New Book: A Mathematician Plays the Stock Market

Just got a Christmas present from a very good friend of mine (same person who got me the Intelligent Investor for my birthday earlier this year) called “A Mathematician Plays the Stock Market” by John Allen Paulos. It appeals to me right away because of my math background and because I like to understand things like the stock market in quantitative ways. I’ll give you the blurb on the back:

With his trademark stories, vignettes, paradoxes, and puzzles, John Allen Paulos addresses every thinking reader’s curiosity about the market–Is it efficient? Is it rational? How should one pick stocks? Can one quantify risk? What are the most common scams? Is there a way to really outperform the major indexes? Can a deeper knowledge of mathematics help beat the odds? This wry and illuminating book is for armchair mathematicians, market followers, or anyone who wants to know how market work.

Some of the sections within the chapters that caught my eye were: “Technical Strategies and Blackjack,” “Efficiency and Random Walks,” “Fat People, Fat Stocks, and P/E,” “Are Stocks Less Risky Than Bonds,” “The St. Petersburg Paradox and Utility,” and “The Paradoxical EFficient Market Hypothesis.” There are many more topics. Practically everything in the investing world is touched on in some way. I am looking forward to reading it after I finish the book(s) I am reading now.

Renting vs. Buying Calculator

I was going to create a spreadsheet to determine whether buying or renting makes more sense in different scenarios. But then I found this excellent buy vs. rent calculator from Vancity. Here’s how it works:

We calculated your breakeven point by examining how long it would take to create enough equity in your home to exceed the value of investing your cash on hand. We also accounted for differences in your monthly rent and house payments. If your rent payment is less than your net house payment, we add that monthly savings to your investment. If your house payment is less than your rent payment we subtract that amount from your investment. You may notice that on the schedule at the bottom of this report the investment value can be reported as negative. This happens if your house payment is significantly lower than your rent payment. It illustrates that if you continue to rent the extra cost of renting would, in effect, use up your cash on hand.

It can take into account all sorts of fees, mortgage fees, closing fees, annual property taxes, GST on a new home, maintenance/condo fees. The home appreciation rate can be varied as well as the future sales commission. For the investment used to compare with, one can vary the investment return and the inflation rate.

Just make sure that if you include utilities in the “maintenance/condo fees” field that you also include it in the “monthly rent payment” field. The only reason to put utilities in at all is if the amount is at all different in the rental property vs. the owned property.

Note also that there is a bug in their charting which causes the chart to not extend past the 10-year time frame. Scroll down to view the detailed numbers for all years.

Just plugged in some values using the rent that I am paying now ($1050) and the price of a comparable apartment in Vancouver. A quick scan on shows that I’d have to spend at minimum $280,000 for a place of comparable size, with around $200 in condo fees. I haven’t even factored in location (and the location we currently are renting in is hard to beat, so $280,000 is very conservative). I assumed a 0%-down mortgage and the default of 3% annual appreciation on the home. Most of the other things I left at their defaults (except inflation which I lowered to 3% from the default of 4%). For my case, the value of the investment (initial cash-on-hand + monthly contribution of (mortgage payment minus rent) invested at 7% after-tax return) was $830,407 after 25 years. The home equity after 25 years was only $556,903. This assumes a monthly investment of $1300 (mortgage payment minus rent). This is almost what we are contributing monthly right now (we should be up to this level in 2006). So right now, renting is clearly the best option for us.

Yield curve inverts

The yield curve on US Treasury yields inverted today, as reported in this Globe & Mail article an event which has frequently signalled the beginning of a recession:

“Here is the historical record — we have endured eight Fed tightening cycles in the past three decades: the Fed has inverted the curve on five of those occasions, and out of those five Fed-induced inversions, the economy slipped into recession a year later all five times,” said David Rosenberg, North American economist for Merrill Lynch & Co. Inc.

