Monday, June 27, 2022

A Failure to Understand Rebalancing

Recently, the Stingy Investor pointed to an article whose title caught my eye: The Academic Failure to Understand Rebalancing, written by mathematician and economist Michael Edesess.  He claims that academics get portfolio rebalancing all wrong, and that there’s more money to be made by not rebalancing.  Fortunately, his arguments are clear enough that it’s easy to see where his reasoning goes wrong.

Edesess’ argument

Edesess makes his case against portfolio rebalancing based on a simple hypothetical investment: either your money doubles or gets cut in half based on a coin flip.  If you let a dollar ride through 20 iterations of this investment, it could get cut in half as many as 20 times, or it could double as many as 20 times.  If you get exactly 10 heads and 10 tails, the doublings and halvings cancel and you’ll be left with just your original dollar.

The optimum way to use this investment based on the mathematics behind rebalancing and the Kelly criterion is to wager 50 cents and hold back the other 50 cents.  So, after a single coin flip, you’ll either gain 50 cents or lose 25 cents.  After 20 flips of wagering half your money each time, if you get 10 heads and 10 tails, you’ll be left with $3.25.  This is a big improvement over just getting back your original dollar when you bet the whole amount on each flip in this 10 heads and 10 tails scenario.  This is the advantage rebalancing gives you.

However, Edesess digs further.  If you wager everything each flip and get 11 good flips and 9 bad flips, you’ll have $4, and with the reverse outcome you’ll have 25 cents.  Either you gain $3 or lose only 75 cents.  At 12 good flips vs. 12 bad flips, the difference grows further to gaining $15 or losing 94 cents.  We see that the upside is substantially larger than the downside.

Let’s refer to one set of 20 flips starting with one dollar as a “game.”  We could think of playing this game multiple times, each time starting by wagering a single dollar.  Edesess calculates that “if you were to play the game 1,001 times, you would end up with $87,000 with the 100% buy-and-hold strategy,”  “but only $11,000 with the rebalancing strategy.”

The problem with this reasoning

Edesess’ calculations are correct.  If you play this game thousands of times, you’re virtually certain to come out far ahead by letting your money ride instead of risking only half on each flip.  However, this is only true if you start each game with a fresh dollar.

In the real world, we’re not gambling single dollars; we’re investing an entire portfolio.  If one iteration of the game goes badly, there is no reset button that allows you to restore your whole portfolio so you can try again in a second iteration of the game.

Edesess fundamentally misunderstands the nature of rebalancing and the Kelly criterion.  They don’t apply to how you handle single dollars or even a subset of your portfolio; they apply to how you handle your entire portfolio.  If you have a bad outcome and lose most of your portfolio, the damage is permanent; you don’t get to try again.  Unless you’re a sociopath who invests other people's money in insanely risky ways hoping to collect your slice from a big win, you don’t get to find more investment suckers to try again if the first game goes badly.

Warren Buffett has said “to succeed you must first survive.”  This applies here.  The main purpose of rebalancing is to control risk.  It may be true that several coin flips could turn your $100,000 portfolio into tens of millions, but it could also turn it into less than $1000.  The rebalancing path is much smarter; it will give you more predictable growth and make a complete blowup much less likely.  It turns out that the academics understand rebalancing just fine; it’s Edesess who is having trouble.

Friday, June 17, 2022

Short Takes: Dividend Irrelevance, Housing Bears, and more

A popular type of investing is factor investing.  This means seeking out companies with attributes that performed strongly in the past, such as small caps (low total market capitalization) and value stocks (low price-to-earnings ratios).  I can’t say I’ve studied this area extensively, but one observation I’ve made is that these factors always seem to disappoint investors after they become popular.

It’s hard to figure out exactly why factors seem to disappoint, but I’m not inclined to pay the extra costs to pursue factor investing beyond my current allocation to stocks that are both small caps and value stocks.  Several years ago this combination was my best guess of the factor stocks most likely to outperform.  I’m still not inclined to try others.

Here is how I think about whether someone is ready for DIY investing:

What You Need to Know Before Investing in All-In-One ETFs

Here are some short takes and some weekend reading:

Ben Felix
explains why dividends are irrelevant.  His extensive references to peer-reviewed literature make his arguments tough for dividend lovers to refute, but they can always go with “ya, well, I like Fortis.”

