Larry McDonald commented on a paper called Dynamic Lifecycle Strategies for Target Date Retirement Funds, and of course Michael James hit the nail on the head with his response: if you guess too high on the expected market return, you will stay 100% in stocks until retirement, which is unwise.
A more sensible approach occurred to me while reading the paper. Suppose you are invested in a traditional Lifecycle fund, and then suddenly, the market takes a nosedive. You should move your money into another Lifecycle fund that is aimed at the target date at which you could expect to retire considering the market losses.
To explain what I mean, consider someone with $1 million invested, who wants $2 million in order to retire. Suppose they're in a lifecycle fund that unwinds linearly over 20 years, going from 100% stocks (at say 10% nominal return) to 100% fixed-income (at say 4% return). Suppose that he is contributing $20k per year. This person could expect to reach his $2M goal in 12 years.
Now, suppose the market crashes, losing half its value. Since our investor's target date was 12 years away, he was still 60% in stocks, so his portfolio is now worth $700k.
Going on the same assumptions as before, he would simply move his money into a fund with a 17-year target date. This move has the effect of increasing his stock exposure from 60% to 85%, which is almost as aggressive as the dynamic lifecycle strategy. If the market recovers, he can move his money back where it was.
This approach is much less sensitive to errors in the expected rate of return. If you overestimate returns by 1%, this scheme may have you making minor adjustments to your portfolio every so often as you find your actual returns diverging from your plan. In contrast, the dynamic lifecycle approach would have you 100% in stocks until the day you retire, which is clearly unwise.
It also seems more realistic to admit that your target retirement date has been impacted by the market crash and to adjust your plans accordingly, rather than try to go double-or-nothing with the market and risk your retirement entirely.
The statistical analysis of this strategy is left as an exercise for the reader.
Nov 28, 2008
Magnitude of Credit Default Swaps
Imagine being able to turn a single dollar into $7 million. If you handle it wisely, you could retire and live very comfortably indefinitely. $7 million represents more than a lifetime of earnings for most people.
Now, imagine turning each of those 7 million dollars into $7 million. That's a mindboggling amount of money, but it would still be less than the amount of money involved in credit default swaps.
Now, imagine turning each of those 7 million dollars into $7 million. That's a mindboggling amount of money, but it would still be less than the amount of money involved in credit default swaps.
Nov 14, 2008
Mutual funds: "manager risk"
A recent Motley Fool article on picking mutual funds highlighted the importance of researching the fund manager. My reaction is simply this: it is a systemic flaw of mutual funds that their performance depends so much on the skill and temperament of the individuals running them.
"Manager risk" can outweigh all other risks when picking mutual funds. If you're lucky, you get Peter Lynch; if you're not lucky, you get his successors, your funds go sideways for two decades, and you lose 10% of your assets in fees for the privilege.
"Manager risk" can outweigh all other risks when picking mutual funds. If you're lucky, you get Peter Lynch; if you're not lucky, you get his successors, your funds go sideways for two decades, and you lose 10% of your assets in fees for the privilege.
Oct 27, 2008
Bottom-up asset allocation
Over at Thicken My Wallet is an article on The Role of Cash in Your Portfolio. There, he gives an opinion how much cash is the right amount. It's decent advice, but it contains some numbers that seem rather arbitrary, as does all advice I've seen in this area.
My approach is different. I don't start from the top with a target percentage; I derive that percentage from my financial situation.
My allocation is based on two rules:
1. Never be forced to sell stocks. I want to sell them at a time of my choosing, when the market value is fair.
2. Strive for the highest possible return, subject to rule #1.
To handle #1, we keep our expenses down below our income, we have an emergency fund amounting to several months' expenses, and we have other savings accounts for anticipated expenses such as our next car. This puts us in a position where we'll only be selling stocks under extreme circumstances where getting the best value for our stocks will no longer be our highest priority.
Then, rule #2 amounts to investing the rest in a diversified portfolio of stocks. It also includes a small amount of bonds and cash to allow for rebalancing, since it has been shown that a portfolio with rebalancing can outperform every one of the individual assets in that portfolio. Paradoxically, adding some bonds and cash into your portfolio can help it outperform a portfolio of pure stocks over the long term.
I'm aware that maximizing returns, in theory, requires leverage. Personally, I abhor paying interest on debt, and I don't like the additional risk, so I'm not leveraged. I'll just have to live with the returns I can get from my own money in the stock market.
My approach is different. I don't start from the top with a target percentage; I derive that percentage from my financial situation.
My allocation is based on two rules:
1. Never be forced to sell stocks. I want to sell them at a time of my choosing, when the market value is fair.
2. Strive for the highest possible return, subject to rule #1.
To handle #1, we keep our expenses down below our income, we have an emergency fund amounting to several months' expenses, and we have other savings accounts for anticipated expenses such as our next car. This puts us in a position where we'll only be selling stocks under extreme circumstances where getting the best value for our stocks will no longer be our highest priority.
Then, rule #2 amounts to investing the rest in a diversified portfolio of stocks. It also includes a small amount of bonds and cash to allow for rebalancing, since it has been shown that a portfolio with rebalancing can outperform every one of the individual assets in that portfolio. Paradoxically, adding some bonds and cash into your portfolio can help it outperform a portfolio of pure stocks over the long term.
I'm aware that maximizing returns, in theory, requires leverage. Personally, I abhor paying interest on debt, and I don't like the additional risk, so I'm not leveraged. I'll just have to live with the returns I can get from my own money in the stock market.
Oct 12, 2008
Rebalancing with a vengeance
Michael James asks, Do You Have the Nerve to Rebalance Right Now? My answer is a resounding "yes!"
