Wednesday, September 30, 2009
A good example of this phenomenon is the willingness of people to buy lottery tickets. In Canada’s Lotto 6/49, only 47% of money collected is returned in prizes. This means that the average $2 ticket gets back only 94 cents. And from an investment perspective, the volatility of the returns makes the ticket worth even less than 94 cents.
However, none of this makes any difference to the thinking of lottery players. Many will say that they play for fun, but the truth is that they can imagine winning, and that’s enough to keep them playing. A long run of lottery ads even used the line “imagine the freedom.”
Most businesses that sell goods attempt to sell extended warranties along with their electronics, furniture, and other items. Part of the sales pitch is to plant the idea that something could go wrong (but not until after you seem fully committed to buying the item). You imagine that something might go wrong, and you become tempted to buy the warranty.
Of course, most of these goods have at least a year-long manufacturer’s warranty. Odds are that if something does go wrong, it will happen in the first year. And the price of extending the warranty to 3 years usually vastly overstates the odds that something will go wrong. Thus, the warranty price is almost pure profit. But, these facts carry little weight with people who become nervous and imagine their new purchase breaking.
Online poker sites offer “free rolls,” which are tournaments that require no money to enter, but have prizes. The idea is to draw players in and ultimately get a fraction of them depositing some of their money to play.
One free roll I’ve tried takes 9000 players and gives the top 72 players a ticket to a second level tournament (with about 5000 players) that pays a total of $2000 in prizes. The average player in the first level tournament gets only about one-third of a cent. However, the tournament has $2000 written at the top, and players imagine winning that money.
Even financial advisors use the power of imagination to steer prospective clients. They start with gloomy projections about government old-age programs that leave you imagining being homeless and eating cat food. Then your new plan has a nice chart showing you retiring a millionaire, which conjures up images of an affluent lifestyle.
Much of the advertising we see is designed to get us to imagine something that suits the advertiser. We would do well to focus on the numbers instead of our imaginations when it comes to big financial choices in life.
Tuesday, September 29, 2009
A number of factors go into making the best choice of mortgage, and one of those factors is the interest rate offered for the different terms of fixed-rate mortgages. As an example, let’s use the best interest rates on fixed-rate mortgages available from one mortgage broker, Invis, which are as follows:
1 year: 2.55%
2 years: 2.89%
3 years: 3.39%
4 years: 3.74%
5 years: 4.09%
7 years: 5.05%
10 years: 5.40%
If you’re already thinking of taking a 1-year term, you may wonder if you would be better off taking a 2-year term for only an extra 0.34% each year. To compare these choices, it is better to think of the 2-year mortgage as having a rate of 2.55% in the first year and 3.23% in the second year. This second year rate is calculated so that the two years compound out to the 2-year average rate of 2.89%.
So now it’s a little easier to make a choice. If you’re already planning to pay 2.55% in the first year, are you willing to lock in a rate of 3.23% for the second year? If not, stick to the 1-year mortgage.
This reasoning can be extended across all of the terms to produce the following table of rates for each year of a 10-year mortgage:
Year 1: 2.55%
Year 2: 3.23%
Year 3: 4.40%
Year 4: 4.80%
Year 5: 5.50%
Year 6: 7.49%
Year 7: 7.49%
Year 8: 6.22%
Year 9: 6.22%
Year 10: 6.22%
You would use this table as follows. To choose between a 2 or 3-year mortgage, you have to decide whether you’re willing to lock in a rate of 4.40% in the third year. To choose between a 5 and 7-year mortgage, you have to decide whether you’re willing to lock in a rate of 7.49% in years 6 and 7.
This is the way I looked at things when I chose my first mortgage. I found it to be the only way to make sense of all the choices.
For the Math Geeks:
For those interested in how I came up with the table, here is an example for year 4. If the lender’s interest rates for 3 years and 4 years are r3 and r4, then rate for year 4 in my table (call it R4) satisfies the following rule:
(1+R4)*(1+r3)^3 = (1+r4)^4
This can be solved as
R4 = ((1+r4)^4)/( (1+r3)^3) – 1
The cases where the gap between mortgage terms is longer than one year are a little more complicated. For the case of table entries for years 6 and 7 (R6 and R7), we use the 5-year and 7-year lender rates (r5 and r7) as follows:
(1+R6)*(1+R7)*(1+r5)^5 = (1+r7)^7
Arbitrarily setting R6=R7 allows us to solve this for the year 6 and year 7 rates.
