Benoit Mandelbrot is famous for developing the idea of fractals and showing that many aspects of nature follow fractal-based laws. In his book The (Mis)Behavior of Markets he shows how his theory of fractals applies to financial markets and manages to do it with very little mathematical discussion. Mandelbrot takes a very visual approach. His starting point is to randomly generate fictitious price charts according to modern portfolio theory and observe that the charts don’t look right. When they are placed next to real price charts, the fakes can be picked out by people just looking at them. As it turns out, the problem is that extreme price changes are more frequent than portfolio theory predicts, and the bigger price moves tend to come in bunches. The distribution of real price changes doesn’t follow the standard Bell curve. Mandelbrot makes convincing arguments that price changes follow a distribution that is wilder than a Bell curve. Using fractal-based methods, he is a...

This is a Sunday feature looking back at selected articles from the early days of this blog before readership had ramped up. Enjoy. In an earlier post I showed how over time an investment with a given expected return is likely to have a lower actual return due to volatility . The more volatile an investment is, the bigger the difference between the expected return and the actual returns you get. One way to reduce volatility and increase the actual return from investments is diversification. To diversify means to spread your money among multiple investments. This is the “don’t put all your eggs in one basket” advice that we often hear. Let’s go back to the example in the earlier post where we have an investment that each month either doubles or loses 60% with equal probability. This kind of extreme case is unrealistic, but makes it easier to understand how diversification helps. We saw before that the most likely outcome was that this investment would lose almost everythi...

1. Potato gives a thoughtful explanation of why option collars for limiting risk do not give a good balance between risk and reward . As a bonus, Potato had two other interesting posts. One explained why options are a zero-sum game, but stocks are not . The other one is about student rental discrimination .  2. Where Does All My Money Go? explains that your dog could end up costing you $38,000 . Based on the vet bills for some of my friends, this estimate seems low.

My recent experience with accidentally paying my credit card bill late sent me back to my credit card agreement to figure out how long I’d be paying interest. The agreement does not seem to be consistent with how my account has been handled. Here is what my credit card agreement says about the test for not having to pay interest: We don’t charge interest on purchases appearing on your account statement for the first time if: - you pay your new balance in full by the payment due date, and - you also pay the new balance shown on your previous account statement in full by the due date shown on that account statement. So, you have to pay your bill in full on time two months in a row to get back to interest-free purchases. That should have meant that my most recent bill wouldn’t have any interest on it, but I was charged interest. My best guess is that the way a purchase is handled is related to the status of your account at the time the purchase was made rather than the time i...

I admit it. I forgot to pay my credit card bill back in June. By the time I realized what had happened, my payment was 10 days late. Unfortunately, it’s been three months now and I can’t seem to get off the credit card interest rollercoaster. I’ve received good advice in the past to just call the credit card company and get them to reverse the interest because this was a simple mistake. I didn’t bother because the amount was small, and I felt like I deserved my fate. Initially, in an attempt to get back on the straight and narrow, I found out what I owed in total (including recent purchases) and paid a little more thinking that that would end the interest cycle. When the next bill came it had interest on it again. The amount was even smaller, but still annoying. Once again, I found out my total amount outstanding including recent purchases and paid a little more. Once again, this month’s bill has interest on it. The amount of interest is smaller still, but somehow more annoying...

The recommended maximum debt levels for homeowners have always sounded high to me. But this has been little more than a feeling until I looked over some old numbers from when I bought my first house. This exercise has confirmed for me that the maximum debt levels are alarmingly high. According to the Canada Mortgage and Housing Corporation, housing costs (including mortgage payments, property taxes, and heating expenses) should not exceed 32% of your gross income. When other payments on such things as car loans, lines of credit, and credit cards are added in, the total should not exceed 40% of your gross income. I agree that people shouldn’t exceed these levels, but how sensible is it to even come close to these percentages? I decided to compare these figures to my own experience buying my first house. My wife and I had a 27% down payment, and although the mortgage amount looks small now, it was scary for us back then. We spent a little more on the house than we planned to (...

The title of this post is how an ad I received for life insurance starts. This line seems intended to exploit the fact that older people have a desire to leave money for their children and grandchildren when they die. This is an admirable goal, but the particular type of life insurance offered isn’t a good way for most of us to leave money for family. The ad goes on to explain that if you’re between 40 and 75 years old, “you cannot be turned down for any reason,” and “there’s no medical exam – and no health questions.” Wow! You’d think that everyone with a terminal illness would be lining up for this deal. The ad contains no hint of any kind of restrictions, but the web site of the bank offering this insurance has additional information. It turns out that if you die in the first two years, your estate doesn’t get the coverage amount. Instead, your estate gets an amount that is calculated based on how much you’ve paid in premiums. If you’re closer to the 75-year old end of the sca...

