Algorithms to Live By

August 12th, 2017 by Potato

I recently read Algoirthms to Live By: the Computer Science of Human Decisions and enjoyed it. It takes a few important problems for which algorithms are used in computer science, explains what they do and some of the challenges associated with them, and then relates that back to everyday life.

This is the sort of book where I am clearly the intended audience: the authors do a decent job of making everything understandable and relatable, and there’s some humour… but you’re going to have to have some interest in the foundational problems or you will likely lose interest. That’s not to say that you have to have a math or computer science background, they do explain it all, you should just come to this with some interest and not just my recommendation.

To give you an idea, they spend the first chapter on the Secretary Problem. They explain the problem (you want to hire the best possible secretary, but have to balance that against not wanting to spend forever interviewing; oh, and after you interview and reject someone you can’t go back to them), and how this might crop up in different situations in your life (if you want the best tomatoes at the grocery store might be one example of a secretary-like problem in action). Then some practical insights from the solutions in computer science — in this case, the optimal answer is likely 1/e, or about a third. That is, if you have 100 candidates for your job, you may want to interview the first 30-40 or so with no intention of hiring them just to get an idea of the quality of the field, then after that hire the first one that’s better than any of those previous ones.

A great take-away is from the chapter on caching. In particular, the least recently used (LRU) algorithm is the scientific justification for why your desk is covered in papers where the only organizational principle is that you dropped them there, and the ones you need more are in the pile closer to your keyboard. “What might appear to others to be an unorganized mess is, in fact, a self-organizing mess.”

I also really liked the description of thrashing and context-switching in the discussion on scheduling tasks. This is not unique to this book — lots of time-management books and articles talk about having set times to handle tasks (“interrupt coalescing”), and to turn off your phone and email notifications to handle time-intensive tasks. But for some reason this one resonated a bit more for me — when I read their description of a processor thrashing I was like “this is happening to me right now.” Of course, that’s likely idiosyncratic to me and the fact that at the time I read it, I was struggling with low productivity because I had a large number of small, equally urgent tasks (vs. the usual case of having one big important project on my plate to balance with a few smaller fires) and had to keep dropping something to…

A neat new term I came across in the book to apply to some aspects of the housing bubble is “information cascade.”

“[…] under the right circumstances, this mixing of private and public data can prove toxic.

Imagine the bidders are doubtful about their own estimations of the value of an auction lot—say, the right to drill for oil in some part of the ocean. As University College London game theorist Ken Binmore notes, “the amount of oil in a tract is the same for everybody, but the buyers’ estimates of how much oil is likely to be in a tract will depend on their differing geological surveys. Such surveys aren’t only expensive, but notoriously unreliable.” In such a situation, it seems natural to look closely at your opponents’ bids, to augment your own meager private information with the public information.

But this public information might not be nearly as informative as it seems. You don’t actually get to know the other bidders’ beliefs — only their actions. And it is entirely possible that their behavior is based on your own, just as your behavior is being influenced by theirs. […]

Just as with the tragedy of the commons, this failure is not necessarily the players’ fault. An enormously influential paper by the economists Sushil Bikhchandani, David Hirshleifer, and Ivo Welch has demonstrated that under the right circumstances, a group of agents who are all behaving perfectly rationally and perfectly appropriately can nonetheless fall prey to what is effectively infinite misinformation. This has come to be known as an “information cascade.”

[…] imagine there are ten companies that might bid on the rights for a given tract. One of them has a geological survey suggesting the tract is rich with oil; another’s survey is inconclusive; the reconnaissance of the other eight suggests it’s barren. But being competitors, of course, the companies do not share their survey results with each other, and instead can only watch each other’s actions. When the auction begins, the first company, with the promising report, makes a high initial bid. The second company, encouraged by this bid to take an optimistic view of their own ambiguous survey, bids even higher. The third company has a weak survey but now doesn’t trust it in light of what they take to be two independent surveys that suggest it’s a gold mine, so they make a new high bid. The fourth company, which also has a lackluster survey, is now even more strongly inclined to disregard it, as it seems like three of their competitors all think it’s a winner. So they bid too. The “consensus” unglues from reality. A cascade has formed.