Monday, September 28, 2009
In a consumer proposal, you are essentially telling your creditors than you can’t pay all you owe them but can pay back a lesser amount. Your creditors may agree to this if they think that bankruptcy is the only other option because creditors usually get more money in the case of a consumer proposal.
However, once you’re in a consumer proposal, you can’t expect new creditors to be excited about lending you money. The second comment in this Ellen Roseman blog entry is from a “Frustrated” lady who was turned down for a lease on a new Ford vehicle because she and her husband had filed a consumer proposal that was accepted by her creditors.
This lady is very unhappy and thinks that because she is a loyal customer of Ford’s she should be able to lease another vehicle. It doesn’t take too long in thinking about this from Ford’s point of view to see why she was turned down. Her other creditors won’t get all of their money back; why should Ford expect to get all of its money back?
In the end she had to resort to private financing at nearly 30% interest, which she describes as “usurious.” However, the lender has to be compensated for the extra risk of lending to a couple who can’t always pay back their loans. I have no idea whether 30% is appropriate in this case, but a higher than normal rate is in order.
Sunday, September 27, 2009
Everything I read about asset allocation says that investors are very conservative and must put a significant fraction of their money into fixed income investments like bonds even though stocks have historically given much higher returns.
All of these commentators may be right about their assessment of investor psychology. Of course, this says nothing about what would be best for investors; it is just a reflection of how investors think.
Morningstar has formalized this view of investors in a formula for assessing investments called the Morningstar Risk-Adjusted Return (MRAR). All the math in the Morningstar explanation tends to obscure what is going on. Let’s look at a simple example. Suppose that each year a particular investment either returns 50% or loses 20% with equal probability.
A simple view of this investment is that its average return is (50%-20%)/2 = 15%. Morningstar’s MRAR calculation can handle different degrees of conservatism, and this simple kind of average corresponds to MRAR(-1).
Another way to look at this investment is that after two years you will probably make 50% once and lose 20% once. So, $1 would grow by 50 cents to $1.50, and then lose 20% of $1.50 (30 cents), leaving $1.20. The two-year return is 20%. This corresponds to an annual compound rate of 9.5%. After many years, the odds are about 50/50 whether your long-term annual return would be above or below 9.5%. This kind of average corresponds to MRAR(0).
You can think of the drop in return from 15% to 9.5% as a penalty for volatility. And this high penalty is appropriate. This is a very volatile investment.
But Morningstar thinks that the volatility penalty should be much higher than this to match the “risk tolerances of typical retail investors”. I’m not sure, but I think “retail investors” is a reference to dolts like you and me. Presumably, professional money managers have different risk tolerances.
Morningstar says that the typical investor is so conservative that we should use MRAR(2), which labels our hypothetical investment with a risk-adjusted loss of 0.2%! If Morningstar and other commentators are right, investors would rather stick their money in a zero-interest bank account than go for a 50/50 shot at either making 50% or losing 20%.
Maybe most investors really are this conservative, but I’m not. I make sure that I have adequate cash reserves, and have safe investments for any money I will need in the next three years. After that everything is invested for the long term, and my risk tolerance is consistent with MRAR(0).
Friday, September 25, 2009
2. Canadian Capitalist points out that it is not just stock investors who underperform indexes; fixed income investors get lower returns than the bond indexes as well.
3. Big Cajun Man has a video from 1985 explaining how pennies are a waste of time. It’s sad that we still use pennies even though they’ve been near worthless for a generation.
4. Larry MacDonald reported on new research into mutual fund fees (although for some reason the post seems to have fallen off his blog). The authors of the paper The Relation between Price and Performance in the Mutual Fund Industry claim that funds with worse before-fee performance tend to charge higher fees than better-performing funds. One explanation they consider is that poor funds spend more on marketing.
5. At Where Does All My Money Go?, guest writer Daniela Garritano has some tips on maximizing the sale price on your home.
6. If you’ve ever had to pay income tax in instalments, you likely found the three options for the amount that you have to pay confusing. Million Dollar Journey explains the three options for income tax instalments.
7. Canadian Financial DIY brings us some research indicating that financial advisors do not bring enough value to offset the fees they charge.
