Leaving Money on the Table

I spent Sunday helping out my brother in organizing his finances. He joined a major Canadian corporation a little over 11 months ago, and is approaching the point of vesting for his defined contribution pension plan. Within this context, vesting means that his employer will start matching any pension contributions he makes, subject to certain rules and maximums. This is a very common investment vehicle available to Canadians: many companies do not have Defined Benefit (DB) pension plans anymore, opting to provide Defined Contribution (DC) pensions instead. As an incentive for employees to save towards retirement, companies that offer DC plans often provide a “match”. A “match” is a provision wherein the employer will match any contributions an employee makes, subject to certain conditions. For example, one company I know of offers this match structure:

  • Match 100% for the first 2% of contributions
  • Match 50% for the next 2% of contributions
  • Match 25% for the next 2% contributions

In the above, the “2% of contributions” means 2% of the employee’s salary. A more concrete example would be as follows: Assume an individual makes $40,000/year, and wishes to maximize her employer match. The numbers would add up like so:

Employee contribution %

Employee contribution $

Employer match %

Employer match $













As you can see above, the employee contributed $2,400 of their salary, but the employer contributed $1,400. This means that the employee received an instant 58% return for doing nothing! This is quite literally free money: your employer is giving you an instant top-up as incentive to save for your own retirement. Let’s take the example a little further: assume someone starts working at age 30, works for 35 years to age 65, and maximizes their contributions every year. Moreover, assume they get a 1% raise every year. If we plot this example over the duration of the person’s employment, the difference—while still a 58% gain—is even more pronounced.

By the end of 35 years, the employee would have contributed $103,000 on their own, if they had contributed 6% of their salary. But, thanks to the employer match, their effective contribution was $164,000! They have received an additional $61,000 all for doing nothing.

However, when an individual contributes to a plan such as the above, they don’t just save the money; they typically invest in mutual funds which are made available to them through the DC plan. We can modify the above graph to show the theoretical balance at retirement, assuming 2%, 4%, and 6% returns on the investments.

Again, there was a 58% gain when you compare the Employee only to the Employee and Employer Match:

Employee Only

Employee + Employer

2% returns



4% returns



6% returns



The astonishing thing is that many people don’t take advantage of the employer match that is offered in their pension plans (here is an interesting read from the Financial Post). This means that there are people who are literally giving up free money. Often some people say that the reason they don’t do this is that they can’t afford to contribute money to their company sponsored pension plan, because that means that they will have less money paycheque to paycheque. To that, I have a couple of comments:

  • If you are truly living paycheque to paycheque, then there are more systematic issues at hand that you need to look at; you really need to sit down and plan out a proper budget for yourself.
  • You really can’t afford not to take advantage of a pension plan: if you don’t save now, then you will ultimately have to work longer later.
  • Contributing to your pension plan is a tax-advantageous activity: meaning that if you wish to contribute $500 to your DC pension plan, your effective contribution is lower because your taxes will be lower; I will be writing about this in a future blog post.

So there really is no reason not to contribute. Imagine this: you are walking home and there is a fork in the road to go around a building. Both roads from the fork lead you to the same place at the opposite end of the building. From your vantage point, you can see a $20.00 bill lying on the ground up ahead on the road to the right, and on the road to the left, you can’t see any money lying around. Would you take the fork to the left? Of course not, you would be foolishly ignoring money that was just lying around. Your pension is the same: don’t take the road of no contributions, but take full advantage of the free money your employer is willing to give you.

Onwards and upwards!

A Risk Free Rate for Retail Investors

The risk free rate is one of the key inputs to measuring your portfolio performance. It is a fundamental element of two key measures, those being the CAPM (Capital Asset Pricing Model), and the Sharpe Ratio. The CAPM is a basic measurement which is central to many aspects of present day portfolio theory, and states that the expected return on a portfolio (or equity) is equal to the risk free rate, plus some variance against the excess return of the market over the risk free rate:

\bar{r_e} = r_f + \beta_e(\bar{r_m} - r_f)

Where \bar{r_e} is the expected return on our equity (or portfolio), r_f is the risk free rate, \bar{r_m} is the return of the market, and \beta_e is the beta of our equity (or portfolio). A deep dive of CAPM is beyond the scope of this blog post, but for more information you can check out Investopedia.

Another measure is the Sharpe Ratio:

s_e = \frac{\bar{r_e} - r_f}{\sigma_e}

Where s_e is the Sharpe Ratio of the equity (or portfolio), \bar{r_e} is the expected return of the equity (or portfolio), \sigma_e is the standard deviation of the equity (or portfolio) returns, and r_f is the risk free rate of return, as with our CAPM above.

Both the CAPM and the Sharpe Ratio are great indicators of how well you, as an investor, are performing. Of the variables above, the expected return and standard deviation of returns on your own portfolio (\bar{r_e} and \sigma_e respectively) are easy enough to calculate, since you should have the historical returns of your portfolio already. The expected return on the market in the CAPM is easy enough to proxy—you can easily use the expected return of an ETF such as the iShares XIC—but the risk free rate takes a little more effort.

Conventionally, theory dictates that we use a truly risk-free asset such as a treasury bill yield (Canadian T-Bills or US T-Bills for North America), since one would hope that treasury bills issued by Canadian or American governments are relatively safe. However, as a retail investor, this presents some challenges:

  • T-bills are not necessarily readily available to us in the conventional sense. It is pretty difficult for us to go out to our investment brokerage and ask to buy a t-bill. The reasons for this are varied, but for the most part it boils down to availability, and minimum purchase required. E.g. the minimum t-bill purchase may be $5,000 or $100,000!
  • T-bills, by definition, mature in less than one year. To position this in practical terms for the retail investor, we would have to buy a new t-bill every year for the duration of our investment, which means we would have to build a yield-curve based on the expected future prices of those future t-bills. This simply isn’t practical for our needs.

Ignoring the theoretical risk-free instrument, there are a number of practical options which are available to retail investors, including real bonds, bond funds, GICs, and high interest savings accounts.

Real Bonds

Real bonds are just as they sound: bonds that you would purchase from your brokerage, backed by governments or companies. Theoretically, since real bonds are backed for corporations or smaller governments (e.g. municipal governments, provincial governments), there is still a degree of risk involved in the backing body defaulting on the bond. The inherent default risk aside, the key reasons I do not consider real bonds a suitable substitute are:

  • Availability. Depending on your brokerage, there may or may not be sufficient inventory to fill your needs.
  • Minimum purchase. Depending on the bond, the minimum purchase could range anywhere from $1,000 to $10,000.