No single bidder has acted irrationally, yet the net result is catastrophe.”

This immediately reminded me of bidding wars in Toronto, where a common algorithm is to count the number of noses at the table and multiply by some constant, say $10,000, and add that to the phony asking price. An extra bidder (or 10) should not in any way affect your perception of value for the house, yet there are many instances where this sort of bidding strategy is reported.

The quotation above also shows the one caveat — it is a slightly academic style, with references and names dropped throughout (though quite readable despite that). This is great for being authoritative, but can slow the read down.

Burn Your Mortgage

August 12th, 2017 by Potato

So this is going to be a review of Burn Your Mortgage, and TLDR, it’s mostly going to be me ranting and nitpicking so if you don’t want to get into that, just know that most of it is fine but there are some particular issues. This image sums it up:

Figure from page 9 of Burn Your Mortgage. The caption reads: Canadian real estate prices have been trending upward over the past 25 years. That’s more than we can say about the stock market over this same time. A commentary is superimposed showing that the stock market return goes off the scale of the real estate one before the halfway point in the data displayed, proving the caption wrong.

Before getting to the book itself, some quick background on the tale. Sean is famous for buying a place, living in the basement, renting out the rest, and working super-hard to pay off the mortgage before he turned 31. The Sean Cooper Story boils down to: guy makes $150-200k/yr, lives cheaply in a basement apartment, saves up $500k over 7 years. Yawn. Oh wait, he didn’t just save and invest that money: he bought a house and then burned the mortgage. Now that’s a marketable story!

The biggest problem with Cooper’s story is that it happened at all. In the book and several articles, Sean has said that the reason he was so motivated to burn his mortgage was because of his mother and how she struggled to pay off the mortgage. He had a nearly irrational fear and distaste for debt.

So what should a debt-averse single person who is frugal and content living in a basement apartment do? Rent, of course! No, wait, I meant buy a house you don’t need! Then you can rent out the top floor while you live in the basement apartment, adding risk, losing your principal residence exemption, stressing about the mortgage and pouring everything into paying it off. I have referred to this as Cooper’s Folly.

Indeed, back when Sean first set off on the journey I pointed out that renting out the top floor of his house wasn’t as good a deal as he made it out to be — he was effectively paying something in the neighbourhood of $800-900/mo to live in a basement apartment based on the numbers he was publishing, which is what basement apartments cost anyway. In hindsight, the Toronto real estate market has been on fire, but because he didn’t stay crazy levered, he actually would have been wealthier if he had just rented a basement apartment, saved himself some stress and worry over debt and space heaters, and invested in a diversified portfolio (thanks to the markets also having a great 5-year run — over 12% annualized for an aggressive e-series portfolio vs ~9%/yr for Toronto real estate).

Anyway, this is just the background to the book: Sean bought a house, rented most of it out, lived frugally, worked an insane amount, and paid off the mortgage in 3 years (or, because the downpayment was also significant, the alternative title might be “local man works three jobs, lives in basement, saves $500k over 7 years.”).

The first chapter relates that story, and talks generally about buying a house, while barely even analyzing whether anyone should be buying a house or if renting might be better in their situation. Where it does touch on the topic, it does an egregiously bad job of it, so if you happen to know something about how to compare the options it comes across as extremely biased towards buying. The figure above says volumes about the dismissive tone towards renting and investing. He takes a dig at bears (throwing shade at Garth Turner in particular), but then sets up a strawman version of the rent-and-invest thesis to then make a show of toppling. Sean ignores interest in the rent-vs-buy comparison (implying it’s insignificant), then on the same page says that mortgage interest is a compelling reason to pay down your mortgage (implying it’s an important factor). Within a few pages he talks about the power of leverage as a reason to buy over renting (indeed, 2 of his 8 pros to buying relate to leverage)… then excoriates the reader to not use leverage and burn the mortgage.