8. Four Pillars gives us the benefit of experience in how to select a tenant for a rental property.
9. Moneygardener has an amusing rant about pundits incorrectly predicting that the stock market recovery would falter. I suppose they will be right eventually, but who knows how far stock prices will rise before they falter.
Thursday, September 24, 2009
In his book Enough Bull: How to Retire well without the stock market, mutual funds, or even an investment advisor, Trahair ignored dividends from stock returns in his comparison with GICs and Canadian Capitalist took him to task for this. In the interview, Trahair quotes both returns with and without dividends. However, because the returns without dividends are irrelevant for comparison, we’ll ignore them.
Trahair quoted the following return figures over decades ending August 31, 2009:
Past 10 years: 3.35%
Past 20 years: 5.11%
Past 30 years: 7.28%
Past 40 years: 7.71%
Past 50 years: 7.35%
S&P/TSX Composite Total Return Index:
Past 10 years: 9.41%
Past 20 years: 8.86%
Past 30 years: 10.76%
Past 40 years: 9.77%
Past 50 years: 9.80%
Stocks do perform better, but the gap does appear to be modest. However, it can be misleading to compare average returns over long periods like this. What actually happened to real money invested over this period?
The following chart shows what would have happened to $10,000 invested solely in GICs or solely in the TSX index with dividends reinvested:
Over one decade, an initial investment of $10,000 in GICs grew to $13,900, but stocks ended at nearly double this amount: $24,600. For periods of 20, 30, and 40 years, the final value of stocks was more than double that of GICs, and for 50 years stocks gave more than triple.
As the chart shows, the seemingly small average advantage of stocks added up to a big difference over long periods of time.
Wednesday, September 23, 2009
I was unable to square the wording of my credit card agreement with the way I’ve been charged interest. It seemed to me that I shouldn’t have been charged any interest the third month. So, I was left unsure of my status.
This led me to start my own personal battle with the credit card company. I haven’t paid for anything with a credit card for a month now. My latest bill arrived with no interest charged and no amount owing. Hopefully this means I can start using it again without being charged interest. If not, I’ll have to break down and call them (shudder).
Based on my experience, it seems that you could fail to pay your bill in full just a few times per year to end up paying interest on almost all purchases.
Tuesday, September 22, 2009
The window repair companies claim that they can solve moisture problems by drilling a hole in the window, inserting some moisture-absorbing material, and plugging the hole with a one-way valve to let moisture out.
Every year my neighbourhood is filled with signs saying some variant of “Moisture problems in your windows? We can help!” The trouble is that every year the signs are different and the company name is different. This doesn’t exactly inspire confidence.
From what I’m told, window repair is significantly cheaper than replacing windows, but it’s still expensive. And if window repair doesn’t really work, then paying for a repair and later replacing the window is the most expensive option.
I’m interested in whether any readers have experience with these window repair companies. Do the repairs work? How long have your windows remained moisture-free? How expensive were the repairs compared to window replacement?
Monday, September 21, 2009
The phone companies appealed to the Supreme Court to spend the whole $650 million on broadband, and consumer groups wanted the whole amount given back to customers. In the end the Supreme Court decided that the CRTC’s middle of the road plan was reasonable.
So, you can expect to get some money back if you’ve had a land line for a while. But, don’t expect too much. Although the refund amount isn’t set yet, various estimates are between $5 and $20.
Sunday, September 20, 2009
What a great sounding idea: unlocking the value of your home. Whenever I hear this phrase, I picture piles of cash stored in my walls. What could be more reasonable than taking some of this cash out to make my life better?
I usually hear advice about unlocking my home’s value from a bank that wants to sell me a loan or a financial advisor who wants to sell me mutual funds. But, so what? Do I really need to have so much of my money tied up in real estate?
Some financial advisors even talk about the dangers of investing too heavily in just one asset class: real estate. For the sake of safety and diversification, do we need to take some money out of our houses and buy some stocks and bonds?
To begin with, the idea that you can take some money out of your home without selling it is just a trick. You own 100% of your home regardless of how much you owe on your mortgage. If your house drops in value, the loss is yours, and the bank will still want the same mortgage payments.
So, “using home equity to invest” is just a fancy way of saying that you are borrowing money to buy stocks and bonds. And “using home equity to travel” is just a fancy way of saying that you are borrowing money to go on vacation.