At the start of this year, I calculated that we had a 57:43 split between stocks and bonds+cash, which I considered to be too conservative for us. However, the market being what it was back then, I thought stocks were overpriced, so I held off on rejiggering our assets.
My first rejiggering happened on September 9, after the TSX had fallen from 15,000 to 12,000. The second occurred on Friday, when the TSX dipped below 9,000. Now our ratio is 76:24, which is where I've wanted it for months; and I'm delighted that there are folks out there willing to sell me stocks at such bargain prices.
At the start of this year, I calculated that we had a 57:43 split between stocks and bonds+cash, which I considered to be too conservative for us. However, the market being what it was back then, I thought stocks were overpriced, so I held off on rejiggering our assets.
My first rejiggering happened on September 9, after the TSX had fallen from 15,000 to 12,000. The second occurred on Friday, when the TSX dipped below 9,000. Now our ratio is 76:24, which is where I've wanted it for months; and I'm delighted that there are folks out there willing to sell me stocks at such bargain prices.
Oct 10, 2008
Oct 7, 2008
Ok, I don't own an SUV
Lest my faithful readers (and I flatter myself by using the plural) think I've lost my mind, I'd like to make perfectly clear that my last post was not about gas prices. It's about fretting over the price of an asset that you were never planning to sell anyway.
I'm in the stock market for the long haul, so lower prices just mean that my biweekly paycheque deductions are buying more shares than before. My May contribution bought me just 33 units of one fund I invest in, while the same contribution last week bought me 51 units. That suits me just fine.
I'm in the stock market for the long haul, so lower prices just mean that my biweekly paycheque deductions are buying more shares than before. My May contribution bought me just 33 units of one fund I invest in, while the same contribution last week bought me 51 units. That suits me just fine.
Oct 6, 2008
I'm worried about falling gas prices
My SUV has a pretty big gas tank (150 litres), and I don't drive it much, so I don't need to fill it up often. It still has about 100 litres of gas I bought three weeks ago at $1.38 during hurricane Ike, and it's gut-wrenching to know that my $138 investment is now worth only $109.
My neighbour has made a modest proposal to buy this gas from me before its value drops any further. What do you think—should I take him up on it?
My neighbour has made a modest proposal to buy this gas from me before its value drops any further. What do you think—should I take him up on it?
Oct 4, 2008
Open letter on the RESP tax deduction
As long as I'm re-posting old letters I've sent, here's one I sent to my federal representative back in March regarding the proposed tax deduction on RESP contributions:
In the name of conciseness, this letter left other issues unaddressed. One issue is the fact that this tax deduction would strangely benefit the parents rather than the students. If we're spending a billion per year on education, it stands to reason that the money ought to reduce costs or improve quality. This plan would do neither; instead, it would hand cash back to the parents, whom we then rely upon to improve the child's education rather than buy a big-screen TV.
Dear Ms Ratansi,
As someone who stands to benefit a great deal from a tax deduction on RESP contributions, I think I can be considered unbiased when I urge you to reject this alarming misallocation of federal tax revenues.
Nobody believes more strongly than I do that education should be subsidized. However, until the country can afford to make post-secondary education free to all Canadians, we must target our spending to benefit those who need it most. A tax deduction on RESP contributions is directly opposed to this goal in two ways:
- It pays more to those in higher tax brackets, causing most of the money to reach people like me, whose children are in no danger of being unable to afford tuition.
- It pays less to those who can't afford to put money into RESPs in the first place, offering the least support to those most in need.
If you choose to allocate a billion dollars per year to subsidize tuition, you have a duty to ensure the money benefits those who need it most—or, at the very least, benefits all students equally. An RESP tax deduction does neither.
I trust you will give this matter due consideration.
In the name of conciseness, this letter left other issues unaddressed. One issue is the fact that this tax deduction would strangely benefit the parents rather than the students. If we're spending a billion per year on education, it stands to reason that the money ought to reduce costs or improve quality. This plan would do neither; instead, it would hand cash back to the parents, whom we then rely upon to improve the child's education rather than buy a big-screen TV.
Sep 22, 2008
The fallacy of large numbers
Today's post from Michael James just reminded me of a letter I sent to the editor of Money Sense magazine last summer:
In your recent article "10 Laws of Building Wealth", you scoffed at the investor that would choose a guaranteed payment of $3000 instead of an 80% chance of $4000. Your rationale was that the expected payoff for the latter is $3200, which is more attractive than $3000. However, the justification for using the "expected value" to compare alternatives is based on the Law of Large Numbers, which does not apply if we're given the choice just once. In that case, there's no way to combine risk and reward into a single neat metric, and the choice of $3000 versus an 80% shot at $4000 depends, quite rationally, on the risk aversion of the individual.
Sep 21, 2008
Frugal living for the visually inclined
Today I thought I'd put up a few diagrams I usually end up drawing in the air with my fingers when I talk to people about this topic.
If your expenditures always equal your income, you'll have a situation like this:
In this diagram, the green line represents your income, which (hopefully) will increase over time. The red line represents your expenditures, which will also increase as your standard of living grows with your income. In this scenario, you end up spending every dollar you make.
How can you improve upon this? You could increase your income more, but if your standard of living grows along with it, you still won't have any money left when you retire.
The most obvious way to improve the situation would be to reduce your expenditures:
To achieve this, always put away a fixed amount of your income toward savings, and live your life as though your income were a little lower.
The light-green area between income and expenditures is your savings. The larger this area, the more you have when you retire (ignoring inflation, investment growth, etc).