MegaMaid from Spaceballs. She’s gone from suck to blow!

After that, the rest of the first section is generic advice on frugality, with a lot of lists… Most of it is fine, but parts of it read weirdly. To take one particular example, he suggests that you could save $500/yr on gas by planning your trips better and driving more efficiently. I spent $400 total on gas last year. Yes, I don’t drive much and have a pretty efficient car, but even with a normal car getting 10 L/100 km, that would take about 4500 km/yr of “extra trips” to get that kind of savings — it really just isn’t realistic. Similarly, who spends $1000/yr on taxis (actually, more than that, if they can save $1000/yr by cutting back or splitting with friends)? A lot of what he talks about in the frugality tips are outside his expertise and it shows.

Weirdly enough, there’s only ~4 pages on work ethic and time management. This really could have been almost the whole book, as the side hustle thing is a huge part of how Sean did what he did and is within his circle of competence to talk about. In some of his better times, Sean made more in a month (on top of his regular job!) than I made in a year as a grad student.

Let’s not understate this: he’s a very hard-working guy. He worked 80+ hr weeks for years at a time — not just a few months holding the world together while his wife was sick or ahead of a major deadline. And he kept that grind up without burning out.

Part of why I didn’t like the book is because of the massive missed opportunity there — I kept expecting to hear how I could also burn my hypothetical mortgage by hustling to earn more than my day job income, and how to fit all those hours in a day and avoid burning out. But the formula for success remains a secret. There is a side hustle appendix at the end, but it’s almost an insult, full of vacuous tips like “Childcare: Look after other people’s kids.” Yes, that is seriously the entire tip. He also suggests donating plasma for money, but there are only two clinics in Canada that do that (Moncton and Saskatoon), and Canadian Blood Services does not and will not pay for donations (though Wayfare is only alive because of the work of ~200 blood/plasma donors, so please do that one anyway). The rest of the list serves similarly as a brainstorming session with no regard to practicality — and clearly isn’t the way that he did it.

Anyway, from the generic middle we come to the FOMO section:

“Although foreign buyers help prop up the economy, many locals are finding themselves being priced out of the market. It’s probably wise, if you’re in the financial position to do so, to buy now while you can still afford to.”

Yep. He also suggests turning to the bank of Mom & Dad, so they can tap a HELOC on their house to help you buy one. Or buy with a friend (“great way to build equity and get your foot in the door” — BTW there will not be a giveaway as I threw up on my copy).

Only late in the chapter, after fanning the FOMO, does he include a note of temperance: “Buying a home is a good long-term investment — most of the time. But it doesn’t always make good sense. (With a book title like Burn Your Mortgage, I bet you weren’t expecting me to say that.) In fact, you may jeopardize your financial freedom if you buy a home before you’re ready and end up selling it within a year, say.” I for one, could have done with a lot more temperance.

The book pays a fair bit of lip service to buying what you can afford and staying within your budget, so it seems like a huge gaping hole that it’s not until much later that he does actually provide a rule-of-thumb on what affordable means. Though that gets immediately undercut because after introducing the figure for affordable, he says to spend more in a pricey market (no justification on how that’s still affordable, or why you couldn’t spend more of your income in a less hot market).

There’s actually a lot of detailed information after that on buying a house, features of a mortgage, and getting wills and insurance, and there’s a lot of promise here… except the FOMO stuff makes it hard to recommend. Not just on getting in before being priced out, but things that are very Toronto/Vancouver red-hot market centric like going in with a “clean” offer, or a bully offer for good measure.