Somehow, it doesn’t sound like such a good idea when you phrase it differently. Don’t be fooled by marketing language designed to get you into debt. If you decide to borrow anyway, at least you’ve done it with your eyes open.
Friday, September 18, 2009
2. Jonathan Chevreau explains the battle over Questrade’s attempt to refund mutual fund trailer fees to its customers.
3. Thicken My Wallet explains deal fatigue as a negotiation strategy. I think I’ve been a victim of this one.
4. Larry Swedroe says don’t believe the hype about gold.
5. Preet explains the tax implications of a difference between Vanguard’s ETFs and other ETFs.
6. Canadian Capitalist gives us the lay of the land in Canadian high-interest savings accounts.
7. Big Cajun Man looks at monthly bank fees as an interest charge. He’s not too impressed with a chequing account with a negative 31% interest rate. Viewing bank charges as interest makes sense if the cost of providing the account is essentially nil. If the banks do have real costs, then it makes less sense. The truth is likely somewhere in between.
8. Mr. Cheap at Four Pillars gives a rundown of the investments he thinks beginning investors should avoid.
9. Million Dollar Journey gives 5 steps for simplifying your finances.
10. Scott Adams wrote a funny, but unrelated to money, post about inappropriate witticisms. The additional stories in the comments section are worth a look as well.
Thursday, September 17, 2009
The coins I examined were collected over a great many years from change; none of the coins were purchased from other collectors. So, the “investment” cost was just the face value of each coin (adjusted for inflation).
For this little test, I decided to focus only on coins at least 50 years old. Among these coins, I was surprised to discover that their total current value exceeded the total face value (adjusted for inflation based on each coin’s date) by 19%. This means that the average rate of return was about inflation plus 0.25%. In fact, the return is a little better than this because some coins were saved in a later year than the year that they were minted.
By stock market investing standards, beating inflation by less than 1% over several decades is quite dismal, but I was surprised that the collection even kept up with inflation. I remain pessimistic about collectibles as investments, but many collectors are in it for the love of collecting rather than investment returns.
Wednesday, September 16, 2009
Allen-Vanguard has had serious debt problems and its share price has dropped over 99% in the last two years. A Friday press release announced that Versa Capital Management would take over Allen-Vanguard, but that all existing shares would be “cancelled on closing of the transaction, with no consideration paid to holders.”
To the average shareholder, this can be baffling. Don’t shareholders get to vote on this? If a company is willing to take over Allen-Vanguard, doesn’t that mean it still has value? Investors can’t be blamed if they think that their shares were simply stolen away.
The reality is that Versa only took over some of Allen-Vanguard’s debts. If creditors agreed to only partial repayment, this is a strong sign that the company was indeed underwater and had negative value. Without any further information, it is plausible that the shares were worthless. Of course, it would certainly be nice to know whether some impartial third party was present to confirm that the shares were worthless.
All indications are that shareholders were treated fairly, but perceptions matter too. It isn’t good for Canada’s stock markets to have investors believing that they were robbed.
Tuesday, September 15, 2009
RCMP were investigating the scheme for more than three years before charges were laid. This will be maddening for those who lost money over the last three years. To lose money in a scheme already believed to be a fraud by authorities has to be infuriating.
This type of story is all too familiar lately. Shocked investors will be hoping that the money will be found, but if it really is a Ponzi scheme, it is very likely that almost all of the money is long gone. To investors in Ponzi schemes, it feels like the money disappears suddenly. In reality years of account statements were fantasies because the money was stolen over time.
Some media reports feed into this feeling that investor money disappears suddenly just before the Ponzi scheme is detected. One gets the feeling that if authorities just look hard enough for the money, they might find it. Sadly, this just gives hapless investors false hope.
Monday, September 14, 2009
One part of the poll had respondents rate the ethical behaviour of individual market participants. Here are the results from most ethical to least ethical:
Pension Fund Managers
Mutual Fund Managers
Corporate Boards of Public Companies
Executive Management of Public Companies
Private Equity Managers
Financial Advisors to Private Individuals
Hedge Fund Managers
Note that financial advisors didn’t fare very well in this survey. The comments section on a survey is often more interesting than the dry numbers. Here is what some experts had to say about financial advisors in Canada:
“Investment advice should be provided by investment professionals. Unfortunately, financial/investment advice is too often being given by salespeople with little experience/training.”