Bond Funds

Bond funds would include ETFs such as iShares’ XBB or Vanguard’s VAB, which hold bonds as their underlying securities, usually in the proportion of some known bond index. ETFs such as these would fall in the fixed income category, which I wrote of previously. However, the key reason I would not consider a bond ETF as a risk-free investment, is that with a bond ETF you are still exposed to loss of capital, and the actual distributions are not necessarily fixed. For loss of capital, a quick look at the 10 year share price of XBB should suffice:

XBB 10 Year Price History as of October 10, 2016

XBB 10 Year Price History as of October 10, 2016

Inspecting the 10 year history, depending on when you had invested, you may have lost your initial investment. This is evidence of a bond ETF not being truly risk-free, even though it is composed of “risk-free” assets.

High Interest Savings Accounts

Just as they are named, high interest savings accounts (“HISA” for short) are savings accounts you can open at your local financial institution, which offer higher than average interest rates. Typically, a HISA is a very safe option. Being offered by major financial institutions, your deposit should be insured by the CDIC up to $100,000. Moreover, because it is a regular savings account, you have virtually instant access to the capital when you need it.

The biggest risk with a HISA is that the “high interest” may not be guaranteed. Here is a snippit of historical interest rates for Tangerine Bank:

Effective Date New Rate
July 24, 2015 0.80%
February 3, 2015 1.05%
March 6, 2014 1.30%
March 29, 2012 1.35%
August 5, 2010 1.50%
June 30, 2010 1.30%
December 15, 2009 1.20%
September 9, 2009 1.05%

Since 2009, Tangerine (formerly ING Direct) has changed their rate 8 times! Hardly risk-free!

Guaranteed Investment Certificates

I consider a Guaranteed Investment Certificate (“GIC” for short) the closest approximation to a truly risk-free asset.

  • You can select the term you wish to invest for, and the interest rate will be locked in for this term. Terms may range from 30 days to 6 years at most institutions.
  • The rate is guaranteed, with some exceptions as listed in the terms and conditions of the GIC (e.g. there may be an early redemption penalty).
  • Your investment is most likely insured, up to $100,000, by the CDIC, provided the institution is a member of the CDIC.
  • Depending on the GIC you chose, you can select one with an early redemption clause, giving you access to your capital if you need it in an emergency.

Selecting the Appropriate Vehicle

There are undoubtedly other options available to retail investors for risk-free investments. I know that some brokerages offer money market funds and other term-deposit vehicles. Moreover one could argue that, given the paltry returns available on some of the options above, you may be better off putting your money in a REIT or other high yield “low risk” vehicle. However, investing in conventional equities often entails risks, illustrated by the use of a bond fund: ironically, the fund is made up of riskless investments, yet the capital itself is subject to depreciating market values depending on overall market conditions (e.g. change in interest rates). This risk exposure is counter to the entire notion of selecting a risk-free rate: a risk-free rate is meant to minimize risk, not maximize returns.

Moreover, you have to select the best vehicle to use as the risk-free rate. If you are deciding on an investment with a one year time horizon, the 5-year GIC may not make the best sense to use for the risk-free rate. For example, as of October 10, 2016, the best 5-year GIC rate on rate hub is 2.50%, and the best 1-year GIC rate is 2.00%. Lets crunch some numbers:

  • You have an opportunity for a 1-year investment with a guaranteed return of 4.00%; you invest $1,000 today and receive $1,040 exactly 1 year from now.
  • The 5-year GIC rate is 2.50%.
  • The 1-year GIC rate is 2.00%.

Using the 5-year GIC rate as your risk-free rate, the investment has an NPV of $14.63; meaning you would make $14.63 with the investment, vs. investing in the 5-year GIC. Using the 1-year GIC rate as your risk-free rate, the investment has an NPV of $19.61. All things being equal you may pass up on the investment if you use the 5-year GIC rate as your risk-free rate, even though your absolute return would be better when compared with the 1-year GIC rate.  Realistically, you would select the 1-year GIC rate as your risk-free rate, since the duration of the GIC matches the duration of the investment opportunity.

When I look to purchase an investment, I typically look at the 5 or 10 year horizon. For that reason, I typically use the 5-year GIC rate or 10-year bond rate of a bond currently available at my brokerage as the risk-free rate. By doing this, I have a full understanding of the opportunity cost of my investment decision: I can either invest in the 5-year GIC or 10-year bond, or in the investment at hand.

In summary:

  • HISAs and GICs present two of the more effective vehicles available to retail investors for approximating a risk-free rate of return, when determining the performance of your portfolio.
  • You should pick the risk-free rate that best suits the time duration of your calculations.

Onward and upwards!

The Case of Misleading False-Negative Returns


Total returns since inception may be artificially low (or negative), due to early losses which have far reaching effects on total compounded returns over the life of a portfolio. For this reason trailing N year returns should always be considered, when looking at the "true" performance of a portfolio.

Background on Time Weighted Returns

Returns are the key indicator as to the performance of your portfolio, and the the investment decisions you have made. In the simple case, with no external cash flows, the return for any given period as a percentage is defined by:

Return=\left(\frac{Ending Portfolio Value}{Starting Portfolio Value} - 1\right) \times 100

When you introduce cash flows into the equation, you would measure the value of the portfolio immediately before the cash flow, and apply that to the numerator:

Return=\left(\frac{Ending Portfolio Value}{Starting Portfolio Value + External Cash Flow} - 1\right) \times 100

Your total return is then obtained by linking the individual period returns together. Others have written about this much better than I have, and two good articles may be found on Investopedia and Wikipedia. In summary though, the key formula to understand is the following, which measures the true time weighted return:

Return = \left(\left(\frac{M_1}{M_0+C_0}\times\frac{M_2}{M_1+C_1}\times\cdots\frac{M_n}{M_{n-1}+C_{n-1}}\times\right)-1\right) \times 100

Where in the above, M_n is the value of the portfolio at period n, and C_n are any cash flows occurring in period n (conventionally the cash flow is measured "immediately before" the valuation before period n+1).

