*Are you a savvy investor? Take this quiz to find out*caught our attention. Would we get the right answers? Is there something we could learn since no one can know everything? But we quickly found that most questions had several possible answers, or "none of the above", as several commenters also noted. Let's go through the questions and add what else we think needs to be considered.

**Q1 An investment pays 5-per-cent annual interest. If you put in $1,000 today, how much money will you have two years from now?**

The correct answer is said to be more than $1100 but less than $1200. There is an implicit assumption that the investment will pay compounding interest to arrive at $1102.50 (1000 x 1.05 x 1.05). But as we saw a few weeks ago in a post on finding the highest rate GICs, the compounding assumption is not always the case and some investments pay only simple non-compounding interest. The investment could then pay $50 per year (1000 x 0.05) for two years giving a total of $1100. Furthermore, almost every investor with $1000 to spare to invest must surely have enough income to pay at least some tax. Even at a minuscule 10% tax rate, the $102.50 interest would be reduced by $10.25 after-tax. The correct answer would thus more probably be a) "$1100 or less". The truly savvy investor will ask beforehand how interest will be calculated on an investment.

**Q2 If you earn $1,000 on the money in your RRSP, when will this income be taxable?**

The supposed correct answer is "when you take the money out of your RRSP". In a purely mechanical and superficial sense, that's true. Any and all money withdrawn from an RRSP, whether it's contributions, gains or earnings, must be reported on your tax return for that year and has tax applied to it at the ordinary income rate. But the economic reality, the one that matters for understanding how an RRSP works and what makes it valuable, is quite different.

As RetailInvestor.org shows in step by step detail in

*Nitty-Gritty of the RRSP Model*, the essence of what happens is that earnings from

__your__money put into an RRSP are not taxed, period - not while inside and not when withdrawn either. That is also what makes an RRSP and a TFSA equivalent, except that the investor in the RRSP is allowed to defer payment of the original tax that was due in the year when the original contribution was made, i.e. the RRSP refund is the government deferring receipt of, and lending you, the tax. The tax refund is not your money it's government money.

The government wants it tax money back, plus interest. Plus interest? Yes, indeed. The key sentence in the RetailInvestor.org article is "

*The taxes paid by the RRSP on withdrawal are not taxes on the portfolio's profits. They are the Future Value of the unpaid tax on the original employment income.*" The interest rate charged - the number that generates the future value in the calculation - is whatever rate of return your investments have managed to achieve while inside the RRSP. Thus, we believe a savvy investor would more likely answer choice d) "

*The earnings are never taxed*".

**Q3 If you know you will need all of your savings to pay for expenses two years from now, stocks are a safe place to park your money until you need it.**

On this question we agree, the savvy investor knows that the enormous possible variation in the short term, most critically on the downside - remember 2008 when the TSX Composite Index fell by 33% - makes stocks a very bad place to put money. As we argued in a couple of our early posts on

*Setting Investment Objectives*and

*Risk: What Can You Afford and What Can You Put Up With?*the type of investment chosen must suit the objective in terms of risk for the time horizon.

**Q4 Over the next 20 years, the stock market will probably earn more money than a savings account.**

For this question as well, we think the Globe's correct answer - highly agree - is the best choice. It all hinges on the word "probably". Has there actually ever been any 20 year period over which stocks have not earned more than a savings account? We cannot tell as the data for bank accounts does not seem to be readily available online. There is suggestive data out there - e.g. charts like the one below from Retirementbydesign.ca that show the TSX Composite Index always generating a healthy positive return over any rolling 20 year period from 1935 to 2007,

and others like the

*Credit Suisse Global Investment Returns Yearbook 2013*that show Canadian equities handily outpacing T-Bills, whose return would be similar to that of a savings account, since 1900.

Finally, of course, the future may not be like the past so the cautionary note in the use of the word probably adds the necessary realism about the unknown future. The savvy investor knows the difference between a probable outcome and a sure thing.

**Q5 Over an average 20-year period, what annual rate (what per cent a year) would you reasonably expect to earn by owning a typical basket of Canadian stocks?**

The Globe's correct answer is 6-8 percent. Let's do our own calculation to see on what basis this may be true. The summary chart below shows the enormous impact on returns of the following factors.

*Critical Factor #1 - Fund fees & costs cause under- or out-performance*

We'll have to assume that the typical basket refers to the TSX Composite. Since this index represents well over 200 stocks (the number has varied between just over 200 to 300 stocks over the years), the only way we retail investors can own such a basket is through a mutual fund or an ETF. That's important because the index return does not account for the return reduction resulting from fund fees and costs. A passive index-tracking ETF such as the iShares S&P/TSX Capped Composite Index Fund (TSX symbol: XIC) currently has an expense ratio of 0.27%. That figure is about the amount by which XIC will under-perform the index. Our data source - StingyInvestor's Asset Mixer - uses 0.3% annual under-performance for an ETF. Stingy Investor assigns annual performance vs the index - what it calls a Global Alpha Assumption - as follows: Index mutual fund minus 1.0%; Average mutual fund minus 1.7%; Bad mutual fund minus 4.1%; Good mutual fund plus 1.8% i.e. out-performance. The numbers come from research into the spread of historical mutual fund results.