The Big Picture quotes Alan Greenspan, who says “it’s different this time”:

Fed Chairman Alan Greenspan has noted that “its [sic] different this time.” He has challenged the view that “inversion signals economic trouble, pointing out that the shape of the curve is less predictive than it once was.” [emphasis theirs]

Others agree:

“[The inverted yield] has been taken as a negative omen, but I think you have to be cautious in today’s circumstances,” said Andrew Busch, global foreign exchange strategist for BMO Nesbitt Burns Inc. The yield has inverted at relatively low levels of interest rates and not the normally high levels of rates when the Fed tightens to subdue inflation, he said.


During the past 20 years, 10-year yields have exceeded two-year yields by an average of almost one percentage point, according to Bloomberg.

“This clearly suggests we are very close to the end of the tightening cycle … and it is not an indication of a recession,” said Michael Rottman, a strategist at Germany’s Hypovereinsbank.

S&P TSX 60 Equal-Weighted Index

For those who don’t already know, I am not a fan of market-cap-weighted indexes like all the S&P Canadian indexes and the US S&P 500. In the US S&P has the S&P Equal-Weight Index and there is an ETF that tracks it, the Rydex S&P Equal Weight ETF. In Canada there is no such index provided by S&P and no ETF. I knew that there was no Canadian ETF in existence that was equal-weighted but I thought that there must be at some theory, data-mining, or an informal index out there.

Yesterday, I finally found something: an equal-weighted index for the S&P TSX 60. After what seemed like hours digging through Google search results and varying the keywords I gave to Google, I finally found a company called Shaunessy Investment Counsel in Alberta that has formed such an index which they invest in using their clients’ money. The performance as of September 30, 2005 is shown here, where they also mention that the index is “equal weighted, re-balanced quarterly.” An older Shaunessy news article I found on Google compared this index to the S&P TSX 60 Index and shows excellent results, which I will reproduce below:

Canadian Large Cap versus Index Comparison
Rates of Return Ended June 30 2004

Q2 04 Year to Date One Year Three Years Five Years
TSX 60 TRI -0.1% 4.1% 22.1% 4.1% 4.7%
SIC 60 EWI* 2.5% 4.3% 26.2% 8.9% 9.9%
Mercer Median 0.9% 5.4% 25.3% 6.9% 10.0%
Source: RBC Capital Markets, Mercer Investment Consulting, Shaunessy Investment Counsel (SIC)
* Price Index only constructed by Shaunessy Investment Counsel

The “Mercer Median” is the median performance of a whole bunch of mutual funds, from the “Mercer Institutional Pooled Funds report.” They also note that “the EWI is a price index and does not include dividends which would add at least another 1-1.5% to total returns.” The results are even more impressive if you take into account the dividends paid.

Don’t get your hopes up about buying a piece of the index from Shaunessey. They require a $2 million minimum to be a client. To just buy the index and not have a “fully-managed” portfolio with them, you will need to invest $6,666,666 million (0.15% as percent of assets, minimum fee is $10,000). More evidence that the more money one has, the more access one has to better investment advice and services.

It is possible to create your own S&P TSX 60 Equal-Weighted Index (EWI), however, paying $50 commission for each stock would become prohibitively expensive. To keep your commissions to 1% of your initial purchase you would need $300,000 total assets. And rebalancing every quarter would also become very expensive.

Another way to have an approximation to Shaunessey’s index would be to buy certain amounts of sector ETFs and rebalance the allocation of each ETF regularly; however, within each sector ETF the stocks would still be market-cap-weighted.

The best way I can think of to create your own S&P TSX 60 EWI is to use Shareowner . It looks like you could buy 60 stocks for $36 using Shareowner and have your dividends reinvested for free.

