments instead. Not sure if I’ll go ahead with it, I’ll have to see how easy it is to import transactions from statements downloaded from online banking sites into Quicken. Only 1 of our 3 institutions allows us to connect right from Quicken. For the other 2 I have to go to the website myself, and click on “download statement.”

Popularity: 12% [?]

My Portfolio’s Performance for 2006

I finally crunched the final numbers and here is how we did in 2006:

Annualized returns
From: 2006-01-01 to 2006-12-31
TD Stuff: 14.24%
Templeton International Stock Fund: 28.79%
S&P TSX 60 Index ETF: 13.28%
E&P Growth Opportunities Fund: 5.97%
CI Value Trust Fund: 8.89%
TD Canadian Bond Fund (Wife): 8.30%
TD Canadian Bond Fund (Dave): 4.19%
Cash (Wife): 1.71%
Cash (Dave): 6.17%
Overall: 12.17%

I got these numbers by making a list of all the inflows and outflows; not just into the entire RRSP but into cash, into the investments, out of the investments, out of cash, and so on. Every transaction is a double-entry transaction, except for the final balance (outflow) and the cash inflows from my chequing account (inflow). I could have just looked at cash flows into my RRSP and the final balances but I wanted to see the breakdown between the different components. Once I had the cash flows for each individual investments I did an Internal Rate of Return for each individually. I also did an overall calculation for the entire portfolio (shown at the bottom). Considering that the EAFE index went up 23.47% last year, the S&P 500 went up 13.62%, and the TSX went up 14.51%, we didn’t do too well. All of the stuff there except for the “TD Stuff” we only owned since March when we switched to Clearsight from TD. So I lost to the the indexes I mentioned above. The reason is because we had a sizable bond portion of about 25% and we were also carrying around a lot of cash (not literally) this year for whatever reason. Well part of the reason was that Clearsight dumped my advisor after they were bought by Wellington West and I ceased communication with them after that as I switched to E*Trade. So I didn’t do any trading during that time and our cash pilled up a bit too much.

The reason that my cash account went up by 6.17% annualized is because the dividends from the iShares S&P TSX 60 Index ETF (XIU) do not get reinvested (ie. it’s not a DRIP) but instead go into my cash account. So the dividends show up as sort of a capital gain in the cash account. One way for me to fix this would be to aggregate the cash inflows and outflows from cash and the iShares XIU and get the annualized return for that combination. That would give the annualized return including inflation. But once I buy another dividend-paying ETF, then what? The final 12.17% annualized return takes into account all the unrealized capital gains and dividends that went into the cash account and the dividends on the TD Canadian Bond Fund that were reinvested.

I really love these calculations. It really shows how well YOU did regardless of that the mutual fund’s NAV or the ETF’s market price did. Look at the TD Canadian Bond Fund for example. My wife got 8.3% annualized on hers and I only got 4.19%. This was because I bought it at a worse time. What’s the lesson here? That you should try to time the market? NO! You can’t time the market (so give up trying). The best way in my opinion is to trade completely randomly (hard to do) or just trade at some regular interval (easy to do) regardless of what the market is doing. Too many investors panic when their investments lose value and chase performance in bull markets. These behaviours lead to lower annualized returns for your portfolio, regardless of what the underlying mutual fund or ETF’s published returns were.

I wrote about investors and their bad timing before. Here is one of the quotes from that blog post:

The results indicated that, as with most active funds, investors’ timing decisions were costly when it came to index funds. The dollar-weighted returns for virtually all large-cap index funds were worse than their official returns for the trailing 10-year period through the end of the third quarter 2005. As the table below shows, poor timing cost Vanguard 500 shareholders 2.7 percentage points of returns per year over the past decade. That’s not chump change.

So I hope to see from these calculations how good/bad my timing is. By this time next year I will have an all ETF portfolio so I will be able to compare my annualized return in index X with the return of index X over the same period.

Popularity: 10% [?]

Foreign Exchange Costs Associated With USD Investments in an RRSP

I have been looking at adding an emerging markets component to my portfolio. I look at my choice as either being Vanguard’s VMO ($USD), iShares’ EEM ($USD), or a Canadian mutual fund offering (such as the TD Emerging Markets Fund or the Altamira Global Discovery Fund. Unfortunately there are no Canadian ETFs investing in emerging markets.

The Vanguard Emerging Markets Fund has an MER of 0.30%. The iShares MSCI Emerging Markets Index Fund has an MER of 0.70%. Once again Vanguard seems to have the lowest-cost ETFs around. The TD Emerging Markets Fund has an MER of 2.88%, and the only thing the Altamira Global Discovery Fund is discovering is how to take MERs to astronomical levels, with an MER of 3.42%. Looks like the Altamira fund is beating the MSCI Emerging Markets Index (CAD$) but those gains are paying for the MER and it ends up just matching the index.

I decided that between the Vanguard VWO and the iShares EEM I would rather go with VMO as the MER is smaller. They hold virtually the same indexes underneath. The VMO one is a “Select” MCSI Emerging Makrts index that was designed especially for Vanguard a long time ago for one of their mutual funds. VMO also has more stocks. It’s daily volume is less than EEM but still high at 400k on average which is what EEM was at a few years ago.