False-Negative Returns

One key point to make is that when you are looking at returns, all things being equal, your return after a loss must be greater than the loss itself, to get back to where you started, on a percentage basis. For example, if your portfolio drops from $100 to $90, that is a 10% loss. However, to get from $90 to $100, you need an 11.1% gain. To further explore this example, consider a portfolio which is valued at $100 on Jan 1, $90 on July 1, and $100 on December 31. The return on the first period is -10%, the return on the second period is +11.1%, and the total return by linking those returns is 0%. So even though you did extremely well in the latter half of the year, your net return is still 0% overall (since you finished where you started).

So, for better or for worse, the TWR measures the true performance of your portfolio over time, reflecting every investing decision you have made. But when you are reviewing your total returns over time, you may have misleading results. Consider the following hypothetical portfolio from Jan 2000 to Dec 2002. In this portfolio, I have invested $100 on Jan 1, 2000, and the company I invested in tanked completely, losing me $98 on my $100 investment. Then on Jan 1, 2001, I heard of an even better opportunity, and invested another $1,000. Unlike the initial $100 investment, the second investment performed extremely well, more than doubling by the the end of 2002, after which point I closed off the portfolio. Overall, I have invested $1,100, and at the end of it all I have walked away with $2,260.33, a tidy profit of $1,160.33, or 105.48%; more than double my initial investment! But, if you look at my total time weighted return since inception (i.e. Jan 2000)—which includes every trade, both good and bad—my investment decisions show that I am actually down in excess of 95%!

Period Closing Portfolio Value Cash Flows during Period Period Return Return since Inception Total Invested Total $ Gain
Jan 2000 $0.00 $0.00
Feb 2000 $100.00 $100.00 $100.00
Mar 2000 $93.00 $0.00 (7.00%) (7.00%) $100.00 ($7.00)
Apr 2000 $81.00 $0.00 (12.90%) (19.00%) $100.00 ($19.00)
May 2000 $69.00 $0.00 (14.81%) (31.00%) $100.00 ($31.00)
Jun 2000 $57.00 $0.00 (17.39%) (43.00%) $100.00 ($43.00)
Jul 2000 $48.00 $0.00 (15.79%) (52.00%) $100.00 ($52.00)
Aug 2000 $39.00 $0.00 (18.75%) (61.00%) $100.00 ($61.00)
Sep 2000 $30.00 $0.00 (23.08%) (70.00%) $100.00 ($70.00)
Oct 2000 $19.00 $0.00 (36.67%) (81.00%) $100.00 ($81.00)
Nov 2000 $9.00 $0.00 (52.63%) (91.00%) $100.00 ($91.00)
Dec 2000 $2.00 $0.00 (77.78%) (98.00%) $100.00 ($98.00)
Jan 2001 $1002.00 $1000.00 (98.00%) $1100.00 ($98.00)
Feb 2001 $1057.00 $0.00 5.49% (97.89%) $1100.00 ($43.00)
Mar 2001 $1117.14 $0.00 5.69% (97.77%) $1100.00 $17.14
Apr 2001 $1176.24 $0.00 5.29% (97.65%) $1100.00 $76.24
May 2001 $1207.94 $0.00 2.70% (97.59%) $1100.00 $107.94
Jun 2001 $1195.88 $0.00 (1.00%) (97.61%) $1100.00 $95.88
Jul 2001 $1194.69 $0.00 (0.10%) (97.62%) $1100.00 $94.69
Aug 2001 $1276.98 $0.00 6.89% (97.45%) $1100.00 $176.98
Sep 2001 $1322.88 $0.00 3.59% (97.36%) $1100.00 $222.88
Oct 2001 $1355.91 $0.00 2.50% (97.29%) $1100.00 $255.91
Nov 2001 $1434.43 $0.00 5.79% (97.14%) $1100.00 $334.43
Dec 2001 $1516.08 $0.00 5.69% (96.97%) $1100.00 $416.08
Jan 2002 $1503.97 $0.00 (0.80%) (97.00%) $1100.00 $403.97
Feb 2002 $1585.07 $0.00 5.39% (96.84%) $1100.00 $485.07
Mar 2002 $1654.73 $0.00 4.39% (96.70%) $1100.00 $554.73
Apr 2002 $1735.71 $0.00 4.89% (96.54%) $1100.00 $635.71
May 2002 $1838.00 $0.00 5.89% (96.33%) $1100.00 $738.00
Jun 2002 $1894.92 $0.00 3.10% (96.22%) $1100.00 $794.92
Jul 2002 $1980.10 $0.00 4.50% (96.05%) $1100.00 $880.10
Aug 2002 $1980.10 $0.00 (96.05%) $1100.00 $880.10
Sep 2002 $2073.07 $0.00 4.70% (95.86%) $1100.00 $973.07
Oct 2002 $2104.14 $0.00 1.50% (95.80%) $1100.00 $1004.14
Nov 2002 $2192.43 $0.00 4.20% (95.62%) $1100.00 $1092.43
Dec 2002 $2260.33 $0.00 3.10% (95.49%) $1100.00 $1160.33

Clearly, this is misleading: I have walked away with more than double what I invested in overall, however due to a single bad decision at the outset, my total returns are dragged down completely. In fact, to gain ground from a 98% loss requires a staggering 4,900% return over time!!! The nuances of this are tied to the fact that time weighted returns take the geometric average of your historical returns: they multiply everything together, and due to the way the math works itself out, you are virtually never able to get back to where you started after a devastating failure.

Fortunately, there are ways to paint this picture in a different light. Observe what happens if we position the portfolio this way:

1 year return 2 year return 3 year return
49.1% 125.6% -95.5%

By breaking up the returns into tranches, the results look dramatically different.

The point of this is to illustrate that a single bad period can drag down the total return of a portfolio virtually forever. Similar to how when I review a firm I am typically only looking at 10 years of historical data, there is value in truncating the window at when one evaluates their returns as well; we learn as we move forward, and as long as on a historical basis we are increasing our returns, then we are doing relatively well. The final point is that while the "true time weighted return" is "true", one must review it with a grain of salt. True, on a percentage basis, the above example is still down 98%. However, overall the total return based on absolute dollar terms is in excess of 100%.