John Robertson
hasn’t found it easy being a housing bear over the years, but now that prices are falling, he looks at what type of buyer would enter the market at different reduced price levels.

Justin Bender examines the merits of bond ETFs vs. GIC ladders.  Investors who want to reduce duration to reduce interest rate risk can consider an ETF of short-term bonds as well.  The way I look at the bond duration choice is whether I’d be happy to hold a 10+ year bond to maturity at current interest rates.  Interest rates have improved lately, but I still prefer to stick with short duration for now.

Thursday, June 9, 2022

What You Need to Know Before Investing in All-In-One ETFs

I get a lot of questions from family and friends about investing.  In most cases, these people see the investment world as dark and scary; no matter what advice they get, they’re likely to ask “Is it safe?”  They are looking for an easy and safe way to invest their money.  These people are often easy targets for high-cost, zero-advice financial companies with their own sales force (called advisors), such as the big banks and certain large companies with offices in many strip malls.  An advisor just has to tell these potential clients that everything will be alright and they’ll be relieved to hand their money over.

A subset of inexperienced investors could properly handle investing in an all-in-one Exchange-Traded Fund (ETF) if they learned a few basic things.  This article is my attempt to put these things together in one place.

Index Investing

Most people have heard of one or more of the Dow, S&P 500, or the TSX.  These are called indexes.  They are a measure of the price level of a set of stocks.  So, when we hear that the Dow or TSX was up 100 points today, that means that the average price level of the stocks that make up the index was up.

It’s possible to invest in funds that hold all the stocks in an index.  In fact, there are funds that hold almost all the stocks in the whole world.  There are other funds that hold all the bonds in an index.  There are even funds that hold all the stocks and all the bonds.  These are called all-in-one funds.

Most people know they know little about picking stocks.  They hear others confidently talking about Shopify, Google, and Apple, but it all sounds mysterious and scary.  I can dispel the mystery part.  Nobody knows what will happen to individual stocks.  Bold claims about the future of a stock are about as reliable as books about future lottery numbers.  However, the scary part is real.  If you own just one stock or a few stocks, you can lose a lot of money.

When you own all the stocks and all the bonds, it’s called index investing.  This approach to investing has a number of advantages.

Investment Analysis

Investors who pick their own stocks need to pore over business information constantly to pick their stocks and then stay on top of information to see whether they ought to sell them.  When you own all the stocks and all the bonds, there’s nothing to analyze or track on a frequent basis.


Owning individual stocks is risky.  Any one stock can go to zero.  Owning all stocks has its risks as well, but this risk is reduced.  The collective stocks of the whole world go up and down, occasionally down by a lot, but they have always recovered.  We can’t predict when they’ll drop, so timing the market isn’t possible to do reliably.  It’s best to invest money you won’t need for several years and not worry about the market’s ups and downs.

To control risk further, you can invest in funds that include both stocks and bonds.  Bonds give lower returns, but they’re less risky than stocks.  Taking Vanguard Canada’s Exchange-Traded Funds (ETFs) as an example, you can choose from a full range of mixes between stocks and bonds:

ETF Symbol 
    Stock/Bond % 
      VEQT           100/0
      VGRO           80/20
      VBAL           60/40
      VCNS           40/60
      VCIP           20/80


Sadly, many unsophisticated investors who work with financial advisors don’t understand that they pay substantial fees.  These investors typically own mutual funds, and the advisor and fund company help themselves to investor money within these funds.  There is no such thing as an advisor who isn’t paid from investor funds.

It’s common for mutual fund investors to pay annual fees of 2.2% or higher.  This may not sound like much, but this isn’t a fee on your gains; it’s a fee on your whole holdings, and it’s charged every year.  Over 25 years, an annual 2.2% fee builds to consume 42% of your savings.  This is so bad that many people simply can’t believe it.

With Vanguard’s all-in-one ETFs, the annual costs are about 0.25%, which builds to only 6% over 25 years.  Giving up 6 cents on each of your hard-earned dollars may not seem great, but it’s a far cry from 42 cents on the dollar.