The next most obvious way would be to grow your standard of living a bit more slowly than you grow your income:
To achieve this, don't spend your raises when you get them. Instead, increase your RRSP contributions.
Finally, an easy one to overlook is just to delay your increases in standard of living for a few years:
To achieve this, hold off for a few years on expensive upgrades on your standard of living. You can still have everything you want; you just get it a little later. For instance, after you get your first real job, all you need to do is continue to live like a student for a year or two, and then grow your standard of living at the same rate as you would have done anyway. This is all it would take to have substantial savings when you retire.
For those of us planning to get rich slowly, the easiest way is through a combination of these three effects.
If your expenditures always equal your income, you'll have a situation like this:
In this diagram, the green line represents your income, which (hopefully) will increase over time. The red line represents your expenditures, which will also increase as your standard of living grows with your income. In this scenario, you end up spending every dollar you make.
How can you improve upon this? You could increase your income more, but if your standard of living grows along with it, you still won't have any money left when you retire.
The most obvious way to improve the situation would be to reduce your expenditures:
To achieve this, always put away a fixed amount of your income toward savings, and live your life as though your income were a little lower.
The light-green area between income and expenditures is your savings. The larger this area, the more you have when you retire (ignoring inflation, investment growth, etc).
The next most obvious way would be to grow your standard of living a bit more slowly than you grow your income:
To achieve this, don't spend your raises when you get them. Instead, increase your RRSP contributions.
Finally, an easy one to overlook is just to delay your increases in standard of living for a few years:
To achieve this, hold off for a few years on expensive upgrades on your standard of living. You can still have everything you want; you just get it a little later. For instance, after you get your first real job, all you need to do is continue to live like a student for a year or two, and then grow your standard of living at the same rate as you would have done anyway. This is all it would take to have substantial savings when you retire.
For those of us planning to get rich slowly, the easiest way is through a combination of these three effects.
Sep 5, 2008
Avoiding index fund fees
Michael James recently said "Small Amounts add up, but Pennies Don’t", and I think the same is true of index ETFs. It's easy to find funds with remarkably low expense ratios under 0.3% per year. If you manage to save 0.1% per year times 30 years, that adds up to 3% of your final portfolio value at retirement, which I daresay you'd be hard pressed to notice.
Go ahead and pick the cheapest index fund you can find, all else being equal, but I wouldn't go to any lengths to avoid these tiny fees. For example, I wouldn't go buying the underlying stocks in one of these cheap funds unless the savings in management fees makes up for the higher trading commissions and the tracking error you'll get from not owning exactly what's in the index.
Go ahead and pick the cheapest index fund you can find, all else being equal, but I wouldn't go to any lengths to avoid these tiny fees. For example, I wouldn't go buying the underlying stocks in one of these cheap funds unless the savings in management fees makes up for the higher trading commissions and the tracking error you'll get from not owning exactly what's in the index.
Aug 31, 2008
Dogbert and log points
(I promise, this is my last math-nerd post on log points.)
Last week's Dilbert cartoon, though facetious, essentially captures how I intend to grow my money for retirement. It also helps illustrate how log points can help you compute compounding in your head.
In the cartoon, Dogbert wants people to multiply their money by a factor 10,000. Because of the long timeframe, compounding will dominate his calculations, so he can't simply say "1,000,000%/5% = 200,000 years" because he will be very far off. However, he can still do the calculation in his head if he uses log points.
We start with three rules of thumb that need to be memorized. Think of these as the "Rule of 72" on steroids:
If 10× is 230 log points, then 10,000 (which is 10×10×10×10) means 230+230+230+230 = 920 points. If our investment gains 5% per year (which is about 5 log points), then we need 920/5 = 184 years. This is a much better guess than 200,000 years, since the right answer is 188.7 years.
(Our estimates are still off by a bit, because all of the rules above are rounded, so each one you apply can introduce a 1% error. We applied four of them here (four 230s) so we should expect a total error of up to 4%. Rule 2 introduces the most error: rather than 70 log points, the correct value would be about 69.3, which I think you'll agree is a much more awkward number.)
You don't have to get all 920 log points from interest though: you could also get some of them by increasing your initial investment. If you start with 10× as much, you get the first 230 log points immediately, leaving you to earn the other 690 of them via interest, which would take about 690/5 = 138 years (which is close to the actual 141.5 years).
However, I have no plan to invest $100 at the beginning and leave it for 184 years. I'm much more likely to invest every month until I retire. How do we compute this with log points?
Suppose I invest $1/month for 10 years. Some of those $1 installments would be invested for the whole 10 years, while others would be invested in the last month or two and would spend very little time invested; overall, each dollar spends an average of 5 years invested.
This gives us our fourth rule of thumb (which, though unrelated to log points, is still very useful in log point calculations):
Thanks to these four rules, I did these calculations entirely in my head, using a calculator only to confirm my results.
Last week's Dilbert cartoon, though facetious, essentially captures how I intend to grow my money for retirement. It also helps illustrate how log points can help you compute compounding in your head.
In the cartoon, Dogbert wants people to multiply their money by a factor 10,000. Because of the long timeframe, compounding will dominate his calculations, so he can't simply say "1,000,000%/5% = 200,000 years" because he will be very far off. However, he can still do the calculation in his head if he uses log points.
We start with three rules of thumb that need to be memorized. Think of these as the "Rule of 72" on steroids:
- Rule 1: a 1% increase is about 1 log point
- Rule 2: a doubling is about 70 log points (which should be reminiscent of the Rule of 72)
- Rule 3: a 20× increase is about 300 log points
If 10× is 230 log points, then 10,000 (which is 10×10×10×10) means 230+230+230+230 = 920 points. If our investment gains 5% per year (which is about 5 log points), then we need 920/5 = 184 years. This is a much better guess than 200,000 years, since the right answer is 188.7 years.
