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 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:
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.
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