The next thing I was worrying about was the foreign exchange. I have CAD dollars sitting in my E*Trade RRSP. If I buy VMO, E*Trade will convert the CAD to USD and purchase VMO. When I sell VMO (eventually) E*Trade will sell the VMO and covert the USD to CAD. So my CAD dollars gets converted into USD once at a rate of say 1.18 dollars CAD for every dollar USD. Then when I sell VMO they will only give me something like 1.14 dollars CAD for every dollar USD. I don’t know what E*Trade’s spread usually is (if anyone knows, please tell me) but I assume it will be 4-5%.

So I did some calculations to see how bad this hit works out to be on an annualized basis. In other words, what would the effective MER of owning VMO as opposed to a Canadian mutual fund be? I’ll assume that VMO always goes up by 10% every year, has an MER of 0.30%, the nominal foreign exchange rate is 1.16% and the spread is 4%. So obviously if you buy VMO and sell it quickly (say, within a year), it will have increased by 10% but the foreign exchange spread has stolen away 4%. A bit worse than the mutual funds then. But what if you hold it for a long time? It’s going to get better over time. If you hold it for two years, it will increase to 1.1*1.1 = 1.21 of it’s original value but it’s multiplied by (1-0.04) due to the foreign exchange, now what’s the effective annualized return there? It’s about (1.12*0.96)^(1/2)=7.78%, so that’s an effective MER of 2.22%. Already we are better than the mutual funds. (I’ve made an approximation above…it’s not exactly 0.04 that I should be using, it’s 1-(1.14/1.18)… but nevermind, if you want to know more, ask me). If you keep going with the years you’ll get the following graph:

Effective MER for USD Investment

So it looks like it falls off pretty rapidly. Gets down close to 0.5% MER which is not bad. Essentially you can just think of the the foreign exchange hit as multiplying the PV by some number, so it lowers your PV. Over time the effect of lower PV is lessened as the investment grows due to compounding. Note also that I neglected commissions in the above analysis.

Keep in mind that with EEM this graph would be shifted upwards a bit. Since I have beaten the two mutual funds above by a long shot as far as cost goes, I think I might by some shares of VMO. I’ll make it about 5% of our portfolio and then I’ll make an effort to hold it for at least 10 years, where that curve really starts to flatten out.

Popularity: 12% [?]

The Case for RRSPs Over Everything Else

Martin Gale form Efficient Market Canada just wrote an amazing piece, laying out the case for RRSPs over non-registered investment in a growth stock, a dividend stock, and a mortgage payment. This article is a MUST READ for anyone who has every wondered if investing outside an RRSP has some advantages over investing inside an RRSP. Or if you have ever wondered if you should pay down your mortgage rather than investing in an RRSP. Here’s the set-up:

Are people really better off saving money outside of an RRSP? Some say buying and holding growth stocks that pay no dividends is another way to defer taxes, and that investments in an RRSP lose access to the dividend tax credit. Others say that it’s better to repay your mortgage than invest in an RRSP There are a lot of people out there who say things like this and they are almost always wrong. The arguments for non-registered investments generally involve a lot of handwaving and grand claims so let’s break it down and look at the numbers. First we’ll look at buying stocks in and out of an RRSP, then we’ll compare an RRSP to a mortgage payment.

This article is going to be a straight-forward proof that investments in an RRSP beat investments outside of an RRSP in terms of expected returns.

A couple notes about his calculations… As he says, “Note that if anything these assumptions bias against the RRSP because for many people the tax on withdrawals from an RRSP will be lower in retirement than the tax saved at contribution time.” He goes on to give a good reason for why this is usually the case. Another reason these calculations are biased against the RRSP is because he neglects the fact that the investments outside the RRSP might be taxed every year if you are selling your investments every year and buying new ones, for example, whereas inside the RRSP your investments will experience tax-free growth. I just did a quick back of the envelope calculation and this does make a difference.

In the end the RRSP wins out in each case, even though some simplifications in the calculations bias the calculations against RRSPs. The key reason the RRSP comes out ahead, as he explains so well, is because of double taxation outside the RRSP. Taxation on your income (off your paycheque), then taxation on the gains made off those investmentes. In the RRSP you are only taxed once, when you withdraw the entire thing, your gross income plus gains from the RRSP as income.

Almost everyone who argues that the non-RRSP is better ignores the fact that the non-RRSP payment was made with after tax dollars, in other words, they ignore the double taxation.

Around this same time last year I looked at a Phillips, Hagar, & North report that compared investing in an RRSP with investing outside an RRSP. It was called “The Retirement Savings Debate: Inside or outside the RRSP structure” and their conclusion was that

saving for retirement using a registered plan (RRSP) is more beneficial than saving in a non-registered, taxable account. There are a few exceptions to this, but for the most part, this conclusion will hold true for the majority of middle- and upper-income earners.

If anyone finds that PH&N report, let me know. That blog post also had a quote from Derek Foster, which after looking at it again, now seems like total bunk.