New PC Financial Accounts

Finally went and set up a PC Financial account last Sunday. This involved finding the nearest Great Canadian Superstore (equivalent of Loblaws/Zehrs for those of you in Ontario) which isn’t so nearby to where we are. It was all pretty painless. We did it on a Sunday at 5:30pm and the lady who helped us out was really nice, and even stayed a bit after their closing time of 6pm to help finish everything up. I really like the fact that they are open on weekends at all the locations in the Vancouver area that I looked at. They are also open late on Thursday and Friday night. I don’t expect to go into the PC Financial “Pavilion” much, but at least the hours are a lot better than the big banks. We set up two no-fee chequing accounts (I’ll describe in a future post why I like 2 chequing accounts). This gives us unlimited Interac transactions, transfers, bill payments, direct deposits, and withdrawals at any CIBC or PC Financial ATM. We are getting free cheques mailed to us for both accounts. I’ve called the 1-866 number twice so far and both times the people I talked to were very friendly and I never waited more than 2 minutes to get through to someone. We don’t need the PC high-interest savings accounts because we use ING Direct (my wife and I can each have up to 4 Canadian dollar accounts at ING making it easy to save up for many different “things” at once) and we can shift money between our ING Direct accounts and either PC Financial chequing account as much as we want now. As soon as we get the new PC cheques in the mail, we just have to send them both off to ING and the chequing accounts will be linked to ING.

The only thing left for us to do is to switch our direct deposits and pre-authorized bill payments to PC from BMO. I’ll most likely arrange this to all happen around the same time, keeping at least some money in each of BMO and PC, just in case the timing is off a bit on the switch.

Bill Miller’s Winning Streak

With just over a week to go in 2005, Bill Miller’s Value Trust fund looks set to beat the S&P for the 15th consecutive year.

Certainly, Mr. Miller’s 14-year winning streak is impressive, especially in the context of professional fund management, an industry in which the average fund manager typically underperforms broad market indices like the S&P 500. Mutual fund screeners (e.g., Yahoo’s, which takes data from Morningstar) show about 11,000 stock funds. Noting that 11,000 sits between 2-to-the-13th power (8,182) and 2-to-the-14th power (16,384), we should expect by pure probability alone to find about one fund manager in 11,000 who has a winning streak of 13 or 14 years (similar to performing 11,000 trials of 13 or 14 coin tosses and finding one streak of all heads). From this perspective, Mr. Miller’s performance is still exceptional (just as a string of all heads is exceptional), but we should not be surprised to find an exceptional performer among the many thousands of mutual fund managers out there. In other words, while Mr. Miller does appear to have a “golden touch,” he is not necessarily a living incarnation of King Midas.

HBC Credit Card – don’t bother

Just bought a Christmas gift for someone on Saturday at The Bay. The lady at the counter said that I could earn 50% more HBC Rewards points if I used my HBC Credit Card. I said something like “no, thanks anyways, but I’d prefer to pay with the cash I have in my wallet, rather than pay off a credit card bill a few months from now.” Even it it means getting a few measly rewards points. The item I was purchasing was $40 (50 rewards points per dollar means 2,000 rewards points). If I paid with the credit card, I would get an extra 1,000 points. A quick check on the HBC website reveals just how much these points are worth. Taking the average points value of the, Blockbuster, and Starbucks gift cards that are redeemable using HBC rewards points, we find that 1,000 points is worth about $0.10. That is comparable to about 1 Air Mile (through the Air Miles rewards program).

So basically what the lady was offering me was an opportunity to save $0.10. This was easy to refuse. But she was persistent. She said that I could charge it to my HBC Credit Card and then she could immediately pay off the balance on the credit card right then and there using cash. I threw up my hands; what the hell, sure, charge it. She charged it and then paid off the balance. It took about 30 more seconds to do these two steps rather than just one, but that was insignificant compared to amount of time it took her to “gift wrap” the item.

Today I saw a similar item at a different store. A little bit better product, for $5 more. I thought about returning the item to The Bay to get this new item, but would I be able to get my cash back? Since I made the purchase with my HBC Credit Card, if I returned the item I would probably be given a credit on my credit card rather than a cash refund. Probably the best I could do would be to get a gift card or store credti. I would owe them some future business one way or another.