“Financial advisers to private individuals are too motivated by the commission they receive on certain products and recommend them to investors regardless of whether or not they meet their investment criteria.”
“The compensation system for financial professionals needs to be changed. All fees should, like a dentist’s or lawyer’s fees, be billed to the clients. This is especially true for financial advisers to private individuals who extract enormous fees for ‘distribution’ unseen to clients as they are bundled as part of mutual fund management fees.”
This last suggestion sounds quite sensible to me. The fees people pay should be visible. Many Canadians would be shocked to learn how much they pay their financial advisors.
Sunday, September 13, 2009
The core argument of the book Worry-Free Investing, by Zvi Bodie and Michael J. Clowes is that stocks are too risky for most investors and they should invest in inflation-protected bonds (called I Bonds in the US and Real Return Bonds in Canada). The justification for this claim is in Chapter 6 where they show the results of some simulations.
Monte Carlo simulations can be a good way to get a feel for the various possible outcomes of investing over a period of time. The authors use historical returns on US stocks from 1926 to 2000 to simulate a one-time investment of $100 in US stocks over 30 years to show what could happen.
To make the numbers more meaningful, I’ll multiply them by 100 so that the initial investment is $10,000. In the three simulations the authors show, here is how much the stocks are worth after 30 years (adjusted for inflation):
Simulation 1: $75,000
Simulation 2: $5200
Simulation 3: $200,000
For comparison, an I Bond with a 3% return above inflation would give $24,300 after 30 years. The authors then point to simulation 2 saying “we see that very bad outcomes can occur for long-time horizons.”
The outcome of Simulation 2 seemed very unlikely to me. I decided to run my own simulations based on choosing each year’s return randomly from the historical returns in Figure 6.2. Instead of only doing 3 runs, I let my PC go for a few hours, and it completed a billion runs. This is more than we need, but it gives a good picture of the possible outcomes.
One thing I learnt was that 25-year olds are about 10 times more likely to die before the end of the 30 years than they are to get stock returns as bad as in Simulation 2. In only one out of every 140 simulation runs the stocks were worth less than $5200. In 87% of runs, stocks beat I Bonds. Half the time stocks were above $86,000 compared to I Bonds at only $24,300.
If we accept Simulation 2 as a meaningful result even though it happens only once out of 140 times, what about the high end of stock return possibilities? In one out of 140 runs, stocks returned more than $1,060,000!
The main result here is that the authors’ three simulations do not give an accurate picture of what is likely to happen. If that result of $5200 were just one out of a list of 100 simulation runs, it wouldn’t seem nearly so scary.
Friday, September 11, 2009
Short Takes: Genetics of Asset Allocation, Fund Fee Court Battle, and Lining Financial Advisor Pockets
2. Thicken My Wallet gives a clear explanation of a court battle over US mutual fund fees. If US courts decide to shake up the mutual fund industry by limiting their ability to charge unreasonably high fees, it will be interesting to see if Canada eventually follows suit.
3. Preet gives us an insider’s look at a financial advisor technique for collecting huge fees just short of retirement. Unfortunately, all these extra fees have to come out of investors’ assets.
4. Larry Swedroe reports that Americans spend about $80 billion on active management for investments each year. That’s pretty good money for a group that collectively adds no value.
5. Rob Carrick reports on Vanguard’s investor forum in Toronto. Despite the title of the article, it seems that Vanguard has no plans to bring their low cost ETF operations to Canada.
6. Canadian Capitalist finds that the book Enough Bull has some good points, but also makes its own contribution to the amount of bull in the world.
7. Big Cajun Man is concerned about bank tactics in attracting new customers on university campuses.
8. Scott Adams shows how to easily manipulate people who like to disagree with everything you say.
9. Million Dollar Journey discusses the advantages and costs of setting up a corporation.
10. Gail Vaz-Oxlade has some practical advice for rebuilding your credit rating.
Thursday, September 10, 2009
In my story Donna collected $2020 in dividends while her $100,000 portfolio of S&P TSX units (ticker: XIU) was unchanged at $16.80 per unit from 2008 October 2 to 2009 September 8. However, if she had reinvested her dividends into XIU units, her gain would have been $2440, assuming a $10 commission on trades. This isn’t such a dramatic improvement, but she might think that an extra $420 is better in her pocket than elsewhere.