Closet Index Funds

Can’t we just find a mutual fund run by a smart guy who can do better than index investing?  Sadly, no, we can’t.  Every year, experts analyze mutual fund results, and every year, they come up with the same answer: most mutual funds do worse than index investing.  A few do better for a while, but sooner or later, they stumble and fall behind index investing.  They simply can’t overcome their high fees for long.  We can’t predict in advance which funds will beat the index in a given year, so jumping from fund to fund is a losing game.

But things get worse.  A great many mutual funds aren’t even trying to do better than index investing.  They are called closet index funds.  They hold portfolios that look a lot like the indexes, but charge high fees anyway.  They focus more on selling their funds to investors than they focus on investment performance.  They hope their investors don’t notice that they’re not really doing much.

Canadians who invest at big bank branches and strip mall offices of big investment companies typically own closet index funds.  If you take the trouble to look through the holdings of their mutual funds, you see a set of stocks and bonds that isn’t much different from Vanguard’s all-in-one ETFs.  The difference is the cost.

Fear, Uncertainty, and Doubt

If index investing is so superior to the typical mutual fund, why doesn’t everyone switch to indexing?  The answer is that there are many people who make their living from the high-fee model.  Their salaries depend on extracting high fees from your savings.

Most advisors in big bank branches and in the strip mall offices of big retail investment companies have a list of talking points to scare people away from index investing.  But the truth is that the only scary thing about indexing is the threat to their salaries.

Going On Your Own

If you chose to invest in Vanguard Canada’s VBAL, which is 60% stocks and 40% bonds, you’re probably going to own close to the same stocks and bonds an advisor at a bank branch or strip mall would recommend.  The differences are that lower fees would leave you with higher returns, but you’d have to open your own investment accounts and make some trades on your own instead of having an advisor tell you everything will be fine.

So, this would involve choosing a discount broker, opening an RRSP and a TFSA and possibly other accounts, adding some money, and performing trades to buy an all-in-one ETF with money you won’t need for several years.  It’s best not to invest in stocks with money you may need soon, such as an emergency fund.  

Handling your own savings this way can be scary at first, and it isn’t for everyone.  The main challenges are getting started with making trades with large sums of money, avoiding selling out when the stock market goes down and you’re nervous, and avoiding changing your plan when something enticing comes along like day-trading, stock options, or cryptocurrencies.

Making the Switch

Getting started with investing on your own using all-in-one ETFs is easier for the beginning investor than it is for someone already working with an advisor.  The good news is that you don’t have to make the switch by talking to your advisor.  The process begins with opening new accounts at a discount brokerage and filling out forms to move your money from the accounts controlled by your advisor.  Your advisor is likely to notice and might try to talk you out of it, but you’re not obligated to work with your advisor when making the switch.

One approach that might make the process easier is to open new discount brokerage accounts and only add small amounts of money first.  After you’re more comfortable with trading and everything else at the discount brokerage, you can then fill out the paperwork to transfer the rest of your assets over to the new accounts.

Not For Everyone

Investing on your own isn’t for everyone.  However, all-in-one ETFs make it as easy as it can be to invest on your own.  As long as you can avoid the mistakes that come with fear and greed, you stand to save substantial investment fees over the decades.

Friday, June 3, 2022

Short Takes: Finding a Good Life, DTC for Type 1 Diabetics, and more

I was reminded recently of the paper The Misguided Beliefs of Financial Advisors whose abstract begins “A common view of retail finance is that conflicts of interest contribute to the high cost of advice. Within a large sample of Canadian financial advisors and their clients, however, we show that advisors typically invest personally just as they advise their clients.”

I didn’t find this surprising.  Retail financial advisors are like workers in a burger chain.  I wouldn’t expect these advisors to understand the conflicts of interest in their work any more than I’d expect workers in a burger chain to understand the methods the chains use to draw customers into eating large amounts of unhealthy food.  It’s hardly surprising that so many advisors understand little about investing well, and that they run their own portfolios poorly.

