What happens to Average and CAGR when deposits are made every year?

So let’s go back and do the next problem in looking at averages and CAGR – as noted previously, I am going to ignore Median results as they are completely without any justifiable foundation. So here we have the same rates and sequence of returns with the only difference being the addition of $50.00 to the fund each year. As you would expect, the end result in terms of dollars is higher – no surprise.

However, check out the CAGR – IT HAS DROPPED from the 5.38% in the previous blog! Why – because there is an ever increasing amount of capital and the compounding effect of the ups and downs – particularly the downs, result in a lower overall calculated Compound Annual Rate of Growth – something that most people do not expect.

Year Rate . . . . . . .$1,000.00
1992 . . .7.8 % . . . . . .$1,131.90
1993 . . -4.6 % . . . . . .$1,127.53
1994 . . 29.0 % . . . . . .$1,519.02
1995 . . -2.5 % . . . . . .$1,529.79
1996 . .11.9 % . . . . . .$1,767.79
1997 . .25.7 % . . . . . .$2,284.96
1998 . .13.0 % . . . . . .$2,638.50
1999 . . -3.2 % . . . . . .$2,602.47
2000 . .19.7 % . . . . . .$3,175.01
2001 . . .6.2 % . . . . . .$3,424.96
2002 . .-13.9 % . . . . . .$2,991.94
2003 . .-14.0 % . . . . . .$2,616.07
2004 . . 24.3 % . . . . . .$3,313.92
2005 . . 12.5 % . . . . . .$3,784.41
2006 . . 21.9 % . . . . . .$4,674.15
2007 . . 14.5 % . . . . . .$5,409.15
2008 . . .7.2 % . . . . . .$5,852.21
2009 . .-35.0 % . . . . . .$3,836.44
2010 . . 30.7 % . . . . . .$5,079.57
2011 . .-14.4 % . . . . . .$4,390.91

Average . . .6.84 % . . . . . .$5,907.68

CAGR . . . . 5.01 % . . . . . .$4,390.91

As you can see the difference between the AVERAGE growth rate and the CAGR has now WIDENED to 1.83% – it may not seem like a lot, but in real dollar terms it is! If you re-run this table and substitute the Average Growth Rate of 6.84%, the resulting value after 20 years is $5,907.68 – a difference of $1,516.77 – or an increase of 33.5% over the actual value using the CAGR or the variable growth rates from the table. What a horrendous error rate!!

How can a potential error rate of this magnitude be justified in any financial plan – retirement, estate or any other component?? All I can suggest is that if you are going to use average rates, you will need plenty of E & O coverage within the next few years!

I am going to presume that readers are now satisfied with my statement that using historical average rates for forward-looking assumptions is a fools game – but remember, this discussion isn’t over as we have to examine the impact of inflation and then taxes – then to complicate matters I am going to compare the sequencing of returns during the both the accumulation phase and the withdrawal or decumulation phase of financial plans. More fun and games with numbers – I am going to stay with the same assumed growth rates in this table – but simply flip them end for end – and see what – if any difference this has on the end results!


Average, Mean/Median and Compound Annual Growth Rate – what is the difference?

Greetings once again and welcome to the next discussion on these topics. I have created a small table (shown below) to illustrate the differences using a simple representative 20-year period that overlaps the market events of mid-2000 years. Charts and tables that project growth rates over long periods of time are always suspect, but we need to start somewhere. I have chosen 20 years as a period to which most people can relate. Most industry charts cover periods of 60 years and longer and show calculated results going back to day one – while interesting, I feel they are of very little value and clients find them confusing and relating to that duration is hard.

Average versus Median versus Compound Annual Growth Rate – initial investment of $1,000.00 January 1st, 1992.

1992 . . . . . . . 7.8 % $1,078.00
1993 . . . . . . .-4.6 % $1,028.41
1994 . . . . . . .29.0 % $1,326.65
1995 . . . . . . .-2.5 % $1,293.49
1996 . . . . . . .11.9 % $1,447.41
1997 . . . . . . .25.7 % $1,819.39
1998 . . . . . . .13.0 % $2,055.92
1999 . . . . . . .-3.2 % $1,990.13
2000 . . . . . . .19.7 % $2,382.18
2001 . . . . . . . .6.2 % $2,529.88
2002 . . . . . . -13.9 % $2,178.22
2003 . . . . . . -14.0 % $1,873.27
2004 . . . . . . .24.3 % $2,328.48
2005 . . . . . . .12.5 % $2,619.54
2006 . . . . . . .21.9 % $3,193.22
2007 . . . . . . .14.5 % $3,656.23
2008 . . . . . . . .7.2 % $3,919.48
2009 . . . . . . -35.0 % $2,547.66
2010 . . . . . . .30.7 % $3,329.79
2011 . . . . . . -14.4 % $2,850.30

Average . . . . .6.84 % $3,755.58

Median . . . . .9.85 % $6,546.38

CAGR . . . . . . 5.38 % $2,850.30

Total Growth Rate includes Interest, Dividend, Capital Gains and Capital Losses for a nominal portfolio based on 100% of the S&P/TSX. Rates are for illustration purposes only.