This is a Sunday feature looking back at selected articles from the early days of this blog before readership had ramped up. Enjoy. In a previous post, I showed how the average real return in the U.S. stock market from 1926 to 2000 is 9.3%, but that this translated into a compounded real return of only 7.4% . The reason for this difference is the volatility of the returns. Let’s go for a better understanding of the cost of volatility without any advanced math. A Simple Example Suppose that you have $10,000 invested for two years. In the first year you lose 10%, and the next year you make 10%. It might seem at first that you have your $10,000 back, but that isn’t exactly right. After the first year you were down to $9000, and then in the second year you earned 10% on that $9000 to get a total of $9900. In the end you lost 1% of your money. However, the annual returns were -10% and +10% for an average return of 0%. The lost 1% over the two years is not due to a negative e...

1. Preet reports that the planned ban on financial advisor commissions in the UK has partially spread to Australia . 2. Canadian Financial DIY takes issue with the MacLean’s article making the case against having kids . The article may be largely correct from an objective point of view, but people are definitely not wired to be objective when it comes to children. 3. Big Cajun Man plans to cut back on cell phone use and switch to a pay-per-use plan . Good luck!

It’s understandable that victims of Ponzi scheme operators like Bernard Madoff and Earl Jones focus mostly on trying to get their money back and on seeing criminals punished. Not being a victim myself (so far) allows me enough detachment to question the mindset of the guilty. Do these people enter into their occupations planning to defraud investors or do they get tempted to dip into the money or to overstate the returns they generate? Once there is a gap between actual amount invested and the amount investors are told they have, it wouldn’t take too long for this gap to grow out of control. The part that is most baffling to me is why more Ponzi scheme operators don’t try to run off to some other country and hide. As the end is drawing near and the amount of money still in their control dwindles, it becomes obvious that they will eventually be found out. Perhaps the onset of the recession sped up the demise of the Ponzi schemes enough that their operators hadn’t finalized plans to ...

You don’t have to look too far to find examples of young people making poor financial choices such as plunging into debt with a car loan. However, a small choice by one of my sons brightened my day. He received a $25 movie theatre card for his birthday. Those who give bad advice about found money might suggest a mini-splurge. Perhaps he could go to a movie and buy enough popcorn and chocolate to wipe out the card in one evening. Instead, he noted that movies cost only $4.25 on Tuesdays, and he can see almost six movies with his card as long as he eats before going. Bravo! A great many adults would do well to show this kind of financial restraint.

The advocacy group CARP has a multi-part plan for pension reform (the web page with this article has disappeared since the time of writing), but they had me at the first part. Currently, a retiree with no income or pension gets $13,636 per year from Old Age Security (OAS) and the Guaranteed Income Supplement (GIS). CARP would like to see these benefits “substantially increased” and for benefits not to be reduced for married couples. Suppose that the total benefits jump to $18,000 per year, and that a married couple would get $36,000 per year. Assuming that no income tax would be paid on this, I think my wife and I could live on $3000 per month. This brings me to a possible new retirement plan. Add up your current total retirement savings and divide by the number of years left until you turn 65. If you think you could live on this amount each year, then you could quit your job right now! Your savings would run out just in time to start collecting the new and improved OAS and ...

This is a Sunday feature looking back at selected articles from the early days of this blog before readership had ramped up. Enjoy. When giving out investing advice, many authors report long-term average stock returns, but the numbers seem to differ from one author to the next. Surely, we have lived only one history. Some differences can be explained by the authors studying different time periods or different baskets of stocks. However, there is another reason for differences that relates to how the average is calculated. In Chapter 6 of Worry-Free Investing , Zvi Bodie and Michael Clowes discuss U.S. stock returns from 1926 to 2000. They give real returns , which means the returns after inflation is subtracted out. Based on the historical data, they calculate the average yearly real return on stocks to be 9.3%. But, others say that the long-term real return on U.S. stocks is 7%. This may not look like a big difference, but if you play around with one of the many free reti...

1. According to a recent report, information overload costs workers 8 hours of productivity each week . They define information overload as the “disruption of the work day with irrelevant material, including e-mails, meetings, automated news feeds and Twitter.” The phrase “information overload” portrays the worker as a hapless victim of these information interruptions. This is silly. People compulsively check their Blackberries and iPhones out of boredom. Noise and visitors are interruptions; Twitter, email, and text messages can be ignored, but are just more interesting than the task at hand. 2. Where Does All My Money Go? hosts a guest article by a financial advisor with some clear thinking on the active versus passive investing debate . 3. Canadian Financial DIY has some fun with an analogy between inflation and alcohol . 4. Big Cajun Man tries to decide whether to drive, bike, join a car pool, or take the bus to his new job . Taking a car is certainly the easiest path.