*Critical Factor #2 - Inflation cause a difference between nominal returns and real "what is your dollar worth" returns*

Inflation is an ever-present menace that constantly reduces the net return to an investor. A high nominal return is of little benefit if inflation is even higher such as during the 1970s. That's why we believe the investor should focus on real after-inflation returns. We cannot tell which type of return the Globe quiz is referring to but our own calculation based on real returns is much closer to the Globe answer than one using nominal returns. Our chart shows that nominal returns have always exceeded real returns by a big margin. The

**blue**and

**orange**lines show nominal returns. The

**yellow line**shows the real return, which is what we believe to be the important relevant line.

*Critical Factor #3 - Compound aka geometric rate of return is lower than average aka arithmetic return*

We believe the long term investor putting his or her money in for 20 years will be interested in the end result, the growth over the period, not the average of the yearly ups and downs. If the TSX is up 10% one year and down 10% the next year, the arithmetic average is 0% but that's not what the investor who held the TSX for two years would have at the end. The compounding method works like this - $100 invested goes up 10% to $110 after year 1; then a 10% market drop would take away $11 and the end result is $99. The result in total is minus 1% or about minus 0.5% per year compounded, which would be the geometric rate of return. The geometric return will always be less than the arithmetic and the wilder the TSX swings the more the difference. Our chart shows the difference between the historical nominal arithmetic and geometric rates. It's about 1% per year. For real returns the difference is about the same 1%. The yellow line in our chart shows the net return adjusted for both inflation and the compounding method of calculating return but not fees.

*Critical Factor #4 - The Average ignores the range of possible outcomes*

The yellow line shows the compound returns from the TSX index over various 20 year periods ending December 31st of the years on the horizontal axis. The variation was anything from 2.4% ending in 1992 to more than triple that - 8.2% ending in 1997 - just five years later. As the bad joke goes, if you stick your head in the oven and your feet in a freezer, on average you will be comfortable. It so happens that an investment in T-Bills for the same time period would have produced a compound annual real return of 3.3%. As we noted regarding Question 4, probably means usually stocks out-perform, not always.

The fee-adjusted real compound returns for the various actual investment fund options would run parallel to the yellow line. To keep the chart tidier, we have inserted only the points for all the funds where the real return was highest, lowest and one in-between. For example, in the lowest year 1992, a bad-performing mutual fund would have suffered negative returns 4.1% per year lower than the index so the net positive index return of 2.4% would have become a negative 2.7% (2.4 - 4.1) per year compound loss. Ouch!

*Bottom Line*- Through most but not all of recent market history an investor holding a low cost efficient index ETF would have made anywhere from 2.1 to 7.9% before tax. Taking away taxes if held in a non-registered account at marginal rates somewhere around 30% for a mix of capital gains and dividend returns (see TaxTips.ca's marginal rates by province), the highest tax bracket investor might have achieved a net return of only1.5% or so at the low end. It's not the reasonable expectation but it could happen again. The savvy investor is cautious and conservative in forming expectations.

Disclaimer: this post is my opinion only and should not be construed as investment advice. Readers should be aware that the above comparisons are not an investment recommendation. They rest on other sources, whose accuracy is not guaranteed and the article may not interpret such results correctly. Do your homework before making any decisions and consider consulting a professional advisor.

## 2 comments:

On Q1, I agree that it makes sense to be sure of how interest is calculated, but to advertise "5-per-cent annual interest" and then fail to compound it would be lying. $1102.50 is the only reasonable answer.

On Q2, I have said myself in the past that you should only think of the after-tax portion of RRSP holdings as yours. With this way of thinking, your share grows tax-free and the government's share grows as well. However, the question doesn't ask about a gain on your share of your RRSP; it asks about a gain on the whole RRSP. It takes tortured logic to choose answer d).

MJ, If the logic seems tortured, that can only be the result of a poorly worded question that confounds the part that belongs to the government and that of the investor. Asking about the "gain on the whole RRSP" as the question does, muddies the water. It's a bit like asking how long it takes the sun to go around the earth. There is an insidious fallacious assumption in the question that the whole of the gain is subject to tax. The gain on the part belonging to the investor is taxed at zero, the gain on the part of the government is taxed at 100%, if one wants to look at it in real taxation terms. The tortured logic is in the question.

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