(Our estimates are still off by a bit, because all of the rules above are rounded, so each one you apply can introduce a 1% error. We applied four of them here (four 230s) so we should expect a total error of up to 4%. Rule 2 introduces the most error: rather than 70 log points, the correct value would be about 69.3, which I think you'll agree is a much more awkward number.)
You don't have to get all 920 log points from interest though: you could also get some of them by increasing your initial investment. If you start with 10× as much, you get the first 230 log points immediately, leaving you to earn the other 690 of them via interest, which would take about 690/5 = 138 years (which is close to the actual 141.5 years).
However, I have no plan to invest $100 at the beginning and leave it for 184 years. I'm much more likely to invest every month until I retire. How do we compute this with log points?
Suppose I invest $1/month for 10 years. Some of those $1 installments would be invested for the whole 10 years, while others would be invested in the last month or two and would spend very little time invested; overall, each dollar spends an average of 5 years invested.
This gives us our fourth rule of thumb (which, though unrelated to log points, is still very useful in log point calculations):
- Rule 4: Periodic equal payments at equal interest are (practically) equivalent to one lump sum invested at the same rate for half as long
Thanks to these four rules, I did these calculations entirely in my head, using a calculator only to confirm my results.
Aug 29, 2008
Log points
Ok, you may all think I'm crazy for this one, but I find the easiest way to get a quick picture of the performance of my investments is through the formula 100×ln(x), a metric I refer to as log points (though its technical name is the rather unfortunate "centinepers"). "Log points" columns crop up in most of my financial spreadsheets.
Why on Earth would I use this formula? It makes the spreadsheet do the hard math, so that whenever I want to compare two numbers, I only need to do simple mental subtraction of relatively small quantities.
Suppose you have an asset worth $36316 one day and $35596 the next day. Quick: what percentage did you lose? Well, you need to subtract them, then divide by an unwieldy 5-digit number. That's ok if you program your spreadsheet to do it, but if you have a large amount of financial numbers and you want to compare them all to get the gist of them, you'll have a lot of pairwise formulas to enter into your spreadsheet. Instead, suppose we convert these two numbers to log points, using the above formula. So what?
Here's the trick: the difference between two log-point amounts equals the percentage difference between the original two dollar amounts. This works whenever the difference is small; anything less than about 10% works just fine. In our example, the first number comes out to 1050, and the second is 1048, so we've lost 2 log points, which indicates that we've lost very nearly 2%.
If we let the spreadsheet compute each number's log-point equivalent, we can pick any pair of dollar quantities and compare the percentage difference just by mental subtraction. This greatly aids visual scanning to find patterns.
Log points have a number of other interesting properties with regards to compounding and amortization that I may describe in a future article if anyone's interested.
(Nobody was interested, but I wrote another article anyway. Part 2 is here.)
Why on Earth would I use this formula? It makes the spreadsheet do the hard math, so that whenever I want to compare two numbers, I only need to do simple mental subtraction of relatively small quantities.
Suppose you have an asset worth $36316 one day and $35596 the next day. Quick: what percentage did you lose? Well, you need to subtract them, then divide by an unwieldy 5-digit number. That's ok if you program your spreadsheet to do it, but if you have a large amount of financial numbers and you want to compare them all to get the gist of them, you'll have a lot of pairwise formulas to enter into your spreadsheet. Instead, suppose we convert these two numbers to log points, using the above formula. So what?
Here's the trick: the difference between two log-point amounts equals the percentage difference between the original two dollar amounts. This works whenever the difference is small; anything less than about 10% works just fine. In our example, the first number comes out to 1050, and the second is 1048, so we've lost 2 log points, which indicates that we've lost very nearly 2%.
If we let the spreadsheet compute each number's log-point equivalent, we can pick any pair of dollar quantities and compare the percentage difference just by mental subtraction. This greatly aids visual scanning to find patterns.
Log points have a number of other interesting properties with regards to compounding and amortization that I may describe in a future article if anyone's interested.
(Nobody was interested, but I wrote another article anyway. Part 2 is here.)
Aug 24, 2008
Reducing gas price volatility
When a gas station increases the price at the pump, they should be required to sell it at the new higher price for, say, seven days before lowering it again.
With this rule, a gas station that increases its price too much too soon will get stuck being the only one selling at that high price for a whole week, during which drivers will buy their gas elsewhere. Every time this happens, they may lose a week's worth of revenue, which is about 2% of their annual revenue.
Gas stations will be forced to absorb price fluctuations to keep their prices competitive. They'll have to keep inventories higher so that they can ride out whatever supply situations they normally use to justify raising prices. They may need a cash reserve on hand in case they do get stuck with lower revenues for a week. Existing competition laws will make it illegal for different companies to agree to keep their prices high and nullify this effect.
What do you think?
With this rule, a gas station that increases its price too much too soon will get stuck being the only one selling at that high price for a whole week, during which drivers will buy their gas elsewhere. Every time this happens, they may lose a week's worth of revenue, which is about 2% of their annual revenue.
Gas stations will be forced to absorb price fluctuations to keep their prices competitive. They'll have to keep inventories higher so that they can ride out whatever supply situations they normally use to justify raising prices. They may need a cash reserve on hand in case they do get stuck with lower revenues for a week. Existing competition laws will make it illegal for different companies to agree to keep their prices high and nullify this effect.
What do you think?