For the record, the above is a simplified version of my own portfolio. When I started investing in 2005 I followed “hot tips” from my coworkers who were “good friends” with traders on the trading floor, and I invested in two firms, First Calgary Petroleum (FCP.TO), an Alberta based refinery, and Paincare Holdings (PRZ.N), a US healthcare provider. Luckily I had only invested ~$1250 at the time: 50 shares of FCP.TO at $18.40/share, and 50 shares of PRZ.N at U$5.00/share. FCP.TO tanked, no pun intended, when one of their exploration operations did not pan out as expected. FCP.TO was eventually bought out by a foreign interest at $3.60/share, netting me a loss of 80%. Paincare Holdings was victim to a lawsuit, and the company eventually de-listed except for over the counter pink slips, and is now a private holding. The shares of PRZ.N virtually went to $0.00; they are actually still “in” my portfolio at BMO InvestorLine with a market value of $0.005, or U$0.0001/share, netting me a loss of 99.998% on that trade. As these are the first trades in my portfolio, they have been a constant drag on my true TWR. Since then, I definitely regained the original $1,250 investment in dividend income alone from other investments, so on an absolute (i.e. actual dollars profit) I am well ahead. So, if we carve out those outliers, every other investment I have completed has performed relatively well, something I hope to continue doing as time moves forward.

Reset button.

It has been a little over a year since my last post, and there have been a number of changes occurring personally, professional, as an investor, and with this site, all of which are intertwined.

The biggest event was that I was displaced in June 2015 due to downsizing at my former employer.  This was a massive hit professionally and financially, as I saw my defined benefit pension fly the coop, and I took a drastic paycut.  The summer of 2015 was a rocky one: instead of going to the beach, enjoying the weather in a park, or drinking on a patio with my mates in Toronto’s downtown core, I was hunkered down at home applying for jobs all summer.  Towards the end of August 2015 I landed a contract position, and from there started up my new life as an independent project management consultant.  So, in the end, things worked out, but it was still a bit of a professional roller coaster; and I will miss the defined benefit pension.

Personally, my family purchased a home earlier in 2016, just ahead of the massive Toronto Housing Bubble.  We lucked out; similar properties in the neighbourhood we moved into have gone up about 10% since we purchased our house earlier this year.  Needless to say, the market is hot, and I am certainly glad not to be part of that fire!

Which brings me to the changes as an investor.  The majority of my investments were being saved for the next big purchase, or retirement, whichever came first.  Needless to say, retirement is a far way off, so I ended up liquidating a number of my holdings to help pay for the house.  While the sting of selling off those holdings is still wearing off, I am happy that overall my previous investment decisions were good ones.  The biggest sale I had which contributed to the house was my long position of CCL Industries, which netted me a tidy return of 517.8%; I had purchased a while back in the high $30 range and sold in the $220 range.  I had some other big gainers (e.g. High Liner Foods returned in excess of 200%), but CCL was definitely my big winner!

Which brings us to today.

With the cashing out of my defined benefit pension, and the selloff of a number of positions in my portfolio, my portfolio has taken a net hit of about 17%.  Moreover, the tax distribution in my portfolio has changed drastically: before all of these major changes, 45% of my portfolio was taxable (i.e. non-registered), and 55% was in non-taxable or tax-deferred accounts, such as an RRSP or a TFSA (i.e. registered).  Now, the mix stands at 10% in the taxable portion, and 90% in the non-taxable.

This split is both good and bad.

The good, is that the majority of my US investments are now in my RRSP – this means I save an instant 15% of withholding taxes, since Canadians do not pay withholding tax on dividends from US corporations if they are in an RRSP.  Moreover, having 90% of my portfolio “locked away” means that I truly am saving for retirement: taking the money out of the registered portions of my portfolio would result in an immediate tax hit.

The bad, is that only 10% of my investments provide present day disposable income.  So, if I need to use any dividend income to offset present day purchases, I am unable to do so.

From a salary perspective, I am not yet at the point where I can pay myself the same salary as before I was displaced, since I have to build up some capital in my corporation.  My salary today is 17% less than one year ago, not including  any short-term bonuses, the losses of which may be even larger.  Contrary to popular belief, independent consultants are not rolling in cash!  Due to this change in salary, I am not able to invest as aggressively as before, which means my portfolio growth will be seriously constrained until I can increase my net cashflow.

As investors, diversification should be one of the primary objectives of our investment portfolios.  I’m happy to report that during the ups and downs of the past 24 months in the markets, my portfolios have done relatively well, all things considered.   With that in mind, the irony of the situation is that my income streams were not diversified.  While I received some income from dividend investing (in 2015, dividends attributed approximately 3% of my net cashflow), like most normal people, the majority of my income came from my place of employment.  So when your job changes, your net income could take a massive hit; such was my case.  With that in mind, I am looking at diversifying income streams as well.

I have moved this blog from a WordPress.com hosted site, to one hosted on my own servers.  This will give me more opportunities for revenue generation through the site; what that means, I am not quite sure, but at least the option is there.  You may see some ads on the site going forward, and clicking through to those will help me in keeping this site on its feet.

I started off by noting that it has been over a year since my last post, and I have a whole slew of ideas and things to write about.  While the original focus of this blog was on dividend investing, I will be branching out into new areas.  From an investing perspective, dividends are typically the payouts a shareholder receives from the profits of the company in which they own shares.  However, a broader definition is “anything received as a bonus, reward, or in addition to or beyond what is expected.”  That said, future posts will also focus on other methods of generating net positive cash flows: this could either be from hard inflows of cash (i.e. income), or cost avoidance, which ultimately results in more disposable income to use in other investing activities.

One thing is certain: I am certainly glad to be back here blogging and sharing my views and ideas, and I look forward to receiving criticism and feedback from my readers.

Welcome back.

Investing Roadmap Part 2: How much do you need to retire?

In my previous post, I spoke about having goals for investing. My goals fall into the second category, Investing to achieve some target and/or goal, and that goal is to not have to work.