It’s bad enough that the victims of Bernard Madoff and Earl Jones have lost their money, but now they have a tax mess spanning many years. Fortunately, there are tax rules in place to alleviate some of the pain. To illustrate the potential tax unfairness, consider a hypothetical investor Ian who invested $200,000 with a charismatic guy who turned out to be running a Ponzi scheme. For 10 years, Ian received a cheque for $1000 every month along with a statement showing his savings rising steadily. Ian’s last statement before the Ponzi scheme was uncovered showed a balance of $300,000. Each of the last 10 years Ian has been paying taxes on the $12,000 interest at his marginal tax rate. If the tax man treats Ian’s $300,000 as suddenly going to zero, then Ian will have a net capital loss of $200,000. Unfortunately, Ian doesn’t have other investments with capital gains, and so he can’t make much use of this large capital loss. In reality, though, Ian’s money didn’t evaporate sudde...

One of the advantages of typical asset allocation where investors maintain fixed percentages of stocks and bonds is that portfolio rebalancing makes us automatically sell high and buy low. However, this advantage only exists if you actually do the rebalancing. Unfortunately, many investors seek reasons to avoid rebalancing at the very time it would give the greatest advantage. Catherine Gordon on the Vanguard blog discussed rebalancing recently. I don’t want to pick on her too much, but her remarks include the following: “This is a good time to take a hard look at that allocation and ask questions such as, ‘Was I really too aggressive for what I was trying to do?’ or ‘Was I truly diversified?’” It may not be her intention, but when stocks are down, many investors asking themselves these questions would decide that they had been too aggressive and should not rebalance from bonds to stocks. This past March would have been a fantastic time to have sold bonds to buy stocks to ma...

Typical advice for investor portfolios is to choose some asset allocation such as 50% stock and 50% bonds, and rebalance as necessary to maintain this balance. PŮR Investing Inc. offers a different approach that focuses on risk. Their approach actually combines two strategies that are sometimes at odds. PŮR is critical of typical target date funds that slowly reduce portfolio risk on a fixed schedule as the target retirement date nears. PŮR proposes two strategies: 1. Rebalance individual portfolios to maintain a fixed level of risk rather than a fixed percentage asset allocation. 2. Choose a level of risk over time designed to get the portfolio to a target dollar amount. The first strategy involves selling out of investments when volatility increases. So, when stock prices start to jump around, shift money to bonds to maintain a fixed risk level, and when stock prices becomes less volatile, shift back. The second strategy involves choosing a level of risk that maximizes t...

The rating agency DBRS released a pension analysis this month: Canadian Private Pension Plans – Losing or Cruising? As Canadian Financial DIY reported , the executive summary says that we’re closer to ‘cruising’ than ‘losing’ and that “the outlook for pension plan funding remains manageable.” We’re to believe that the silver lining for the recent bad news in pensions is that we’re going to be okay in the end. However, this summary appears to be a rosy view of the report details. The detailed tables show the average private pension plan to be underfunded by 5.5%. This doesn’t sound too bad, but it lumps under- and over-funded pension plans together. However, Bank of Nova Scotia isn’t going to give its $1.1 billion pension surplus to Air Canada, BCE, Manulife, and Nortel which are collectively underfunded by $5.7 billion. If we treat over-funded pension plans as simply full, then the average pension plan’s shortfall rises to 8.2%. Again, though, this understates the problem be...

The giveaway winners of 5 copies of the book Ravens by random draw are Mike, Bella, Blair, Lyne, and Gene. The winners have been contacted by email. Thanks to all who entered the draw.

This is a Sunday feature looking back at selected articles from the early days of this blog before readership had ramped up. Enjoy. One of the arguments for using financial advisors is that they provide a steady hand that helps keep you from making rash investment decisions that will hurt your returns. A study by Bullard, Friesen, and Sapp released in December 2007 casts doubt on this argument. The study showed that mutual fund investors actually get lower returns than the funds’ reported returns because of poor market timing. You would think that working with a financial advisor would keep investors from making such mistakes, but apparently not. Another aspect of the study was to examine how investors working with a financial advisor fared compared to other investors. The study’s authors summarize: “We find that investors who transact through investment professionals using conventional distribution arrangements experience substantially poorer timing performance than investor...