Aug 2, 2008
Descriptive budgeting
Budgeting can be a real downer if you've never done it before, since it seems to limit your freedom to do what you want with your own money.
However, let me point out an important budgeting fact: everyone has a budget; it's just that many people don't know what theirs is.
If you've ever wondered why your income doesn't afford you more savings or a better standard of living, the first step in budgeting is to look at it as descriptive rather than prescriptive. What I mean is: don't start by designing a budget to control your expenditures; rather, simply write down what your expenses are.
In the first draft, it doesn't even have to be that accurate; just include the expenses you can think of off the top of your head: housing, groceries, utilities, entertainment, transportation, etc. Then, for a couple of months, make your purchases by debit card, or (a bit more dangerous for those who aren't good with money) credit card, so you can track your expenses and see whether they match your prediction. Adjust your prediction until you get to a precision that satisfies you, call the remainder "petty cash", and now you've got a good picture of your cash flow.
The bigger the petty cash account, the easier it is to write the budget, but the less precise it is. If you're ok with not knowing where, say, 20% of your income goes, that's fine. Hey, it's your budget.
Once you have a budget that matches your actual situation, you can look at it and decide whether you are getting the results you want from your hard-earned money. Only if you are unsatisfied with your budget do you need to modify it and change your spending habits, making your budget increasingly prescriptive until you like what you see. Start with the biggest expenditures, since changes there will have the largest impact on your bottom line. You can refine your budget as you go until you get the effect you want.
And take it easy: unless your debt is spiraling out of control, there's no big rush. For our family, we took a leisurely 7 years or so to refine our initial descriptive budget into our current budget. We tweaked it every time we felt we weren't getting the results we wanted. Encouraged by watching our savings grow, we've now got quite a detailed budget, with just 3% of out income going to petty cash, and the rest accounted for.
However, let me point out an important budgeting fact: everyone has a budget; it's just that many people don't know what theirs is.
If you've ever wondered why your income doesn't afford you more savings or a better standard of living, the first step in budgeting is to look at it as descriptive rather than prescriptive. What I mean is: don't start by designing a budget to control your expenditures; rather, simply write down what your expenses are.
In the first draft, it doesn't even have to be that accurate; just include the expenses you can think of off the top of your head: housing, groceries, utilities, entertainment, transportation, etc. Then, for a couple of months, make your purchases by debit card, or (a bit more dangerous for those who aren't good with money) credit card, so you can track your expenses and see whether they match your prediction. Adjust your prediction until you get to a precision that satisfies you, call the remainder "petty cash", and now you've got a good picture of your cash flow.
The bigger the petty cash account, the easier it is to write the budget, but the less precise it is. If you're ok with not knowing where, say, 20% of your income goes, that's fine. Hey, it's your budget.
Once you have a budget that matches your actual situation, you can look at it and decide whether you are getting the results you want from your hard-earned money. Only if you are unsatisfied with your budget do you need to modify it and change your spending habits, making your budget increasingly prescriptive until you like what you see. Start with the biggest expenditures, since changes there will have the largest impact on your bottom line. You can refine your budget as you go until you get the effect you want.
And take it easy: unless your debt is spiraling out of control, there's no big rush. For our family, we took a leisurely 7 years or so to refine our initial descriptive budget into our current budget. We tweaked it every time we felt we weren't getting the results we wanted. Encouraged by watching our savings grow, we've now got quite a detailed budget, with just 3% of out income going to petty cash, and the rest accounted for.
Jul 1, 2008
The reality of dollar-cost averaging
The notion of dollar cost averaging has its share of critics. It doesn't take a great deal of insight to see that investing later will reduce one's returns, so I agree that anyone with a big lump of cash to invest should invest it as soon as possible. However, most of us don't have a huge lump of cash waiting to be invested, and instead invest biweekly or monthly anyway.
The question that interests me is: what is the effect of spreading out one large investment into many smaller investments? I specifically want to exclude the effect of investing earlier or later, as that will naturally have predictable results.
To answer this question, I started with the daily closing values of the S&P 500 over the last 50 years. I simulated a series of investment strategies, each of which involves investing N dollars every N trading days, then looking at the total investment value after waiting for N/2 trading days. A year has about 250 trading days, so the time horizon I used was 256 days, and the N values were all powers of 2 ranging from 1 to 256. Every dollar in any of these schemes is invested for an average of 128 days, which means no scheme has the money invested any longer than any other scheme. Each day for the last 50 years, I computed the value that each scheme would produce over the prior "year" (where a year is 256+N/2 trading days).
So, with a total $256 investment over a year, each scheme produces the following results:
So on average, it seems spreading out your investments over the course of the year has very little effect. I wasn't expecting that. I guess you learn something every day.
According to these results, there's no point at all in investing more often than once per month. With a single lump sum invested for a year, your standard deviation is only 30% more than it would be with daily investments.
Is dollar-cost averaging a myth? What other conclusion could I draw?
The question that interests me is: what is the effect of spreading out one large investment into many smaller investments? I specifically want to exclude the effect of investing earlier or later, as that will naturally have predictable results.
To answer this question, I started with the daily closing values of the S&P 500 over the last 50 years. I simulated a series of investment strategies, each of which involves investing N dollars every N trading days, then looking at the total investment value after waiting for N/2 trading days. A year has about 250 trading days, so the time horizon I used was 256 days, and the N values were all powers of 2 ranging from 1 to 256. Every dollar in any of these schemes is invested for an average of 128 days, which means no scheme has the money invested any longer than any other scheme. Each day for the last 50 years, I computed the value that each scheme would produce over the prior "year" (where a year is 256+N/2 trading days).