Here’s where I want to take a bit of a side-bar discussion: this is a dumb thing to do. If you actually need financing to close, then you have to including a financing condition, because if for whatever reason you can’t get a loan (which could be due to an unforeseeable event like changes to mortgage regulations or a weak appraisal), you can’t close and are liable for damages that can be costly without that condition as an out.

Realtors put a positive spin on this and call it a “clean” offer, but you might as well call it a “naked” one (and that gets into another sidebar about the incentive to make a deal happen vs. protect a client). Now, in a flaming hot real estate market (such as Toronto has seen up until recently), those are the lengths buyers have been driven to. So if you want to give advice to people that helps them “win” a bidding war and get a house, you have to be pragmatic with the prevailing conditions and suggest they put in a naked offer. And that’s one approach and I get that and it’s fine — but it should also come with the appropriate warning label, and at the very least acknowledge that most readers in the country are not facing such dire competition and can proceed with more sense.

The other approach is to try to give people unpopular advice to protect them, in which case you can acknowledge that the stupid thing is happening, and tell people not to do it. It’s a small risk, sure: most deals close and the buyer finds a way to finance; most pre-construction purchases end with the market flat or higher and a buyer is able to get a mortgage and close. But in a book that also suggests buying life insurance for young healthy people, this is a comparable risk and deserves similar discussion. As a bestseller, it could have helped turn the tide on foolishness. Besides, in markets where you “have” to go in with a naked offer and completely expose yourself to the risks of not being able to close, the price-to-rent might favour renting anyway.


Burn Your Mortgage is mostly harmless. The lead-in ignores the alternatives and serious risks involved in buying, it has a strong pro-buying bias throughout, and there are better sources to go to for frugality hacks, budgeting advice, and side hustle tips. But if you’re going to buy a house anyway, the middle section does have a fair bit of handy information on what’s involved in the purchase and financing process. To be fair I’ve focused on nit-picking the other sections, so the truly helpful middle chunk is not reviewed in detail.


And just as this post was being put up, this from the Star: “Others, who bought unconditionally, have discovered they can’t get the financing to meet their purchase obligation. In some cases, the bank appraisal has come in at a value below what a purchaser agreed to pay, leaving the buyer scrambling to make up the difference.”

Rent and Invest the Difference. Or Not.

August 4th, 2017 by Potato

In some markets there’s a difference in the cash flow between buying and renting. Particularly in Toronto and Vancouver, it can cost a lot less each month to rent a house than to buy the same place (this is why there’s commentary about these cities being in a bubble). You can (should!) save up that difference and invest it, and come out much better as a renter than a buyer.

I’ve been banging that drum for a while. I made a rent-vs-buy calculator to help you estimate how much better off you might be.

But a very important point is that you don’t have to save the difference. It’s not just about how much money you have at the end (though that’s important), but the options you have along the way. You can spend the savings on increased lifestyle if you want — living in a bigger/better house than you could otherwise afford, travelling more, eating out more, whatever it is that you want to trade money for to improve your life. Or have Plan A be save and invest the difference.

When the shit hits the fan, you can use the difference as an important safety buffer on your budget. You may “build equity” with each mortgage payment, but you can’t eat equity, and in the meantime you have to keep paying your mortgage.

So when Wayfare was in the hospital and then continued being sick so we’re down to basically one income, we were (and still are) able to stay in our house. Firstly, because we had an emergency fund. Secondly, because we have awesome parents who can help pick up Blueberry so I could keep that one job (and who gave us the confidence that there was another backstop behind our emergency fund if needed). But also because, as expensive as Toronto rents are, we’re actually able to (almost) afford to live here on (almost) one salary.

Let’s do a quick comparison (not our personal numbers, but taken from real GTA listings of similar houses on the same street, and the ratios would be the same):

  Owned house Rented house
Mortgage/Rent $2933 $2200
Insurance $100 $40
Property tax $550 0
Maintenance* $700 0
Total $4283 ($3583) $2240

(All else equal, see notes, * – maintenance can be deferred/ignored temporarily in a crisis, but not long-term).