Now, most people don’t want to work. Given the choice, I would rather sit on my balcony all day sipping an espresso reading books, researching companies, or in the living room watching a good film. However, work is a reality of life: we have to pay the bills somehow (how will I buy the espresso?). So, to be able to get to the point where I don’t have to work to make money, I need to have some inflow of cash which handles all of my regular expenses. This is a fairly mechanical exercise:

  1. Identify your monthly expenses, and multiply by 12 to annualize
  2. Add in any annual expenses (e.g. property tax on your residence, if you own a home)
  3. Add inflation up to the point that you wish to retire
  4. Factor in personal taxes

After the four steps above, you’ll have your required annual pre-tax income for when you wish to stop working.  Here is an example:

Monthly Expenses
Rent $1,500.00
Groceries $300.00
Entertainment $400.00
Insurance $100.00
Utilities $200.00
Transportation $200.00
Pet care $75.00
Mobile phone $85.00
Internet $50.00
Netflix / TV $10.00
Computer / Technology $100.00
Maintenance Fees $350.00
Emergency Funds $200.00
Total Monthly $3,570.00
Annualized $42,840.00
Annual Expenses
Vacation $5,000.00
Property Taxes $3,000.00
Total Annual Expenses $8,000.00
Total Expenses $50,840.00
Implied Tax Rate 40%
Total Annual (Gross) $84,733.33

From the example above, if I were to stop working today, I would need ~$84.7M ($M=000) in annual income to maintain my current lifestyle.

However, there is a small wrinkle in that this is in today’s dollars, and we need to factor in inflation (step #3 above).  For example, if we assume 2% inflation (i.e. on average costs will go up 2% next year), our pre-tax income shoots up to ~$86.4M.  And to further complicate things, inflation is an unknown: we don’t know what inflation will be.  Say for example I wish to stop working in 10 years, in 2025.  What inflation rate do I use for 2016, 2017, 2018, etc.?

My own workplace uses a 2.25% inflation assumption for each year.  I would prefer to account for some variability, and one way to account for this variability is to run a simulation, using a range of acceptable inflation values.  Specifically, a Monte Carlo simulation, wherein I have run 100,000 trials using an inflation assumption of 2.25% +/- 1.00% per year for the next 27 years.  One iteration of the simulation gives results such as the following:

Year Pre-tax income
(Jan 1)
Inflation Assumption Pre-tax income (Dec 31)
2015 $85,000 3.21% $87,729
2016 $87,729 3.13% $90,474
2017 $90,474 2.68% $92,899
2018 $92,899 1.29% $94,098
2019 $94,098 1.89% $95,876
2020 $95,876 2.56% $98,330
2021 $98,330 2.13% $100,425
2022 $100,425 2.67% $103,106
2023 $103,106 3.15% $106,354
2024 $106,354 1.39% $107,832
2025 $107,832 1.87% $109,849
2026 $109,849 1.93% $111,969
2027 $111,969 2.64% $114,925
2028 $114,925 1.67% $116,844
2029 $116,844 2.60% $119,882
2030 $119,882 3.24% $123,766
2031 $123,766 2.79% $127,219
2032 $127,219 2.88% $130,883
2033 $130,883 1.88% $133,344
2034 $133,344 1.91% $135,891
2035 $135,891 1.79% $138,323
2036 $138,323 2.36% $141,588
2037 $141,588 2.85% $145,623
2038 $145,623 2.85% $149,773
2039 $149,773 2.67% $153,772
2040 $153,772 2.89% $158,216
2041 $158,216 2.17% $161,649

As you can see, by the time we hit 2041, to live at my current lifestyle, I would require $158.2M in annual income.  The inflation also bounces around a lot, as each year the inflation is estimates to be somewhere between 1.25% and 3.25%.

Now, if we run this simulation 100,000 times, we get the following for the required income in 2041 (only first 10 entries shown):

Sequence # 2041 pre-tax income
1 $158,216.33
2 $160,945.75
3 $142,668.57
4 $160,712.46
5 $160,133.85
6 $160,235.08
7 $146,449.32
8 $150,616.91
9 $161,482.05
10 $152,456.35

But, what do we do with those numbers?  The answers is to perform some statistical analysis on each year, and come up with what we feel is a reliable number.  If we focus on 2041 as our example, here is the histogram:

Histogram of Required Income in 2041

For the above, we have a median required income of $154,922.16, and a mean income of $154,991.19.  However, the median and mean are the mid-point and average required incomes respectively.  Whilst the median is $154,992.16, there is a chance that it will be above that.  What I am interested in is the required income with a certain level of confidence.  If we do some more analysis on the histogram, we can break up all of the salary ranges into buckets, and from there interpolate the expected required income in 2041 with 95% confidence:

Bucket # Low High Count Cumulative Probability
1 $134,510.51 $135,685.09 1 0.0010%
2 $135,685.09 $136,859.67 0 0.0010%
3 $136,859.67 $138,034.25 1 0.0020%
4 $138,034.25 $139,208.83 6 0.0080%
5 $139,208.83 $140,383.41 12 0.0200%
6 $140,383.41 $141,557.99 55 0.0750%
7 $141,557.99 $142,732.57 156 0.2310%
8 $142,732.57 $143,907.15 338 0.5690%
9 $143,907.15 $145,081.73 682 1.2510%
10 $145,081.73 $146,256.31 1296 2.5470%
11 $146,256.31 $147,430.89 2098 4.6450%
12 $147,430.89 $148,605.47 3325 7.9700%
13 $148,605.47 $149,780.05 4653 12.6230%
14 $149,780.05 $150,954.63 6419 19.0420%
15 $150,954.63 $152,129.21 8000 27.0420%
16 $152,129.21 $153,303.79 9048 36.0900%
17 $153,303.79 $154,478.37 10070 46.1600%
18 $154,478.37 $155,652.94 10061 56.2210%
19 $155,652.94 $156,827.52 9678 65.8990%
20 $156,827.52 $158,002.10 8773 74.6720%
21 $158,002.10 $159,176.68 7376 82.0480%
22 $159,176.68 $160,351.26 5833 87.8810%
23 $160,351.26 $161,525.84 4249 92.1300%
24 $161,525.84 $162,700.42 3006 95.1360%
25 $162,700.42 $163,875.00 2057 97.1930%
26 $163,875.00 $165,049.58 1224 98.4170%
27 $165,049.58 $166,224.16 721 99.1380%
28 $166,224.16 $167,398.74 453 99.5910%
29 $167,398.74 $168,573.32 214 99.8050%
30 $168,573.32 $169,747.90 126 99.9310%
31 $169,747.90 $170,922.48 43 99.9740%
32 $170,922.48 $172,097.06 14 99.9880%
33 $172,097.06 $173,271.64 7 99.9950%
34 $173,271.64 $174,446.22 5 100.0000%
100000 100.0000%

Based on the above, our required income, at 95% confidence, is $162,647.28.  In other words, I can say with a degree of confidence that my required income in 2041 will always be at, or less than, $162,647.28; put another way: there is only a 5% chance that I will need more than $162,647.28 in annual income to live comfortably in 2041.