So, with a total $256 investment over a year, each scheme produces the following results:
N (days) Average Std deviation
1 $266.73 8.4%
2 $266.77 8.4%
4 $266.77 8.4%
8 $266.77 8.4%
16 $266.77 8.4%
32 $266.77 8.5%
64 $266.77 8.6%
128 $266.77 8.9%
256 $266.65 10.3%
So on average, it seems spreading out your investments over the course of the year has very little effect. I wasn't expecting that. I guess you learn something every day.
According to these results, there's no point at all in investing more often than once per month. With a single lump sum invested for a year, your standard deviation is only 30% more than it would be with daily investments.
Is dollar-cost averaging a myth? What other conclusion could I draw?
Jun 16, 2008
Fixed vs. variable mortgage rates
Today, I agree with Larry MacDonald. Today, he recommends variable-rate mortgages over fixed-rate. The reason I agree? It actually has to do with something Michael James once said: that if you're going to pay a bank to take all the risks for you, they're going to charge you for it. In this case, a fixed-rate mortgage is the bank's way of taking all the risk on your behalf, and like every other service a bank provides, it stands to reason that they will charge you more than it's worth.
May 30, 2008
That's diversification?
In Larry MacDonald's recent blog post, he made clear his uneasiness with having your whole wealth invested in your home—a position I agree with. He went on to say that he'd suggest keeping 15-20% of your wealth in the form of other assets to protect yourself from a drop in housing prices that may amount to as much as 30%.
Let's examine this diversification strategy for a moment. If you have 20% of your wealth in other assets, you still have 80% of your wealth in your home. This means that a 30% drop in your home's value equates to a 24% drop in your wealth. The undiversified home owner would end up with 70¢ for each dollar he has today, while the "diversified" one would have 76¢. That doesn't sound like much protection to me.
In contrast, I have no real estate, but suppose I invest in funds that have 10% invested in Real Estate Investment Trusts (REITs). If the unit prices of those trusts were to drop by 30%, I would still have 97¢ for each dollar I have today. Now that is the protection that diversification is supposed to provide.
Naturally, I also don't stand to gain as much if REITs suddenly rise in unit price. But let me tell you what does happen. If REITs suddenly double, I'd have 20% of my assets in REITs. The managers of these funds aim to have 10% in REITs, so to achieve the target asset balance, they would sell half of my REIT holdings and buy other assets instead. Conversely, when REITs drop, they would buy more to keep the target asset balance.
In other words, they buy low and sell high. It's hard to complain about that.
Let's examine this diversification strategy for a moment. If you have 20% of your wealth in other assets, you still have 80% of your wealth in your home. This means that a 30% drop in your home's value equates to a 24% drop in your wealth. The undiversified home owner would end up with 70¢ for each dollar he has today, while the "diversified" one would have 76¢. That doesn't sound like much protection to me.
In contrast, I have no real estate, but suppose I invest in funds that have 10% invested in Real Estate Investment Trusts (REITs). If the unit prices of those trusts were to drop by 30%, I would still have 97¢ for each dollar I have today. Now that is the protection that diversification is supposed to provide.
Naturally, I also don't stand to gain as much if REITs suddenly rise in unit price. But let me tell you what does happen. If REITs suddenly double, I'd have 20% of my assets in REITs. The managers of these funds aim to have 10% in REITs, so to achieve the target asset balance, they would sell half of my REIT holdings and buy other assets instead. Conversely, when REITs drop, they would buy more to keep the target asset balance.
In other words, they buy low and sell high. It's hard to complain about that.
Apr 12, 2008
Save money by renting your home
If you're renting, you're throwing your money away, right? Well, if you're paying mortgage interest to the bank, that's throwing money away too. Which costs less over the long term?
I pay $1200 per month in rent, including my parking space. That rent includes a number of items that would come out of my own pocket if I owned a home, such as property tax, repairs, maintenance, and some utilities. All told, I get about $500 in value every month included in my rent. That leaves $700 that is truly "thrown away" just like mortgage interest.
How large a mortgage would cost $700 per month in interest? Today's variable-rate mortgages are going for about 4.6% per year. At that rate, a mortgage of $182k would have interest charges of $700 per month. That means if I could stop renting and move into a house with a mortgage of $182k or less, I would save money every month.
Houses in my area don't sell for $182k. They sell for more like $482k, meaning I would need a $300k downpayment. With that large a downpayment, I'd need to look carefully at the opportunity cost of moving $300k worth of assets into a single piece of real estate. $300k in the stock market would earn about half the Canadian median household income every year, so that's a pretty high opportunity cost.
What if I get a larger mortgage instead? If I get a $300k mortgage instead of $182k, that would cost an extra $452 per month. I'd have to justify that extra cost either using the appreciation in the value of the property I buy, or else using non-financial arguments (e.g. I just really want to own a house). Since I don't particularly want to own a house, that leaves me with the appreciation argument.
So the question I ask myself is: do I want to borrow several times my gross salary to bet my entire net worth on a single real-estate investment? Given the current climate of the real estate market, I'm pretty happy with my current diversified portfolio, thank you very much.
I pay $1200 per month in rent, including my parking space. That rent includes a number of items that would come out of my own pocket if I owned a home, such as property tax, repairs, maintenance, and some utilities. All told, I get about $500 in value every month included in my rent. That leaves $700 that is truly "thrown away" just like mortgage interest.
How large a mortgage would cost $700 per month in interest? Today's variable-rate mortgages are going for about 4.6% per year. At that rate, a mortgage of $182k would have interest charges of $700 per month. That means if I could stop renting and move into a house with a mortgage of $182k or less, I would save money every month.