However, this doesn’t mean the conflicts of interest don’t exist.  It is those who run organizations that employ, train, and design pay structures for financial advisors who have the conflicts of interest.  The extra layers between the clients and those who understand the conflicts make the situation worse.  It’s easier to tell someone else to do bad things to people than it is to do bad things to people yourself.  It’s even easier at higher levels to yell at underlings to create more profits and let them tell the clueless advisors at the bottom layer to do bad things to clients.

Of course, not all advisors in this sort of environment are clueless, and many manage to escape to run practices where they are able to treat their clients better.  Unfortunately, this type of advisor usually either only takes clients with a lot of money or charges fixed amounts that are large enough to scare off clients with modest savings.

Here are my posts for the past two weeks:

Taking CPP and OAS Early to Invest

Why Do So Many Financial Advisors Recommend Taking CPP Early?

Measuring Rebalancing Profits and Losses

Here are some short takes and some weekend reading:

Benjamin Felix has an interesting paper called Finding and Funding a Good Life.  He looks at the research on happiness and how to achieve a good life.   One of the reflective questions he poses is one I’ve thought about a lot: “Are there unpleasant tasks in your life that you could outsource?”  I often decide that it’s easier to clean my house myself than to become an employer, but maybe that’s just an excuse for not taking action.  Another interesting point is that “when people are told what to do they are more likely to rebel against the instruction to regain their sense of freedom.”  I think that explains why I lost any desire I used to have for working for a boss, no matter how well I was treated.

Big Cajun Man
reports that Canadians with Type 1 Diabetes should have an easier time getting the Disability Tax Credit (DTC) after recent changes.

Kerry Taylor discusses how to raise your credit score with licensed insolvency trustee Doug Hoyes.  Among the many good points Doug makes, he says that it’s your credit history over time that matters more than a snapshot of your credit score.

Thursday, June 2, 2022

Measuring Rebalancing Profits and Losses

Investors often seek to maintain fixed percentage allocations to the various components of their portfolios.  This can be as simple as just choosing allocations to stocks and bonds, or it can include target percentages for domestic and foreign stocks and many other sub-categories of investments.  Portfolio components will drift away from their target percentages over time, requiring investors to perform trades to rebalance back to the target percentages.  A natural question is whether rebalancing produces profits, and if so, how much.

A long-time reader, Dan, made the following request:

I have a topic request. On the subject of portfolio rebalancing, I have read your many posts and whitepaper [see Calculating My Retirement Glidepath]. I have actually implemented something similar (but not exactly the same) myself.  I saw in one blog post, cannot find where, that you said something to the effect of “my rebalancing trades last year produced a profit”.

My topic request is, could you detail specifically, your method for tracking & determining profitability of those rebalancing trades?

It’s true that the rebalancing I did through the brief but fairly deep stock market decline at the start of the pandemic produced nontrivial profits for me.  These profits came from purely mechanical trades I made when my spreadsheet declared my portfolio to be too far out of balance.

However, I don’t consider profit to be the primary purpose of rebalancing.  I do it to maintain a sensible risk level for my portfolio given my age and the fact that I’m retired.  In fact, I expect to lose money over the decades from rebalancing, as I’ll explain before I get to the details of how investors can measure the profits and losses from rebalancing.  

There are two different effects that can occur as the prices of portfolio components vary.  One effect creates profits, and the other creates losses.

Rebalancing profits

Rebalancing is profitable when one asset, say U.S. stocks, rises faster than another asset, say Canadian stocks, and later the Canadian stocks catch up.  By selling some U.S. stocks to buy Canadian stocks just before Canadian stocks begin to perform better, the rebalanced portfolio outperforms just holding through the whole period.

In general, when two assets grow at roughly the same long-term rate, but the lead seesaws back and forth between them, rebalancing is profitable.

Rebalancing losses

Rebalancing gives losses when one asset, say stocks, consistently outperforms another asset, say bonds.  In this case, rebalancing usually involves periodically selling some stocks to buy bonds, and the rebalanced portfolio won’t perform as well compared to buy-and-hold.

Of course, there are times when bonds outperform stocks by a wide margin, mainly when the stock market crashes.  So, there will be periods when rebalancing will produce short-term profits to offset the long-term rebalancing losses from mainly selling stocks to buy bonds.