However, that is only for the year 2041.  It would be nice to see a bunch of years, say, from 2026 to 2041.  I won’t display all of the histograms and such, but here is the summary table:

Year Income Required at 95% confidence Mean Income Required Median Income Required
2026 $114,667.71 $111,013.30 $110,991.02
2027 $117,397.60 $113,512.43 $113,484.70
2028 $120,183.67 $116,061.47 $116,037.66
2029 $123,019.43 $118,672.26 $118,654.49
2030 $125,975.59 $121,345.28 $121,319.06
2031 $128,935.52 $124,077.19 $124,044.14
2032 $131,995.18 $126,871.97 $126,845.13
2033 $135,073.08 $129,724.75 $126,845.13
2034 $138,286.34 $132,644.87 $129,688.96
2035 $141,521.77 $135,624.14 $129,688.96
2036 $144,833.57 $138,672.78 $138,639.86
2037 $148,260.68 $141,794.27 $141,765.55
2038 $151,705.86 $144,983.10 $144,948.96
2039 $155,291.29 $148,242.42 $148,193.00
2040 $158,933.22 $151,579.05 $151,517.82
2041 $162,647.28 $154,991.19 $154,922.16

At the outset of this post, I said that my goal was to not to have to work.  From the above, I now know how much income I need in any given year, to maintain my current lifestyle, while factoring in inflation.  So, if my investments happen to generate at least $114,667.71 in income in 2026, I know that I can then quit my job and not have to worry about anything.

In one of my upcoming posts, I’ll talk about forecasting my expected income, which is the flipside of this discussion.

Why do you invest?

A few people may stumble into financial security. But for most people, the only way to attain financial security is to save and invest over a long period of time. You just need to have your money work for you. That’s investing.

Simply put, you want to invest in order to create wealth. It’s relatively painless, and the rewards are plentiful. By investing in the stock market, you’ll have a lot more money for things like retirement, education, recreation — or you could pass on your riches to the next generation so that you become your family’s Most Cherished Ancestor. Whether you’re starting from scratch or have a few thousand dollars saved, Investing Basics will help get you going on the road to financial (and Foolish!) well-being.

Now that the markets are showing signs of life, the pundits and financial writers are pumping out investing articles of all kinds. Gold is prominently mentioned as are a wide variety of stocks, mutual funds, and exotic ETFs. More so than ever, when I read these articles I ask myself this question: Why should I invest in that? Or taken one step further, the question becomes: Why do I invest?

I actually struggled for a long time on how to open up this post, but taking a page from Finding Forrester, sometimes it is easier to let someone else write the intro for you.

It should come as no surprise that many folks have asked the age old question of, “why?”.  In fact, everything that I say in this entry, has likely been written in greater detail, depth, and clarity, by someone else.  However, it is a necessary step in my overall roadmap of investing.

So, the question as it stands, why do you invest?  And as an extension to that, how do you know that you did it well?

The three quotes cited above contain a wealth of information on the how and why of investing.  At the end of the day, If we ignore the mechanics of investing (e.g. compound interest, “buy low, sell high”, “long time horizons”, etc.), the reason that any of of invest is a deeply personal one.  However, in my view the reasons for investing can be broken down into one of three categories:

  1. We invest for personal gain
  2. We invest to achieve some target and/or goal
  3. We invest for someone else

Fundamentally, these three reasons cover pretty much every scenario.  Saving for retirement?  That is #1 or #2.  Helping a relative?  That is #3.  Saving for school?  #2.

The reason that I have broken everything down into three categories, is that the why of investing is useless without some type of barometer as to how well you are investing . If you are saving for school, you know if you are successful if you have enough for your tuition.  If you are saving for retirement, then you have enough if you know that you can be financially secure after you stop working.  If you are saving for personal gain (e.g., “I just want to be rich”), you are successful if the personal decisions you make in your investing are better than those that would be made if you paid someone else to handle your money (e.g. a financial advisor).

There are really only two ways to monitor your performance: absolute, and relative.  In absolute measurements, you have some fixed, quantifiable goal against which you are measuring yourself.  If you are saving for your child’s education, and you know that the total cost will be $50,000 with tuition, books, and residence fees, then you have an absolute target against which to work.  Contrasting this are relative measurements.  These measurements are typically against some benchmark, and fundamentally reflect the opportunity cost of investing relative to some other means.  For example, if your benchmark is one of the couch potato portfolios, the performance of your investment decisions shows how much better (worse) you have done by managing your own money, instead of following the couch potato formula.

With the above in mind, the question should not be “Why do I invest?”.  Rather, it should be, “Am I meeting my investment goal?”  Defining your investment goal will lay the foundation on which you base all of your future decisions.


Stock Indices

ETF investing has become one of the primary vehicles for many individual investors, since it offers a low-cost, low-maintenance approach to investing, with results that match the overall market. The reason for this is that most ETF strategies revolve around investing in market-index ETFs. A great reference for this type of investing can be found at the Canadian Couch Potato blog, or at the original couch potato site at MoneySense Magazine.

When I started off investing on my own, I purchased Canadian Market Index Stocks such as XIC and XIU. At a high level, I understood that an index based ETF basically held the holdings of the index it represented; for example, XIC holds all of the equities in the S&P/TSX Capped Composite Index. But what is an index anyways?

In its broadest sense, an index provides an overview of the performance of the underlying securities, either through a price-weighted or value-weighted average. What constitutes inclusion in that group of securities depends on what the index is trying to achieve. Standard & Poors is one of the primary index publishers, and they have several such as the S&P/TSX 60, S&P/TSX Capped Composite, S&P/TSX SmallCap, etc. Each of these indices is designed to be representative of one dimension of the overall market. The 60 acts as a subset of the S&P/TSX Composite, but caps the total number of equities at 60. The SmallCap attempts to provide an overall barometer on the performance of small cap stocks on the TSX, etc.

Excluding the focus of the index, the other primary factor to take into account is whether or not it is price-weighted or value weighted.

(For the discussions below, a worksheet is available to play with, which can be found here.)