What if Donna had invested her $100,000 slowly over the year instead of piling it in all at once? Spreading the money into 12 equal-sized purchases at the start of each month, Donna would have come home to just over $117,000! This is a 17% return over a “terrible” year for stocks.
Of course, not many of us have large lump sums to invest like this, but investors in the working phase of their lives can make regular contributions to savings. For these investors, big drops in stock prices are an opportunity to pick up more stock when it is cheap.
Wednesday, September 9, 2009
Back on October 2, 2008, she took the $100,000 equity from selling her house, deposited it into her brokerage account and put all of it into the S&P TSX index (ticker: XIU). The sale went through at $16.80 per unit, and she hurried off to board a plane for what promised to be a rewarding adventure.
After a lot of hard work and making some lifelong friends, but little contact with Canada, Donna arrived back in Canada last night to stay with her parents. After a meal and catching up for a few hours, Donna decided to take a look at her online brokerage account.
Imagine the devastation! Donna is completely oblivious to the turmoil in financial markets over the past year. There was real estate bust, the credit crisis, and the stock market crash. At one point in March, her portfolio was down nearly $32,000.
However, coincidentally, yesterday’s closing price for XIU was $16.80, exactly what she paid for it nearly a year ago. Her stock is still worth $100,000, and her account has $2020 in cash from the three dividend payments. Unaware of the roller-coaster ride her portfolio experienced, Donna is mildly disappointed that she didn’t make more money.
Other investors who held on through this period, but watched their portfolios daily feel like they’ve been through the ringer. Their results match Donna’s, but human nature is such that they feel far worse than she does.
Investors could take a lesson from Donna. If they are comfortable with their mix of investments, then there is no need to monitor them on a daily basis, particularly if the assets are in broad-based index funds.
I’m not advocating ignoring investments for an entire year. After all, you should at least check that your account statements are accurate. But compulsively checking prices multiple times per day is no way to live.
Tuesday, September 8, 2009
Hoping to avoid long line ups at the campus bookstore and hoping to save some money, I did some comparison shopping on both amazon.ca and chapters.ca. I was happy to find a savings of 12.5% compared to the campus store. The textbook prices at both online book sellers were identical before applying Chapter's iRewards savings and since I don't have an iRewards card anymore and since the savings were only half of the cost of a new card, I decided to order my 5 books from Amazon.
All five of the books individually qualified for "Super Saver Shipping" (over $39 of merchandise) so my money wasn’t going to be eaten up by Canada Post. Three of the books were in stock and the other 2 would be shipped in 1-2 weeks. I still had time before classes started so there was time to complete the order.
The first option Amazon presented me with was to choose a shipping speed: FREE Super Saver Shipping: (averages 2-3 business days) or Express (averages 2 business days for $13.70) or Priority (averages 1 business day for $20.94). I decided to go with FREE. I like FREE.
The second option was to A: group the books and ship them all together or B: ship the books as they became available. If I selected B, it would cost me extra to ship the two books that weren't in stock.
What happened to the free shipping that was advertised for each of the books?
What Amazon was encouraging me to do was split up my one order for 5 books into 3 separate orders: one for the three books which were in stock and one for each of the 2 books which had a 1-2 week delivery time. Then the shipping would be free for all the books.
Not willing to risk getting the books late for classes, I changed my Amazon order to include only the 3 in-stock books (they arrived 2 days later) and ordered the other 2 books from Chapters. One of those books arrived 3 days later and the other will be shipped, without extra charge, when it is available.
In the end I saved over $70 by buying online instead of on campus, but perhaps my first lesson of the new school year is to make sure that FREE shipping means FREE, not FREE plus an extra charge.
Monday, September 7, 2009
Your reaction to a game show scenario can reveal important information about your attitudes as an investor. It can even tell you what mix of investments are appropriate for your portfolio.
Let’s get right to it. You are playing Deal or No Deal and you are down to two amounts: one penny and a million dollars! What is the minimum offer you would accept from the banker?
For those not familiar with this game show, here is the situation. You are about to toss a coin. If it comes up tails, you get nothing (and lose nothing). If it comes up heads, you get a million dollars. Just before you toss, someone offers you a sum of money to give up your chance to toss for the million dollars. What is the minimum such offer you would accept?
It turns out that your answer depends on how rich you are. Bill Gates would likely accept an offer of half a million dollars, but not much less. However, someone in a desperately poor country might accept an offer of $5000.