Houses in my area don't sell for $182k. They sell for more like $482k, meaning I would need a $300k downpayment. With that large a downpayment, I'd need to look carefully at the opportunity cost of moving $300k worth of assets into a single piece of real estate. $300k in the stock market would earn about half the Canadian median household income every year, so that's a pretty high opportunity cost.
What if I get a larger mortgage instead? If I get a $300k mortgage instead of $182k, that would cost an extra $452 per month. I'd have to justify that extra cost either using the appreciation in the value of the property I buy, or else using non-financial arguments (e.g. I just really want to own a house). Since I don't particularly want to own a house, that leaves me with the appreciation argument.
So the question I ask myself is: do I want to borrow several times my gross salary to bet my entire net worth on a single real-estate investment? Given the current climate of the real estate market, I'm pretty happy with my current diversified portfolio, thank you very much.
Mar 31, 2008
Saving up for a car
I've figured out a way you can save thousands of dollars on your next car. I call it saving up for it. It's pretty radical, but if you bear with me, I'll explain how it works.
Say it's 2004, you live in Ontario, and you'd like to buy yourself a 2004 Honda Civic. It will cost you about $16,100, plus $2093 tax, plus $2049 interest if you finance it at 6% over 4 years. Total cost: $20,242.
Now, let's suppose instead that you just pretend to buy the car, but actually you decide you'll get by with your current rust bucket, and pay yourself the $378 car payment every month into a a bank account, and -- get this -- the bank pays you 3% interest! After 4 years, you can buy yourself the same car for $12,600. You save $3500 off the sticker price, and $455 in tax. Best of all, instead of paying $2049 in interest, you actually earn $1024 instead (though that income is taxable). Net cost: $13,600.
You save yourself almost $7000, and you end up with the same car. Even if your existing car costs you an extra $2000 in maintenance compared with the new one, you're still $5000 ahead. If you invest that, and it doubles every decade for three decades, you have an additional $40,000 in retirement, which is more than your final two RRSP contributions put together.
And that's why I'm still driving my family of four around in a 13-year-old coupe.
Say it's 2004, you live in Ontario, and you'd like to buy yourself a 2004 Honda Civic. It will cost you about $16,100, plus $2093 tax, plus $2049 interest if you finance it at 6% over 4 years. Total cost: $20,242.
Now, let's suppose instead that you just pretend to buy the car, but actually you decide you'll get by with your current rust bucket, and pay yourself the $378 car payment every month into a a bank account, and -- get this -- the bank pays you 3% interest! After 4 years, you can buy yourself the same car for $12,600. You save $3500 off the sticker price, and $455 in tax. Best of all, instead of paying $2049 in interest, you actually earn $1024 instead (though that income is taxable). Net cost: $13,600.
You save yourself almost $7000, and you end up with the same car. Even if your existing car costs you an extra $2000 in maintenance compared with the new one, you're still $5000 ahead. If you invest that, and it doubles every decade for three decades, you have an additional $40,000 in retirement, which is more than your final two RRSP contributions put together.
And that's why I'm still driving my family of four around in a 13-year-old coupe.
Mar 30, 2008
The phenomenally dumb "RRSP meltdown"
People seem to love to throw away money just so they don't have to pay tax on it. Here's one of the dumbest tax-avoidance schemes I've ever seen: the "RRSP meltdown". I've heard of using leveraged investments to dodge taxes before (like the Smith manoeuvre), but none is more contrived and pointlessly risky.
"Leveraged investing" means borrowing money to invest, on the assumption that you'll earn more on your investment than you pay in interest. What seems to attract people to this idea is that you can deduct the interest from your taxes. This leads people to contemplate all kinds of wacko ideas, not the least of which is the RRSP meltdown.
How does the meltdown work? Let's suppose you have $100k in an RRSP and you don't like the idea of paying tax on it when you withdraw it. The RRSP meltdown works like this: say you borrow $150k from the bank. Let's say you pay $10k/year in interest. You then withdraw $10k/year from your RRSP. You're taxed on the withdrawal, but the interest is deductible, and so you break even! Sounds great, right?
But let's not forget that you're paying $10k/year in interest to the bank. If you have an interest-only loan, then after 10 years, when you're finished your meltdown, you've got no RRSP, you've paid $100k in interest, and you still owe the bank the original $150k principal!
After selling investments to pay back the bank, all you're left with is the earnings you got from those investments. And since you held that $150k outside your RRSP, those earnings are taxable! If you had just left your RRSP intact for those same 10 years, it would have compounded tax-free. You'd pay tax to withdraw it, but you'd still have at least half of it left over, no matter what tax bracket you're in.
Here's the dumbest part of all: what does the $150k loan have to do with your RRSP? Absolutely nothing. You can't use your RRSP as collateral for the loan. If the meltdown advocates were right, and it did make sense to borrow $150k to fund a leveraged investment, then why doesn't everyone do it, RRSP or not?
If your answer is "because they couldn't afford the interest payments", or "because leveraged investing is too risky", then you may be starting to see why this idea is so stupid.
"Leveraged investing" means borrowing money to invest, on the assumption that you'll earn more on your investment than you pay in interest. What seems to attract people to this idea is that you can deduct the interest from your taxes. This leads people to contemplate all kinds of wacko ideas, not the least of which is the RRSP meltdown.
How does the meltdown work? Let's suppose you have $100k in an RRSP and you don't like the idea of paying tax on it when you withdraw it. The RRSP meltdown works like this: say you borrow $150k from the bank. Let's say you pay $10k/year in interest. You then withdraw $10k/year from your RRSP. You're taxed on the withdrawal, but the interest is deductible, and so you break even! Sounds great, right?