When cut down to a single salary of ~$4,350/mo after-tax and CPP/EI ($70k/yr pre-tax), a family in the rental house still has $2,110/mo to spend on food, transportation, utilities, phones, summer camp, and other necessities, so the emergency fund doesn’t get drained too fast with one person out of work. It’s likely a tighter budget than they had before, but they can manage for a fairly long time if needed.

In the owning situation, there’s only $767 left over — not nearly enough to get by on, and then only if they ignore maintenance. The house is eating through the emergency fund, and with nothing being set aside for maintenance they’re one poorly timed major repair away from catastrophe. Unlike the renters, the owners have to worry about a possible forced move on top of the immediate medical crisis.

Having a few years of that kind of cash flow difference with two incomes (and saving the difference) also meant that the renters also go into their medical crisis with a good-sized emergency fund saved up, and instead of being used up in the purchase, the sizeable downpayment is spinning off dividends to help with cash flow. So even if they fell short or lost both jobs, they could manage for a while.

This is why the rent-vs-buy debate matters. In exchange for a little less security of tenancy, the renters gain a massive increase in resiliency and flexibility.

Notes: This is the edge of affordability for a 2-income household where each head makes $70k/yr pre-tax (and on a side note, I had to go north of the 407 to find a matched pair of 3-bdrms to fit that kind of budget, but the price:rent holds in North York). The maintenance amount is a rough estimate and can be deferred/ignored in a crisis for a while. This simple cashflow analysis ignores factors like investment returns/opportunity costs, transaction fees, etc., that would be captured in a full rent-vs-buy calculator. While not our specific numbers, the ratio of the owning cashflow to renting cashflow requirements is still very close to the choice we faced when we moved here.

A Framework for Estimating “Am I On Track?”

July 20th, 2017 by Potato

A very common question people ask is “Am I on track to retire?” It’s usually a good starting place for an engagement with a planner, especially if you’re within a decade or so of your planned retirement date. That plan is going to come with a lot of good discussions of your goals, some contingency plans, how you use your money, etc., etc. It’s also going to cost a few thousand dollars for the support and those conversations (and I’m deliberately avoiding saying “for the plan” as though the document in isolation is valuable outside of the process).

But for some of us, we just want to get a ballpark idea of whether we’re on track or not, and we want to do it ourselves with a whiteboard and spreadsheet. So here’s how I think about approaching the problem:

    1. Define your goals
    2. Add up your resources
    3. Project forward to see what might happen
    4. Analyze
    5. Repeat/Try to break it

Now each of those phases can be more work than the few words make it sound: even “just” defining your goals can be a lengthy conversation about what you want the rest of your life to look like. There is definitely room there for a planner or coach to provide a lot of value in the process, but you can get a large part of the way there yourself.

Unfortunately, the process isn’t going to return a really clean yes or no answer. Instead we’re going to get shades of “maybe, if” or “probably, I think.”

Define Your Goals

Part of defining your goals is the straightforward part: figuring out the kind of lifestyle you want in retirement, and then translating that into a dollar amount for your spreadsheet. But it also involves thinking about trade-offs: would you be ok with a more variable income/spending profile, or do you want a steady stream of retirement income? Will your spending decline as you age (less travel?), stay fairly level (with inflation adjustments) or increase (more health/support needs)?

And when thinking about the future, how much lifestyle inflation will you face? Back in grad school, I was pretty sure I would be perfectly content retiring to a nice, quiet one-bedroom apartment somewhere and would only need $30,000/yr or so. Needless to say, my target has risen over the years, and now I use a figure that assumes a little more lifestyle inflation.

There can be a lot of moving parts that can quickly overwhelm a simple DIY approach.