To make a proper apples-to-apples comparison, we need to take into account your wealth. So, let’s look at how much money is in your portfolio. I’m not talking about your house, cars, and emergency stash of cash. Just consider the value of your investments that you are trying to grow for the long term.
Instead of tossing for a million dollars, imagine that you are tossing for 10 times your current portfolio size. I’ll continue this discussion as though your portfolio size is $100,000, but you will have to multiply or divide all the numbers I use by some appropriate factor.
If you are an investor who seeks to maximize the long-term compounded return on your portfolio, then the lowest offer you accept to give up your chance at the million dollars is $230,000. In the language of portfolio optimization (see this paper by John Norstad), you have a “coefficient of relative risk aversion” of A=1.
If the thought of coming away with nothing after the coin flip scares you enough that you would accept an even lower offer, then your value of this risk-aversion number A is higher. At A=2, the lowest offer you would accept is $83,000.
At A=3, the lowest offer you would accept is $41,000. It might seem ridiculous that someone who has $100,000 in his portfolio would accept only $41,000 and pass up a 50/50 chance at a million dollars, and I agree. So why am I talking about this silly A=3 case?
Morningstar uses A=3 in their risk-adjusted return calculation to rate mutual funds. Morningstar provides detailed information about both US and Canadian mutual funds. When you hear that some fund has a 4- or 5-star rating, this is based on Morningstar’s formula for comparing mutual funds.
From the notes with Morningstar’s formula, “γ=2 [which corresponds to A=3] results in fund rankings that are consistent with the risk tolerances of typical retail investors.” I can’t speak for other investors, but this definitely doesn’t apply to me.
This formula gives strong preference to funds with low predictable returns. Funds with higher returns but more volatility are punished severely.
Everyone has different thoughts about how much risk is acceptable. Personally, I’m in the A=1 camp trying to maximize the long-term compounded return on my investments. This makes Morningstar’s ratings completely irrelevant to me.
Sunday, September 6, 2009
I bought a scanner from a well-known chain store and was surprised to find a note inside the box explaining what was wrong with the scanner written by the last sucker who bought it. The note came with actual pictures of scans gone wrong. I’m grateful to this anonymous person who took the time to help out the next sucker to buy this scanner (me in this case).
The two pages explaining the problem were not exactly hidden. They were the first thing that I took out of the box. Obviously the store employees never even looked inside. They just put it back on the shelf to sell it to someone else. Nice.
I don’t see much point in naming the product or the store. But, I do like the consumer strategy of including a note any time you are forced to take a defective product back to a store. For your altruistic side, you get to help out other people.
For fun, you could even include an email address with your note if you would like to hear from the next purchaser. More advanced strategies could involve leaving more than one copy of the note: one that is very obvious to find, and the other a little more hidden. This way if a store employee opens the box and removes the easily found note, the other note will still be there to be found by the next purchaser.
In the event that the store actually fixes the product, presumably they would find and remove both copies of the note.
I am always annoyed when I have to waste time returning defective products. Playing games with notes takes a little more time, but makes my day a little brighter.
Friday, September 4, 2009
2. There is a small company with a cellphone plan calculator called Cell Plan Expert that is relieved about Industry Canada mothballing their cellphone plan calculator. Cell Plan Expert offers what it calls a basic level of service for free (although it seemed quite thorough). I tried it, and it gave me results consistent with my own research into cell plans, but my very basic cellphone needs aren’t much of a test.
3. Big Cajun Man got Rogers Cable to back down on its unlimited surcharge for internet bandwidth use.
4. Preet shares some amusing hate mail sent to the Mutual Fund Dealers Association, an organization responsible for enforcing rules about how mutual funds are sold.
5. Canadian Capitalist lists his top 5 investment deals.
6. Million Dollar Journey discusses how to convert a principal residence into a rental property the right way so that mortgage interest becomes deductible.
7. Thicken My Wallet explains why life insurance rarely makes sense for children.
8. Gail Vaz-Oxlade shares some letters from people who are desperate and delusional about money.
Thursday, September 3, 2009
The process for me began with choosing a supplier and making sure that the high-efficiency furnace I chose was on the approved list for grants. I negotiated a price of $4209 (including sales taxes).