Price-Weighted Indices

The most popular price-weighted index is the Dow Jones Industrial Average (DJIA). There are a number of articles on the Internet which speak to the history of the DJIA, and my interest is in what it means to be price-weighted.

Essentially, a price weighted index is exactly what it sounds like: an index whose value is more influenced by firms which have a higher price. The value of a price-weighted index is the sum of the prices of firms in that index, divided by some divisor. The divisor is the trickier part of the equation.

\text{DJIA}=\frac{\sum_{i=1}^{30} P_{i}}{divisor}

Where Pi is the price of firm i. When the DJIA was initially started, the divisor was 30, because there were 30 firms in the average. However, over time the divisor has had to be adjusted due to stock (reverse-)splits. I.e., when a stock splits, the total number of shares goes up, but the price of the stock goes down. However, the before and after values of the DJIA should be the same. With a little algebra, we can calculate the divisor after a (reverse-)split as:

\text{divisor}_{\text{new}}=\frac{(\sum_{i=1}^{30}P'_{i})\times divisor_{old}}{\sum_{i=1}^{30}P_{i}}

In the above, Pi are the prices before the (reverse-)split, and P’i are the prices after the split.

Over time, the divisor for the DJIA has become incredibly small, and the divisor as of 2010/07/02 was 0.132129493 (from 0.132319125). The reason for this is that, using the formula for divisornew above, over the years successive splits have made the divisor smaller and smaller.

The other thing to consider with a price weighted index is the weighting of the price itself, and how it affects the overall value of the index. That is, an equal percentage change for a stock will mean more (or less) if the stock price was large (small) relative to the index to begin with. For example, both IBM and Bank of America are stocks in the DJIA. However, they are incredibly different in terms of pricing. At one point during the week of October 29, 2012, IBM was trading at $193.27 a share, and Bank of America was trading at $9.12 a share. But why does this matter? It matters because a 5% shift in either stock will have a different overall effect on the index as a whole. A 5% shift in IBM results in a 77.289 point shift in the DJIA, but an identical shift of 5% for Bank of America only shifts the DJIA 3.6471 points!

This means that one should pay particular attention to what it means when news reports say that the Dow has moved – the context of the movement has to be taken into account to ensure that the movement isn’t being skewed by a heavy hitter such as IBM.

Value-Weighted Indices

On the other end of the spectrum are value-weighted indices.

Looking at the sample spreadsheet, when we enter values for the split multiple, the sum of the market caps does not change. This is because (reverse-)splits automatically account for changes in the number of shares outstanding, and share price. This simplifies computation of the index because there is no denominator which must be continuously adjusted.

The other thing to notice is that changes in share price in a value weighted index are scaled appropriately to the weight of the firm in the index, measured by market cap. This means that the bigger the firm by market cap, the more weight it has. This also demonstrates that movements of the share price will be properly reflected in the index, and that the percentage move of a given security in the index will be properly reflected in the change of the index itself. But why does this matter?

Consider two hypothetical stocks, each with a market cap of $1,000,000,000. Further, assume that stock #1 has a share price of $5.23, and stock #2 has share price of $198.53. This is summarized below:

Stock Share Price Shares Outstanding Market Cap
Stock 1 $5.23 191,204,588.91 $1,000,000,000
Stock 2 $198.53 5,037,022.11 $1,000,000,000

As discussed above for the DJIA, if both stocks change by 5%, this will not have an identical change on the stock. However, based on market cap alone, a movement of 5% in either stock will have the same effect on the inded. For this reason, a value-weighted index is often a better indicator of the performance of the cross-section of the market that the index is monitoring.

Basic vs. Diluted Weighted Average Number of Shares

Whilst perusing the financial statements of firms while performing an analysis, often the EPS is listed in two forms: basic EPS (sometimes just "EPS"), and diluted EPS. Basic EPS is calculated as:

 EPS=\frac{\text{Net Income}}{\text{weighted average number of shares}}

Diluted EPS takes a little more work. With the diluted EPS, the weighted average number of shares is adjusted by the number of shares that would result from converting any dilutive securities to common shares. This adjustment is then adjusted again to adjust for any shares that could be purchased on the open market from the proceeds of the conversion, based on the average share price for the fiscal period. The total list of dilutive securities is vast, but as an example, here are some things to look for:

  • Convertible bonds
  • Convertible preferreds
  • Outstanding warrants
  • Employee options

It should be noted that the treatment of dilution for different types of securities is not the same across the board. For example, proceeds of warrants and options are used to repurchase common stock, but there are no proceeds from convertible preferreds; however convertible preferreds would impact the preferred dividends that are paid, which would also affect the net income.

An example would probably best illustrate the conversion. Say we were reviewing the financial statements for FirmCorp., and their 2011 annual statement had the following information:

  • Net Income: $123,555,000
  • Weighted Average Number of Shares Outstanding (WANS): 591,223,552
  • Series A Warrants: 5,533,000 outstanding, convertible to 5 common shares each at a price of $3.00/share ($15.00 total per warrant)
  • Average share price for the period: $5.23

Our basic EPS calculation is simple:

     \begin{align*} \text{EPS}_{\text{basic}} & =\frac{\$123,555,000}{591,223,552} \\ & = \$0.21 \end{align*}

To calculate the diluted EPS, we have to adjust the weighted average number of shares. From the above, we have 5,533,000 outstanding warrants, and each warrant can be converted to 5 shares at a cost of $3.00/share. If we were to convert all of the warrants, two things would result:

     \begin{align*} \text{NumShares} & =5,533,000 \times 5 \\ &= 27,665,000\\ \text{CashInflow} & =5,533,000 \times 5 \times \$3.00\\ & =\$82,995,000 \\ \end{align*}

In the above, NumShares is the change in shares by converting all of the warrants, and CashInflow is the money received by converting the warrants. The proceeds from CashInflow would then be used to purchase any shares outstanding from the open market:

     \begin{align*} \text{ShareBuyback} & =\frac{\$82,995,000}{\$5.23}\\ &=15,869,025 \end{align*}

Our weighted average number of shares is then adjusted as follows:

     \begin{align*} \text{WANS}_{diluted} & =\text{WANS}+\text{NumShares}-\text{ShareBuyback} \\ & =591,223,552+27,665,000-15,869,025 \\ & =603,019,527 \end{align*}

And our diluted EPS is then calculated as:

     \begin{align*} EPS_{diluted} & =\frac{\$123,555,000}{603,019,527} \\ & =\$0.20 \end{align*}

With the above explanation in mind, why does this matter? I’ve tossed the notion of basic vs. diluted EPS around in my evaluations, but as of late I have settled on basic EPS. Diluted EPS shows you the EPS if dilutive securities were converted to common shares. However, at the time of publishing the financial statements, the dilutive securities were not converted, and hence did not dilute the EPS. That said, I see little point in evaluating diluted EPS for a fiscal period that has already closed.