I don’t even know why I have this stupid HBC credit card. I think I got it a few years ago because I was offered 10% off my purchase that day if I signed up for one. It was a $600 purchase, so I guess it made some sense as I saved $60. But how many people save that $60, then end up spending $60 more over the course of the next year than they would have, had they used cash.

Just tore up my HBC Credit Card right now. Ripped into four pieces. It was actually good timing because I just got a PC Financial account and I need an empty slot in my wallet.

Teaching kids about investing

Interesting story here about someone who has set up a stock account for his 9-year old daughter. The account is actually in her name but controlled by the parent. The original post is here, “My 9 Year Old’s First Investing Lesson” and the update is here, “Update on Sharebuilder Account.” It’s too bad that so many parents don’t teach their kids about investing and many parents don’t even teach their children about personal finance, often controlling their chequing accounts well into their 20s (I can give first-hand accounts of this). I think it’s great that this kid has an account opened up where she can buy stock in her own name. I actually hope that her stocks do very, very badly! Losing money in the stock market is a very important lesson that ever person should learn as as young an age as possible! I didn’t learn this lesson until my early 20s; however, I wish I had learned even earlier.

She owns $28 in Apple stock and $21 in Chesapeake Oil stock (as of last weekend). The only thing I found surprising was that they purchased such low amounts. The commission was $4 per trade. So Apple’s stock has to go up 14% just to break even, and 19% for Chesapeake Oil. Apparently “if she does all the chores we have on the list she stands to make $30 a month.” I would have advised her to be patient, wait a few months until she has enough money to invest such that the commissions become a very insignificant percentage of the stock purchase.

This reminds me of when I first invested in mutual funds in around 1996-1997. I invested my own money that I made through my own jobs, but my dad matched my contributions, much like an employer might. This is another great way to encourage kids to save and teach them about investing. has some other tips for helping children learn about finances.

Another interesting aspect of these articles is this site. The explains:

The great thing about is you can purchase partial stocks or ETF (Electronic Transfer Fund) of any company they carry. This means that I can fund my account with $30 and buy $26 worth of Apple stock. ($30 minus $4 transaction fee per trade) even though I may not have the funds to buy a full share.

You also have the option of setting up monthly automatic investments. For example I can set up my account so that every 2nd Tuesday I purchase $30 worth of Apple, or I can set it up to purchase $10 worth of Apple, $10 worth of Home Depot, $15 worth of Sirius etc. Keep in mind there is a $4 fee for each stock you buy. That is the fee under the plan we have which is the Basic Account, some account have lower fees.

This is certainly an excellent way to invest in stocks using smaller amounts of money. It makes building a diversified group of stocks (20-30) much easier for the small investor. I haven’t yet looked into whether or not Canadians can open an account at I know that a long time ago when I set up an account at a US based discount online trader I had to send in some extra IRS forms, but other than that anyone could set up an account (in US dollars of course).

Asset Allocation and Rebalancing

Interesting example of asset allocation and rebalancing in this article, “What the Heck is Asset Allocation.”

He illustrates two cases (over 2 years):

  • Case 1: Investing $100,000 in 4 different mutual funds (large-cap, mid-cap, small-cap, and bonds), 25% each. Sell the worst performer after the first year and buy the best performer. Hold for one more year. This leaves you with $96,535 after the 2 year period.
  • Case 2: Same as above, but rebalancing the funds after year 1, so that each fund was again 25% of the portfolio. This case leaves you with $103,170.

He also could have shown the case where you just buy & hold for the 2 years:

  • Case 3: Using the returns provided in the article, the final value for each fund would be FV=PV \times (1+i_1)(1+i_2) for each fund, where i_1 is the return of a fund in year 1 and i_2 is the return of a fund in year 2. You would end up with $102,660

It just happens to work out this way because of the data he used. Had he rigged his data so that the Bond fund continued to do poorly in year 2 and the small cap continued to outperform the others, then our results would be different. But in my opinion if you looked at past market data you would find that case 2 above is invariably the best thing to do.