I then arranged for an ecoENERGY home energy audit before the furnace was installed. Now that I’ve had the audit and the furnace is installed, the audit people will come again to check that I actually installed a new furnace. The total cost of the audits is $420 with tax, and then the following grants and tax deductions are supposed to come rolling in:
$790 federal furnace grant
$790 provincial furnace grant
$150 provincial energy audit grant
$125 provincial power authority grant
$150 gas supplier grant
$145 furnace seller rebate
$481 home improvement income tax deduction (15% of $4209 minus $1000)
Total Savings: $2211 (after deducting the $420 for the energy audits)
This is definitely a case of YMMV (you mileage may vary). The various grant amounts seem to change frequently.
The final cost of the furnace to me is $1998, which is less than half of the starting price. Of course, it will take a few months for all of these grants to roll in, and while I did my best to understand how all this works, I can’t be sure I’ll get all my money until it actually arrives.
Wednesday, September 2, 2009
The Canadian government rides to the rescue. Industry Canada developed a calculator to figure out which plan would work best for you. This is a great idea; the government doing something fairly inexpensive to help many Canadians.
Unfortunately, as Michael Geist reports, wireless company lobbyists convinced Tony Clement to kill the calculator. The official reason doesn’t matter because the real reason is obvious enough. Wireless companies make more money from confused consumers than they do from educated consumers.
Cellphone plans are confusing because the wireless industry wants them that way. Fortunately, there are a number of new players competing in the cellphone market offering cheaper service, particularly for infrequent users of cellphones. The next time you have to choose a new plan, you’ll have to do the work yourself; the government won’t be there to help.
Tuesday, September 1, 2009
A partial answer is that a great many phenomena, such as human height, do follow a Bell curve (also called the Gaussian or Normal distribution). In fact, Bell curves come up so often that it is natural to suspect that it would apply to equity prices.
To see why Bell curves come up so often, let’s look at a simple example with dice. If we were to roll a die many times, we expect each face to come up roughly the same number of times. On a frequency chart, this would be a mostly flat curve.
But, if we roll 10 dice many times, adding them up each time, the frequencies of the different possible totals from 10 to 60 would no longer be flat. I had my computer roll 10 virtual dice a million times. Here is a chart of how often each total showed up:
The result is a nice Bell curve with a peak at a total of 35 as we would expect. Whenever we add many independent random values together (as long as they aren’t too wild as I’ll explain later), the result tends to drift towards a Bell curve.
This isn’t a perfect Bell curve, though. If it were, the odds of getting a total less than 10 would be about one in 9000. But the real probability of getting a total less than 10 using 10 dice is zero. The Bell curve models this situation well except for the most extreme events.
What happens if we make our dice “wilder” by replacing each 6 face with a 20? Here are the results after a million virtual rolls:
The beautiful Bell curve has been destroyed. However, we can get it back by increasing the number of dice to 100:
The frequency chart still has a few small bumps, but it is now very close to the familiar Bell curve. So, even wild dice can be tamed if we add up enough of them.
This tendency for all things to drift towards a Bell curve explains why economists would assume that equity price changes follow a Bell curve. A great many factors influence prices, and when we add them all together we might suspect that a Bell curve would pop out.
(For those more mathematically inclined, standard models assume that factors multiply together so that their logarithms are being added leading to a lognormal distribution rather than a normal distribution. This means that the logarithms of equity prices are following the Bell curve.)
However, Mandelbrot argues that the factors being added together are so wild that they cannot be tamed into a Bell curve.
A good example of a wild distribution starts with a blindfolded archer standing between two long parallel walls. The archer spins around and fires arrows in a random direction. We then measure how far along the wall the arrows land.
Most arrows won’t land too far away, but occasionally the archer will fire an arrow nearly parallel to the walls that will travel a long way. Even if we add up hundreds of arrow distances, there is still likely to be an arrow so far out that its distance dominates the total. Unlike the dice with a 20 instead of a 6, the arrow distances cannot be tamed into a Bell curve by adding up many of them.
These wilder distributions are much more likely to produce extreme events than a Bell curve, and Mandelbrot showed that real equity price changes are more consistent with wilder distributions.
All this means that standard theory will give incorrect answers to some questions. Unfortunately, it isn’t easy to know which questions will be answered incorrectly. One thing to look for is situations where extreme events would sink a financial plan such as when an investor is highly leveraged.