I expect the rebalancing between different classes of stocks to produce small profits, and to occasionally get rebalancing profits from rebalancing between stocks and bonds, but I expect the long-term losses from rebalancing from stocks to bonds to dominate.

So, why rebalance if we expect losses?

There is no guarantee that rebalancing will produce losses on balance.  If there is an extremely large drop in stock prices some time in the future, it’s possible that rebalancing will produce net profits.  By maintaining a fixed percentage in bonds instead of letting the bond percentage dwindle, the investor who rebalances will be spared somewhat when stocks crater.

So, even though I expect to lose out over the decades from rebalancing because I’m optimistic about the future of stocks, it’s possible that rebalancing will save me at a terrible time for stocks.  This is the main idea behind the risk-control value of rebalancing.  I’d rather get some protection if future returns disappoint than try to become even richer in case the future is very bright.

Calculating rebalancing profits and losses

Back in 2020, my spreadsheet told me to rebalance several times as stocks dropped sharply and then rebounded quickly.  Each time I rebalanced, I took a snapshot of my portfolio holdings.  Later, I looked at the snapshot from just before the first rebalancing, and calculated what my portfolio’s value would have been if I had never rebalanced through the pandemic.  The difference between this value and the actual portfolio value I ended up with as a result of rebalancing gave me my net rebalancing profit.  This difference proved to be larger than I expected.

In general, any discussion of profit and loss comes from comparing two different courses of action.  In this case, it comes from comparing an actual portfolio with rebalancing to a hypothetical portfolio without any rebalancing over a particular period of time.

I don’t do these calculations often.  I’m satisfied that rebalancing makes sense for me for risk reasons.  I’m not waiting for the outcome of an experiment to see whether rebalancing will be profitable over the long run.  I got interested in rebalancing through the pandemic and did some calculations out of curiosity.

A more serious approach

I don’t think it’s important to track rebalancing profits and losses, but I can understand that some technically-minded investors may be interested.  So, let’s dig into how one might implement tracking rebalancing profits and losses.

The biggest complication comes from portfolio inflows and outflows.  In addition to running your actual portfolio and deciding which assets to buy or sell each time you add or withdraw money, you’d have to make these decisions for a hypothetical non-rebalanced portfolio.  An easier task is to take a snapshot of your portfolio before each rebalancing, and to track inflows and outflows.  This permits you to run a hypothetical non-rebalanced portfolio over any period of time and then compare its results to your actual portfolio’s results.

If the hypothetical portfolio isn’t supposed to have rebalancing, it’s not obvious what assets you should buy or sell when adding or withdrawing money.  The choices you make with the hypothetical portfolio could make a big difference in the measured values of rebalancing profit and loss.

When I looked at my rebalancing gains through the pandemic, I didn’t have any inflows and had only small outflows, so it didn’t make a lot of difference what assets I chose to sell for the outflows.  Over longer periods, the choice of what assets to buy or sell can make a big difference in the calculated rebalancing gains and losses.

Here are some possibilities for how to run the hypothetical portfolio:

  1. Add or withdraw from each asset class in proportion to its percentage of the portfolio.  This leaves asset class percentages unchanged.  This is what I did when I calculated my rebalancing gains through the pandemic.

  2. Add or withdraw from asset classes in a way that takes them closer to their target percentages.  This is a form of rebalancing with cash flows.  With this approach, what you’re measuring is the profits or losses from the “extra” rebalancing in your real portfolio that becomes necessary when asset classes diverge strongly enough that they can’t be kept in balance with cash flows.

  3. Perform cash flows the same way you do them for your real portfolio, and then rebalance on a fixed time schedule.  For those who use threshold rebalancing, this method compares the results from threshold rebalancing to the results of periodic rebalancing.

  4. Use one of the other three methods and reset the hypothetical portfolio to the real portfolio periodically (perhaps annually) after calculating the period’s rebalancing gain or loss.  This will give very different results from letting the hypothetical portfolio diverge from the real portfolio over many years.

No doubt there are many other possible approaches to running the hypothetical portfolio.  


There are so many choices for how to proceed to measure the value of rebalancing that whatever method you choose would be a personal customized measure of something that may or may not represent the long-term value of rebalancing.  For now, I’ll just compute short-term rebalancing gains or losses when the mood strikes.