A simple average of the Annual Growth rates, results in a number of 6.84%, the median/mean is 9.85% while the actual Compound Annual Growth Rate equates to 5.38%. Please note the comments/disclaimer at the bottom of the table.

So now the question becomes, which rate do we use for financial, insurance and estate planning – assuming that the portfolio described matches the risk and KYC profile of the client.

The mean or median rate is obviously not valid as this simply means that half the returns were higher than 9.85% and half were lower – and the answer is really – so what! That leaves the average or the CAGR.

The table shows that if we use the average rate of 6.84% and compound that for the 20 years, you or your client will only have $3,755.58 – significantly MORE than the actual result of $2,850.30 using the CAGR of 5.38%. An argument can be made for using either one, but speaking personally, my comfort with higher rates has reduced over my career and I would always use the LOWER of the two numbers and would recommend this approach to both consumers and advisors. If you use the lower rate, you are unlikely to be disappointed while using the higher figure introduces a higher level of uncertainty into all calculations. I will point out – that I am not satisfied with using the 5.38% rate either as you will see in the next couple of blogs – too many uncertainties still arise – but 5.38% is at least something closer to reality that what I see being used in most financial planning scenarios, software and insurance illustrations.

This discussion is far from over – there are four other issues to discuss in future blogs: first – what about the effects of inflation on the results; second – what about the impact of income taxes; third – so far I have only looked at a single lump sum deposit – what happens with periodic deposits or withdrawals; fourth – what are the effects of reversing this illustrated sequence of results?

BTW, here is a link to a website that can do all of these financial calculations without requiring a financial calculator – I use it regularly! The S&P/TSX Total Returns I pulled from Jim Otar’s Retirement Calculator – I provide a link to his excellent website in an earlier blog. http://bing.search.sympatico.ca/?q=calculating%20rate%20of%20return&mkt=en-ca&setLang=en-CA


It has been said that there are Liars, Damn Liars and Statisticians – and you can throw in Economists for good measure! Another approach is to ask a mathematician, an accountant and an actuary the result of the formula 2 plus 2 equals what? The mathematician will say 4, the accountant will say that depends (explains a lot about some financial reporting!) and the actuary will ask, what do you want it to equal? Through creative choices, numbers can be made to say just about anything a person desires, if you apply enough “logic” – no matter how flimsy!

Apples to bananas! As we explore the effects of growth rate assumptions on financial, estate and insurance planning, I am going to take a slight detour to briefly discuss two benchmarks commonly in use – the most popular being the S&P/TSX – which is an INDEX, and the DJIA which is an AVERAGE – they are NOT interchangeable nor do they measure the same things!

The DJIA measures the 30 largest (by market cap) US Corporations – subject to annual reviews and adjustments. The S&P/TSX measures (allegedly) the 300 largest (by market cap and not necessarily purely Canadian) companies trading on the TSX. At last count, there are apparently about 290 companies included in the S&P/TSX Index. Finally, one is expressed in CDN currency and the other in US currency so variations in the DJIA, as usually seen in Canada, also reflect exchange rate movements.

As you can see, the DJIA is only a very narrow “measurement” of market value and movement while the S&P/TSX is, at least in theory, a reflection of a much broader market. Very different measurements yet for some reason they are entwined as being very similar, if not identical – and not just by the media, many in the financial services industry are also guilty of this “grouping” for comparison purposes.

The closest US market measurement to the S&P/TSX Index is the S&P 500 Index – as the name implies, measuring the movement of the largest 500 US Companies – also in US Currency and then converted to CDN $ for use here – again adding exchange rate movements to the changing index values.

Many people are unaware that we (Canadians) do have a “large cap” index that is SIMILAR, but not identical to the DJIA – it is the TSX60 – which measures the 60 largest companies trading in Toronto. So, if comparisons about movements, trends, etc. are to be made, it is certainly far more appropriate to compare movements (net of currency exchange effects), between the DJIA and the TSX60. Other major exchanges around the world also have narrower, large cap sub-indices similar to the TSX 60.