But let's not forget that you're paying $10k/year in interest to the bank. If you have an interest-only loan, then after 10 years, when you're finished your meltdown, you've got no RRSP, you've paid $100k in interest, and you still owe the bank the original $150k principal!
After selling investments to pay back the bank, all you're left with is the earnings you got from those investments. And since you held that $150k outside your RRSP, those earnings are taxable! If you had just left your RRSP intact for those same 10 years, it would have compounded tax-free. You'd pay tax to withdraw it, but you'd still have at least half of it left over, no matter what tax bracket you're in.
Here's the dumbest part of all: what does the $150k loan have to do with your RRSP? Absolutely nothing. You can't use your RRSP as collateral for the loan. If the meltdown advocates were right, and it did make sense to borrow $150k to fund a leveraged investment, then why doesn't everyone do it, RRSP or not?
If your answer is "because they couldn't afford the interest payments", or "because leveraged investing is too risky", then you may be starting to see why this idea is so stupid.
Who wins with the new Tax-Free Savings Account?
The pundits are all over the new Tax-Free Savings Account (TFSA) introduced this week in the federal budget. They seem to want it to be complex and ambiguous, but it's actually pretty simple.
In an RRSP, you save your money, it grows tax-free, and then you withdraw it and pay all your taxes at the end. Who benefits from paying taxes at the end? Well, anyone who will be in a lower tax bracket when they withdraw the money than when they earned it.
In a TFSA, you pay tax on your money at the beginning, then you save it, and it grows tax-free from then on. Who benefits? Those who will be in a higher tax bracket when they withdraw the money.
Well, who in the world would be withdrawing their money at a higher tax bracket than when they earned it??
Others probably won't benefit a whole lot from the TFSA. I guess people with too many investments to fit into their RRSPs—a very nice problem to have—can move some of the least tax-efficient ones (interest-earning investments like bank accounts and bonds) into the TFSA.
In an RRSP, you save your money, it grows tax-free, and then you withdraw it and pay all your taxes at the end. Who benefits from paying taxes at the end? Well, anyone who will be in a lower tax bracket when they withdraw the money than when they earned it.
In a TFSA, you pay tax on your money at the beginning, then you save it, and it grows tax-free from then on. Who benefits? Those who will be in a higher tax bracket when they withdraw the money.
Well, who in the world would be withdrawing their money at a higher tax bracket than when they earned it??
- Twentysomethings living at home with a low-paying job and even lower expenses. By their mid-30s, they may be in a pretty high tax bracket, and now they can grow their savings tax-free and withdraw it tax free. For instance, their TFSA (which could be as much as $80k) can be plunked down as a downpayment on their first home with no repercussions whatsoever. That's four times as much as the RRSP home-buyer's plan limit, and without the forced repayments.
- Low-income earners nearing retirement. Benefit "clawbacks" can put these people in a tax bracket of almost 90%, making an RRSP completely infeasible because they'd lose almost 90% of their savings. That means the lowest-income people are, ironically, the ones who can't make use of the tax-free compounding of RRSPs. The tax-free compounding of the TFSA puts these people on an even footing with richer Canadians.
Others probably won't benefit a whole lot from the TFSA. I guess people with too many investments to fit into their RRSPs—a very nice problem to have—can move some of the least tax-efficient ones (interest-earning investments like bank accounts and bonds) into the TFSA.
Income tax rant
I recently heard on the radio a proposal to simplify Canada's tax system. The claim was that four tax brackets are too many, and instead, we should have only two. I couldn't help but laugh.
As a resident of Ontario, we have federal tax, provincial tax (with different brackets), the provincial surtax, CPP and EI contributions, and the health premium. Combining all these taxes into one "effective tax schedule" results in 23 different tax brackets, ranging from 1.8% to over 71%. (A retiree receiving the OAS and GIS, with the associated claw-backs, has even higher and weirder tax brackets.)
I'd like to see just three things:
PS. In case you're wondering, here are the brackets:
As a resident of Ontario, we have federal tax, provincial tax (with different brackets), the provincial surtax, CPP and EI contributions, and the health premium. Combining all these taxes into one "effective tax schedule" results in 23 different tax brackets, ranging from 1.8% to over 71%. (A retiree receiving the OAS and GIS, with the associated claw-backs, has even higher and weirder tax brackets.)
I'd like to see just three things:
- The provincial and federal brackets should align with each other.
- The so-called "health premium" and the provincial surtax should both become plain old tax hikes.
- CPP and EI contribution limit should be aligned with the other tax brackets (and the amount paid should be averaged throughout the year).
PS. In case you're wondering, here are the brackets:
0.00-3500.00 @1.8%
3500.00-11262.90 @6.75%
11262.90-11638.90 @12.8%
11638.90-20000.00 @28.3%
20000.00-25000.00 @34.3%
25000.00-35488.00 @28.3%
35488.00-36000.00 @31.4%
36000.00-37178.00 @37.4%
37178.00-38500.00 @43.9%
38500.00-40000.00 @37.9%
40000.00-43700.00 @36.1%
43700.00-48000.00 @31.15%
48000.00-48600.00 @56.15%
48600.00-64274.89 @31.15%
64274.89-70976.00 @32.98%
70976.00-72000.00 @35.392%
72000.00-72600.00 @60.392%
72600.00-74357.00 @35.392%
74357.00-75088.90 @39.392%
75088.90-120887.00 @43.4096%
120887.00-200000.00 @46.4096%
200000.00-200600.00 @71.4096%
200600.00 and up @46.4096%
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