I also wrote about paying down student loans vs. contributing to an RRSP although I neglected a few things (see comments).

Popularity: 7% [?]

Paying Down Debt vs. Contributing to an RRSP

The Canadian Capitalist had a link to article by the Smoke & Mirrors guy, David Trahair, called “Don’t Invest in an RRSP Before Paying Down Your Mortgage (Link no longer available).” He starts off by saying that the conventional wisdom of investing in an RRSP then applying the tax rebate to your mortgage every year is hard to do. Instead, he says, don’t contribute to an RRSP, but put down more principal on your mortgage. If you want to talk psychology about what is “harder to do” I would suggest that contributing your maximum room to an RRSP is a better forced savings plan than applying an extra lump sum on the principal of your mortgage ever year, but that’s just me. Or maybe he’s suggesting you re-amortize for a much shorter period (after forgetting about RRSPs) but he doesn’t say that explicity. His second argument is that banks just want your money for RRSPs so they can charge you “commissions and fees on your contributions,” and because the banks’ ideal is for you to be in constant debt. I don’t buy any of that as a reason to pay down a mortgage instead of an RRSP. What I care about is which one is better for me (regardless of whether the bank benefits). Just like I don’t care about MERs in principle. What I care about is the returns after costs.

In the latter part of the article, he argues why you should pay down your mortgage before contributing to an RRSP by showing an example of a couple in two scenarios. Scenario 1 has them paying their monthly mortgage payment and contributing to an RRSP $4000 each per year and investing the tax refund generated. Scenario 2 has them paying their monthly mortgage payment and instead paying $4000 each year onto the principal value of the home. 11 years into Scenario 2 the home is paid off so they redirect what was their mortgage payment into their RRSP (and they invest the tax refund generated into their RRSP). I’ll give you the punchline:

The debt pay-down scenario shows a net worth slightly higher than for the RRSP scenario—a difference of $14,590. So, after 20 years, the Harts would arrive at a similar point but would have taken a very different journey. The debt pay-down option, however, has two major advantages: it reduces the risk that the Harts could lose their house during the nine years of mortgage-free living, and there is less risk related to investment returns. How much confidence do you have that the markets are going to post better returns than the interest rate on your debt? Are you willing to stake your future on it?

This sounds very reasonable but I am very disappointed in his article for a few reasons. He assumes a rate of return in the RRSP of 5%. This seems unbelievably low to me. There might be a reason for that. Since paying down the mortgage (he assumes a fixed-rate of 6%) is low-risk he’s probably trying to match the risk in the RRSP and the mortgage. I am not sure why you couldn’t at least get 6% in the RRSP for almost the same risk. Secondly I would assume that the majority of people with large mortgages or any mortgage are younger rather than older. We can take on a little risk right? I mean we could at least put half our RRSP in equities and half in fixed income/bonds. A 5% return in an RRSP seems unrealistically low. And this is coming from someone (me) who sets his expectations fairly low (7-8%). Thirdly, he doesn’t explain what would happen if the rate of return were even a bit higher yet the difference in Scenario 1 over Scenario 2 is tiny compared to the other numbers involved. “The debt pay-down scenario shows a net worth slightly higher than for the RRSP scenario—a difference of $14,590.” Clearly his cooked up his numbers so that they work out to be better for the mortgage pay-down scenario. Because it’s not even a difference worth mentioning. He even says in the next line that the end points are similar: “So, after 20 years the Harts would arrive at a similar point but would have taken a very different journey.”

I tried to replicate his calculations in a spreadsheet of my own so I could try out some other combinations of rates. (You can now skip to the next paragraph if you get bored easily). I was pretty much successful, only off by a small percent. This is due to the complicated way that he decided to handle the tax rebates. When Joe and Karen each contribute $4000 per year to their RRSP they get a tax rebate equal to $4000 multiplied by their marginal tax rate (40% in this case). They take that $1600 tax rebate and contribute $4000+$1600 to their RRSP in the following year. Then they get a $2,240 tax rebate and contribute $4000+$2240, then the following year, $2,496 extra, eventually converging to some value. I already talked about this “snowball effect” before. Note that it is non-existent if you maximize your RRSP contributions every year anyways. (Do not NOT maximize your RRSPs just so you can get this effect. It’s not that exciting.) Anyways, another way to handle this in the simulation would have been to just assume the max contribution room every year was $4000 for each of them or whatever, and contribute the excess cash available into a non-RRSP account. Personally I would do the latter since we maximize our contribution room every year. Any excess monthly cash (that might come available after paying down a mortgage) would go into non-RRSP investments.

Anyways, if you just increase the RRSP rate of return a little bit, as you can see in this modified spreadsheet, the RRSP case beats the pay-down-debt case. If you increase the rate it beats it by a wider margin but never by much.

I think the takeaways here are:

  • That paying off a mortgage is a great low-risk investment.
  • Make sure you look carefully at any assumptions used in calculations by accountants and financial advisors. Are they realistic?
  • When looking at a return, never forget about the risk associated with that return.

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