For more specific information about the compositions of the various indices and market averages, please refer to their specific websites – or have fun with Wikipedia.

Inflation has been around since someone started to track changes in prices of various goods and services. In Canada, we use the Consumer Price Index as measured by Statistics Canada. All details can be found on their website plus additional information on Wikipedia. Obviously, the basket of “goods and services” in use today is very different than 50 years ago – even 20 years ago – consumer choices and options change – therefore so does the “basket”. In Canada, inflation is separated into a “full measure” of everything and then a variety of sub-indices such as “core” inflation along with others such Health Care, Education, Recreation, etc.

Comparisons between inflation rates amongst various countries is close to impossible – each country is measuring different items, then of course, we may have currency issues that could also affect published rates – check the websites for each country to determine how currency may impact published results.

All too often, people in our industry and in some cases the media, tend to use a single inflation assumption in our planning – which is patently incorrect. When people retire, the effects of inflation are typically higher due to probable higher costs for Health Care and Recreation, while some aspects of the total inflation rate will drop such as business transportation.

I will discuss inflation in planning in more detail in a future blog – my only purpose here is to caution people to be careful about your chosen basis for assumptions during different phases of the planning process – different rates for education costs, health care, recreation, housing, etc. are all appropriate – a single presumption is not!

BTW, I watch Business News Network each morning to catch Marty, Frances and Michael plus their various guests – plus I regularly use their website – www.bnn.ca – for other updates and information on various indices – including the TSX60.

How to Choose a Financial Advisor

No Hype Book Cover Excerpted from No Hype – The Straight Goods on Investing Your Money By Gail BebeeISBN: 978-0-9784455-0-8
Publisher: The Ganneth CompanyAll the investing basics for Canadians from a savvy financial industry outsider
Gail Bebee photo Gail Bebee is Canada’s Independent Voice on Personal Finance. She is a personal finance writer, teacher and speaker. You can contact her at gbebee@gailbebee.com; her website is www.gailbebee.com.


If you are like the average Canadian, you want and need help with your investments. Your challenge is to find the right hired help, a financial advisor who suits your personal circumstances.

In the marketplace, most financial services companies offer individual investors a bundled package of investment advice and investment transaction services. Whether or not you opt for one of these bundles, you need to think of these two services separately in order to make the best investment decisions for your personal situation.

Entire books have been written on how to choose a financial advisor. In my opinion, this is overkill since there are only a few choices for obtaining advice. You can be your own financial advisor, i.e., hire yourself. You can hire a financial advisor who does not sell financial products and is paid by charging the client a fee for service. You can hire a financial advisor who is associated with a stockbroker, bank, deposit broker, insurance company or mutual fund company that sells financial products. Finally, you can use a financial advisor for part of your portfolio and be your own advisor for the remainder.

Choosing a financial advisor is a bit like committing to a marriage. You want to get it right because divorce is painful. To help you avoid the pain, use the following guide to select the financial advisor who is right for you.

1.    Decide how much time and effort you are honestly committed to spending to:
•    become knowledgeable about investing,
•    keep current on financial matters and the stock market, and
•    set up and maintain your investing portfolio.
Be brutally honest with yourself. Will you really dedicate the time to become sufficiently knowledgeable about financial matters to be your own financial advisor? Do you have the time to keep current on investing issues? Do you have the personal discipline to monitor your investments on an ongoing basis, reach decisions to buy or sell investments and then act on these decisions?
If you are a disciplined person who will spend the necessary time, then being your own financial advisor is an option. If you decide that you do need help, then use the following guide to select the financial advisor who is right for you.

2.    Decide how much money you have to invest now and estimate how much additional money you will be investing over the next few years. You’ll need to know these numbers because some financial advisors only accept clients with a certain minimum amount of money to invest.

3.    If you don’t have a complete financial plan that covers all aspects of your personal finances, consider completing one before proceeding with the selection of a financial advisor for your investments. For this task, I recommend using a professional financial planner such as a person who holds the Certified Financial Planner (CFP) designation.

4.    Write down what you expect a financial advisor to do for you. Typical expectations for a financial advisor might include some or all of the items listed here:
•    Provide a written overall investment strategy that includes realistic projected return rates and meets your particular needs and objectives.
•    Provide specific investment recommendations (purchase and sale) consistent with your investment strategy and the reasons for the recommendation, including the risks and benefits.
•    Answer any questions about investing and provide ongoing education about investing.
•    Provide advice on the tax implications of different types of investments available and the investments he/she recommends.
•    Provide referrals to other professionals, such as an insurance agent or tax accountant, where appropriate to meet your investing needs.
•    Be easily accessible by telephone.
•    Call monthly with an update.
•    Meet quarterly to review your investments.
•    Contact you promptly if current events (e.g., stock market crash, a sudden sizeable rise in interest rates) have a major impact on your investments.
•    Conduct the purchase and sale of investments in a timely manner at the best available price.
•    Provide clear, understandable and complete written statements of your investments and return rates.
•    Disclose all costs, commissions and fees.