However, diluted EPS does give you a preview of the associated internal risks of the company’s financials. By reviewing financial statements, one can determine any potential future impacts if the shares were to be diluted. When analysts post EPS projections, they are often doing so based on the basic EPS; if you are performing a forward-looking evaluation on P/E, P/BV, P/E×P/BV, dividend payout ratio, etc., knowing what could happen if the weighted average number of shares were diluted may have a material impact on your analysis. So at the very least, diluted EPS can serve as a bellwether to potential negative impacts when analyzing a firms.

My Initial Evaluation Methodology.

There isn’t one sure way of evaluating companies, and everybody’s method will depend on factors specific to their situation: time horizon, risk tolerance, experience, knowledge of the industry, etc. I thought it would be a useful exercise to document what I look for in a company when I am evaluating it to see if it would be a worthwhile addition to my portfolio. To that end, here are the key factors I look at.

  • Earnings per Share

    Commonly referred to as EPS, this is an indicator of how much of the net income is left to distribute to share holders for a given period. EPS is calculated as the total net earnings, divided by the total number of common shares outstanding. In addition to EPS, there is another variant called diluted EPS, which adjusts net income and total shares outstanding by factoring in events such as conversion of warrants, options, convertible shares, convertible bonds, etc. In short, the number of shares outstanding for diluted EPS is the theoretical number of shares outstanding if anything that couldbe converted to a common share, was converted, during the period.Typically I would want to see a rising EPS, with some caveats.

    One must be sure to to understand why EPS is rising. For example, since EPS is net income divided by number of shares outstanding, reducing the number of shares outstanding is one way to boost the EPS. If a company reduces the total number of shares outstanding through a share buyback program which uses up free cash from the balance sheet, this is typically a good thing. However, if a company takes out a loan to repurchase shares, that may be a bad thing. EPS can also rise when net income rises, but there are different reasons net income may rise. For example, net income may rise because operating expenses have decreased, but operating expenses may have decreased because the company laid off half of its workforce; this may spell trouble for the comapny, and they are looking for ways to cut corners. But, cutting the workforce may not be a badthing, since the workforce may be cut due to increased operational efficiencies, so the firm simply doesn’t need the staff.In short, rising EPS is good, because it shows that year over year (YoY) the company is making more money. But, one must investigate the rise in EPS to ensure it isn’t rising at the expense of something else (pun intended).

  • Dividend

    As a dividend investor, the dividend is obviously the most important thing to look for; if the company were not paying a dividend, it wouldn’t even be on my radar.Typically a dividend should be rising over time, a topic which I will address in a future post.

  • Dividend Payout Ratio (DPR)

    The dividend payout ratio is the proportion of earnings (from EPS) that are paid out as dividends, and is reported as a percentage, calculated as Dividend/EPS. A typical company will have a dividend payout ratio that is less than 100%, but there are some types of companies where the dividend payout ratio is greater than 100%. Excluding those companies, the dividend payout ratio should be a number which is adequate for the industry, or the peers of the company being analyzed. A dividend payout ratio that is too high means that the company may be paying out too much of its dividend, leaving little cash for internal projects. A dividend payout ratio that is too low means that the company may be burning through too much cash internally, or may not be returning a fair portion of the earnings to the shareholders. I personally like to see a dividend payout ratio of less than or equal to 60%. Such a value provides enough of a cushion that a firm may still be able to pay out a dividend even when net income isn’t as strong as in previous periods. Firms such as those that weathered the recession of 2008 and still managed to increase their dividend would be good examples of firms that did not have a dividend payout ratio which was too aggressive, allowing them to continue to return value to shareholders even when sales were down.

  • Share Price.

    Of course, while dividend are great, one also would like the capital investment to increase over time, or at least stay in line with inflation. To that end, the share price of a firm should be rising over time. The actual growth rate of the share price is relative to the growth in the dividend itself. For example, a firm whose dividend rises YoY by only 1%, but whose share price increases by 4% per year, is better than a firm whose dividend yield rises 4% per year, but whose share price only rises 1% per year.

  • Price to Earnings, Price to Book, and the P/E * P/BV Multiple.
  • This last screen is one that I picked up from Benjamin Graham. Graham felt that the P/E of a stock (Price divided by EPS) should be less than 15, and that the price to book value (share price divided by the book value, where the book value is the equity (assets-liabilities) divided by the number of shares outstanding) ratio should be 1.5 or less, and combining these two numbers gives an upper limit of 22.5. Personally, I prefer an upper limit of 25, and this gives me some latitude with the P/E and P/BV. For example, even if the P/E is higher than 15, if the P/BV is extremely low, I would still consider the stock.

    The point of this combined ratio is not to buy companies that are inherently overvalued. If a company sports a very high P/BV ratio, in theory, if the company were to be liquidated, the total assets remaining would not be sufficient to distribute to all of the shareholders. Likewise, if the P/E is very high, this means that the expectations of the companies future earnings as measured by the share price are extremely out of line with the share earnings themselves.

  • Free Cash Flow from Operations.

    One often overlooked indicator is the free cash flow from operations, which is essentially how much literal cash changed hands as a result of the firms day to day business(es). Dividends are ultimately paid out in cash, and if the dividends paid in a given period outweigh the actual cash that was earned in the period (actual cash excludes items such as accounts receivables, which are obligations for customers to pay cash in the future), this indicates that the dividends may be being funded from another source, e.g. leverage (which would show up as cash flow from financing activities) or selling assets (which would show up as cash flow from investing activities). When a firm starts paying dividends from non-operating cash streams, that is a big warning sign that the dividend is likely not sustainable.

And there you have it. The above points are my initial screens, but I also like to dive into some of the other details as well. However, the above provides a good starting point to identify which companies warrant further analysis.