1. To enter the draw to win one of five copies of George Dawes Green’s novel Ravens ( see review here ), send an email with the subject “Book” to the address shown on the upper right corner of this blog. The draw will close Saturday August 8 at noon. I will contact the winners to get (Canadian or American) postal addresses. 2. Preet outlines the risks of securities lending as practiced by many index ETFs , and Patrick speculates on how this could become a bubble . It’s not clear to me how securities lending is most likely to cost investors a significant amount of money, but the fact that it appears to be free money makes me very suspicious. 3. Big Cajun Man learns a few lessons while cleaning out his basement .

Every so often I play a little game where I see how long I can go without spending any money. It usually lasts for only a few days, but it’s amazing how easy it is do without the small purchases in life when it becomes a competition. I'll leave it to others to stimulate the economy with their spending.  I should point out that I have an advantage over many people in this game because my wife makes almost all of the grocery purchases. What usually trips me up is having to buy gas for my car.  I don’t really keep track of my results, but going for a week without spending a single penny is not unusual for me. I suspect that some of my more frugal friends can go this long without even realizing it, but not so for my more spendthrift friends.  Some people average two stops for drive-through coffee and doughnuts each day. They also buy pop and chocolate bars from vending machines regularly. They seem addicted to spending money in small amounts frequently.  I’d love t...

The Bank of Montreal has begun advertising for former mortgage holders to contact them about possible refund of fees paid.  Back in June Bank of Montreal announced that they had overcharged “penalties on certain mortgage pre-payment and early-renewal transactions” and would be refunding approximately $7.1 million to 28,000 customers. It is not clear whether the latest announcement is part of the same refunding effort, or whether this is a new set of customers who were overcharged. The announcement says “You may be eligible for a refund if between: - September 1, 1998 and July 10, 2005 you paid out your mortgage. - February 1, 2001 and August 31, 2005 you renewed or early renewed into a 6-Year Flexible Below Prime mortgage. - May 1, 2002 and September 30, 2006 you renewed into a fixed rate closed mortgage and paid a penalty on this mortgage as a result of a subsequent early renewal or prepayment. - October 1, 2004 and September 30, 2006 you obtained a new fixed rate closed ...

“The Boatwrights just won $318 million in the Georgia State Lottery. It’s going to be the worst day of their lives.” The book Ravens , by George Dawes Green is a compelling suspenseful novel centered on a huge lottery win that sparks envy, greed, extortion, insincere evangelism, worship, and revenge. For an illustration of one of the critical scenes in the book, have a look at this Ravens YouTube video . One of my favourite parts of Ravens was where an impostor lottery representative laid out the winners’ future: “Sooner or later you’ll tank it [give up your copier business] and get yourself an estate in Hawaii. Then you can all get some sun, which’ll be great except you’ll get too much and you’ll start to look like iguanas. And you’ll try to make friends but who you can trust, right? So you won’t know anybody and you’ll stay home and watch TV and you’ll be lonely as hell and bored ...” This nicely illustrates what can happen in the initial stages after a lottery win. M...

Happy Civic Holiday! This isn’t the most festive holiday, but it beats working. This is a holiday version on the regular Sunday feature looking back at selected articles from the early days of this blog before readership had ramped up. Enjoy. One of the choices investors have to make is whether to handle their investments themselves or work with (and pay) a financial advisor. People have a lot to say on both sides of this issue, but I’ve heard one clever argument several times now. It goes something like this: “You wouldn’t do your own surgery, right? So, why would you try to handle your own investments? Leave this stuff to the experts.” On the surface, this reasoning seems compelling. The image of some guy trying to operate on his own belly is pretty amusing. Anyone who comes up with a catchy line that makes people laugh must be right. But, this analogy breaks down very fast. Exactly who is the brilliant surgeon in the financial world? The financial planning industry would ...

This is a Sunday feature looking back at selected articles from the early days of this blog before readership had ramped up. Enjoy. You may have heard of risk-adjusted returns in connection with mutual funds. The basic idea is that a risky investment may not be better than a predictable investment even if the risky investment has a higher expected return. There is some validity to this, although it is too often used to justify the poor returns of mutual funds compared to the overall stock market. Normally, any discussion of risk-adjusted returns includes some intimidating math. I’ll explain the problems with risk-adjusted returns without needing the math, and I’ll give pointers to where the math can be found for those who are interested. According to the theory, before comparing investments, you should do a risk-adjusted return calculation that will reduce the returns according to how risky they are. The riskier they are, the more the returns are lowered before any compariso...