But for the sake of example, let’s say that Elrond Example has had those conversations, and boiled it down to three numbers: he wants to have at least $40,000/yr in retirement income, but would like to aim for $55,000/yr, and Elrond would like that retirement to start at age 65 (assuming he’s 40 now). I also have to be careful to understand how I’ve framed these numbers. For example, if I figure that Elrond makes $70,000/yr pre-tax now, and in retirement will have a few fewer expenses and won’t have to save $7,000/yr anymore, I get to $55,000/yr pre-tax — Elrond will still be taxed on that income and have a perfectly fine retirement, so I can use pre-tax numbers in my later calculations. But if I mean after-tax dollars, as in the amount he can actually spend, I’ll have to account for the taxes. Or, maybe using a different method I can figure that he’ll want $45,000/yr after-tax to spend in 2017 dollars (with a floor of $34,000/yr). Various tools and methods will use different amounts.

Either way will work for you, you just have to be clear with yourself what it is you’re doing. Same for inflation: it’s easiest IMHO to think about real dollars: when retirement actually comes Elrond may be spending $100,000/yr in 2040 dollars, but I can think of that more easily as $45,000 in 2017 dollars — but I will have to adjust my rates of return to be real rates of return (i.e., subtracting out inflation).

One last number to consider is how long you’ll need this support to last. Living to age 95 is a decent rule-of-thumb to use.

Add Up Your Resources

I’m not going to have to fully fund my retirement goals on my own — I’m going to have CPP, OAS, and possibly a pension to help out. Enumerating how much support I get from those guaranteed sources may go a long way towards setting my mind at ease. If reliable, inflation-adjusted income from secure sources like a defined benefit pension, CPP, OAS covers a large portion of my spending needs, I’m automatically going to be closer to being on track. What’s your ratio of spending needs to secure retirement income look like?

I also need to figure out where I stand already in terms of how much I already have invested.

For the sake of the example, let’s say that Elrond can count on the maximum OAS support (in 2017 dollars that’s just over $7,000/yr), and that I’ve used the CPP calculator to estimate Elrond’s CPP income at $8,000/yr in 2017 dollars. Elrond also has a small defined benefit pension. He looks up the statement, which tells me that at age 65, with a bunch of assumptions, he’ll be eligible for $15,000/yr in (pre-tax, real) pension income.

Elrond can also look at his investment statements to see that he has $60,000 in TFSA, $20,000 in RRSP, and $20,000 invested in a non-registered account, all invested in a “balanced” portfolio. He’s also saving (on top of his pension) $7,000/yr.

I’m not necessarily looking for a net worth statement here. For example, I wouldn’t subtract a mortgage from the amount invested, as I’m already accounting for that in the cash flow: the amount Elrond has to save for retirement is after the mortgage payment is made, and the debt will be paid off several years before his planned retirement age.

Project Forward to See What Might Happen

Once you have your needs and your resources, you can start to play with a variety of tools to see what will happen and try to approach an answer about whether you’re on track. If you’ve got time and an inordinate amount of patience, you can do it all by hand on paper.

If today my example person Elrond has $100,000 in total nominal investments and I assume a 4.5% real return (net of fees), then next year Elrond will have $104,500, plus another $7,000 that he has saved. I can keep projecting forward like that up until retirement (though I’d likely track each account separately, as each dollar in an RRSP is not the same as on in a TFSA).

Then when he hits retirement, I can use a rule of thumb like the ~4% figure for a sustainable withdrawal rate to see if the portfolio will last, or I can model drawing it down based on a more conservative asset mix.

Then I can do it again using different assumptions about whether Elrond might not hit his savings goals in a few hard years, or if returns are different. We’ll come back to the point about using different assumptions.


Now I’ve done a lot of work and really want to know, am I on track?

Well, a quick analysis says that Elrond is at least not in serious trouble: in this example, he had such modest needs (income floor of $40,000/yr / spending floor of $34,000/yr) and enough guaranteed support (CPP, OAS, defined-benefit pension, total of $30,000/yr) that he doesn’t need to draw much from his portfolio. Using a 3.5% version of the 4% rule-of-thumb (to be conservative about rates of return and the effect of real-world investment fees), he only needs a portfolio of $285,715 to support his minimum spending, and in my projections his TFSA alone would get him there.

What about his more ideal target retirement lifestyle? Using the same very simplistic method, he’d need a portfolio of $714,285 to cover the $25,000/yr beyond any guaranteed sources of income, but my simple math and assumed rate of return only puts him at $613,000 by age 65. That’s pretty close, especially with all the assumptions involved, and maybe I was being a bit conservative with my rates of return, so maybe he is on track? Hmm, he’d have to save an extra $2,250/yr to hit that number, which is a pretty big change to his budget… Perhaps I can be a bit more aggressive because the bulk of his investments will be in his TFSA in this example, which won’t have a tax drag… and we quickly see how a black-and-white answer is hard to come to.

Repeat/Try to Break It

Sometimes we just want to be reassured. But often it’s more useful to be better prepared. So try a couple of different assumptions in your planning and see if you’re still ok with the answer — if not, you may have to start adjusting your course (or expectations) now.

A big thing to consider is the rates of return you use: there’s a lot of uncertainty in what your investments might return, and it ties deeply into the core of your saving/investing projections. Professional planners will sometimes use Monte Carlo software that will run thousands of simulations of future scenarios to try to see how robust your plan is. IMHO, when you still have over a decade before retirement, that can be overkill, but you definitely want to look at at least a few scenarios with your straight-line/constant return tools (best guess, good, bad) to see if you need to be more conservative.

When you get closer to retirement, things like sequence of returns risk will be important to consider, and that’s why paying a planner to help can really be worth it. But from afar a bad sequence with decent average returns is still a “bad scenario” that can be approximated as a scenario with just an overall lower straight-line return.

For this example, I used the Ballparkinator (click here to download the spreadsheet with the numbers for this specific example), which lets me get a quick look at a few simplified retirement scenarios in one go (though the straight-line methods are a bit optimistic when looking at when the money runs out).

I can see that Elrond Example can meet his floor spending even under a fairly poor worst-case scenario (0% real bond yields, 2% real equity returns, and paying e-series rates of investment fees). Even if he has to retire 3 years earlier than planned for health reasons (assuming a modest decrease to his pension and CPP benefits), under our base case returns he’s in good shape on his current path to at least meet his minimum spending needs.

However, he’s not guaranteed to be on track for his more ideal retirement: sure, he’ll get there with a rosy scenario where his bonds have a 2% real return and his equities an 8% real return (before fees), which has happened in some points in the past, but even in our base case scenario he’ll run out of money before turning 95 in this example.

Again, a strict yes/no answer is hard: with a relatively optimistic outlook for investment returns over the next few decades, sure, he’s well on track; even with a fairly realistic base case he’ll have money for his ideal retirement goals for longer than he’s likely to live (sometime into his 80’s). But he’s not so solidly there that he can afford to retire any earlier if his ability to work fails a few years early, and a bad few decades for his investments could also put a crimp on his retirement plans. Though he may never see a birthday cake adorned with 90 candles, he wants to prepare for that opportunity.

It’s also hard to come up with an exact amount extra he needs to save. To get his base case scenario to give us 95 as an age where he runs out of money, we have to increase his savings from $7,000/yr to $8,250/yr. But even at that higher savings rate, he can barely cope with an early exit from the workforce at 61 (with associated decreases in CPP and pension income), and an exit at 60 would compromise his minimum spending target, even under the base case investment returns. Is that enough of a cushion?

And there’s no realistic way for Elrond to support his ideal retirement spending level even after worst-case investing returns. How conservative is too conservative?

We can also try a different way of analyzing the numbers. At the bottom of the Ballparkinator is the so-called “backwards method”, which uses a set sustainable withdrawal rate (variations on the 4% “rule”) plus any gaps in spending to see how big a nest egg Elrond needs at the beginning of retirement, then figures out how much he needs to save each year to get to a nest egg that size based on the various real return rates (note that this ignores taxes). If Elrond wants to be somewhat conservative and use 3.6% as his sustainable withdrawal rate, then under the base case scenario, he needs to bump his current savings rate of $7,000/yr up to over $9,500/yr. While under the best case scenario, he’s saving more than he needs (a nice problem to have), it’s not possible for him to save enough to meet his ideal spending needs under the worst-case investment returns scenario. But, using this method and his minimum spending needs, he is saving more than the tool returns for worst-case scenario.

So looking at it from several angles and with a few different assumptions, Elrond appears to be most of the way towards being on-track for retirement. Even if a few things go wrong, he will quite likely still be able to meet his minimum retirement income goals. His ideal retirement is possible for the track he’s on if things go well (he can continue to work to his target age without having to take time off from savings due to an emergency or leaving the workforce early, decent investment returns, etc.). But he may want to re-examine his plan to see if he should start envisioning something a touch more modest (but still well above his minimum), or start finding a way to save and invest more.

And of course, there are other possibilities too. In this example, we used the “balanced” portfolio for Elrond, which in the spreadsheet is a simple 50-50 mix of fixed income and equities. If we believe that equities will have a higher return over the next 25 years, and if Elrond has the personality for more investing risk (certainly he has the time horizon), then moving to a higher equity weighting (like the age-10 rule-of-thumb from the investing course) may also help him achieve his goals — but this is not a solution to take lightly, and it’s all too easy to just be more optimistic on your future rate of return assumptions to magically get back on track.


There’s no simple formula for answering the very simple question of “am I on track?” There’s lots of uncertainty between now and retirement, from what your investment returns will be to how much you’ll be able to save or even how much you’ll want to spend. But if you can meet your minimum needs even under a “bad” scenario and get into a happy range for your spending with a more realistic base case scenario, then you’re probably on the right track.

And as you get within a decade or so of retirement, it can be worth meeting with a planner to examine these questions in more detail and discuss the trade-offs involved.

In Investing, Nobody Knows You’re a Cat

July 7th, 2017 by Potato

I’ve seen multiple versions of the same question chain, which starts easy enough: basically in investing isn’t performance after fees what really matters?

Yes, what you really care about at the end of the day is your performance after fees.

So then isn’t it worth paying a higher MER for Fund X when it out-performed the index last year/over the last 5 years?

And that’s where the arguments start. If you had a time machine, sure, go back and invest in Fund X. Or just buy that one stock that did the best over that time period and do even better. Or see some dinosaurs — it’s your time machine, do what you like. But starting from today and going into the uncertain future there’s no way to say whether Fund X will continue to out-perform net of fees without that time machine. You have to choose where to put your money without the benefit of knowing in advance which fund is going to earn its fees and then some. Then seeing that most actively managed funds don’t beat the benchmark, you can at least control your costs and invest in a low-cost index fund, which is going to do better than most of the other choices you could have made.

But that explanation doesn’t always resonate, so let’s try a different approach.

There’s a clever little expression that I like: on the internet, nobody knows you’re a dog.

And then there’s this interesting little human interest story: a cat won an investing contest. A mash-up of the two gets us this catchier bit of advice: in investing, nobody knows you’re a cat.

Portfolio manager cat reviewing research material.

The manager your favourite mutual fund pays may pick great investments and out-perform the market, even net of fees. And that may be because your manager has great skill and discipline, and is able to continue to beat the market… or it may be because of dumb luck.

It’s extremely difficult for an outsider to tell the difference in a world where cats can beat professionals, a world where even highly paid, ostensibly skilled managers mostly under-perform. So yes, at the end of the day all that really matters is performance after fees, but without a time machine the best chance for getting that is to minimize your fees.