5.    Make a list of questions for a potential financial advisor. Here are some examples of the questions you should ask.
•    What are your qualifications? Look for:
–       a financial designation or designations that fit your specific needs;
–       several years of experience as a financial advisor;
–       knowledgeable in tax laws, as tax plays a major role in the success of your investments;
–       a license to sell at least mutual funds and fixed income products like GICs, as well as any other types of investments of interest to you;
–       a commitment to ongoing education and upgrading.

•    Who else is on your team? Who is your backup if you’re not in the office?
•    How long has your firm been in business? Is the firm a member of an investor protection insurance fund?
•    Does your firm sell investments as well as provide advice? If so, what products are offered?
•    What is your investment philosophy?
•    Do you personally buy and sell financial products for clients? If so, what products are you qualified to sell and what products do you typically recommend?
•    Do you prepare an investment plan for each of your clients based on each client’s personal situation?
•    How often will we talk and/or meet? Where will our meetings be held?
•    How quickly will you respond if I call or email you?
•    How are you paid? What fees does your firm charge for account administration?
•    What research, newsletters, etc., do you and your firm provide to clients? Do you hold educational seminars for clients?
•    What kind of account statements do you provide, and how frequently?
•    How will I know how well my investments are performing? What performance benchmarks do you use?
•    Do you provide statements with the original cost, current market value and return rate of each investment? Will you provide me with an annual return rate for my overall portfolio?
•    What is your firm’s procedure for handling client complaints?

6.    Develop a list of potential advisors. Here are some ways to identify candidates.
•    Canvass your family, friends and business associates to get the names of advisors they would recommend.
•    Find out what financial advisors are available at the bank where you have your account.
•    Consult the “find an advisor” section of the web site of professional financial advisor organizations.
•    Scan the financial media (business sections of newspapers, financial web sites, magazines, etc.) for articles referencing or written by financial advisors.

7.    Sift through the leads you have amassed and make a short list of two or three advisors. Use the questions you have drafted to assist in selecting the candidates.

8.    Interview all the advisors on your short list. Ask each candidate the same questions and take notes on how each one answers.

9.    Take some time to reflect on the interviews and review your interview notes before selecting the best candidate.

10.    Perform your due diligence. Confirm that the chosen advisor and his/her firm have the qualifications and provide the services they have indicated that they offer.

11.    Contact the chosen advisor, indicate your interest in hiring him/her and arrange a meeting to further discuss and finalize your relationship.
Request that the advisor provide a written agreement, usually called an investment policy statement, detailing the terms you have agreed upon. The agreement should cover such things as:
•    the level of risk you are willing to take,
•    the target asset allocation, allowable range in each asset class and process for maintaining the targeted allocation,
•    the range of the expected return rate of your portfolio,
•    any investment restrictions,
•    all fees and when they are charged,
•    frequency and nature of contact with the advisor, and
•    reporting on the performance of your investments including benchmarks used for comparison.

12.    After six months with the new advisor, review the advisor’s performance and decide if he/she has met your expectations. If you are not satisfied, do not hesitate to change advisors. The new advisor should take care of the paperwork required to transfer your account.

So – average interest and growth rates – are they realistic or do they create misunderstandings for both clients and advisors?

Ever since I was a lad (yes, that long ago), all calculations for determining amounts of insurance, how fast savings and investments grew and how retirement income rates were deterimined, have used “average” rates of return – not even median rates – just average rates. And for about 100 years or so, people seeemed happy with that approach until the 1970s and 80s came along with rampant inflation, outlandish rates of return and then a wonderful market “correction” in the latter part of 1987.

No-one knew quite what to do, but a couple of smart young men came up with the idea to put this all on a chart so people could at least examine history – in one place – and hopefully make some better choices and assumptions while planning for their futures – and the ANDEX (copyright) chart was born! I loved it immediately (lots of pretty coloured lines and graphics too – I am easily amused)! Fortunately for our industry and our clients, this chart is not just still available, it has been expanded and updated to include even more useful information under the Morningstar banner (and no, I don’t get any compensation for saying this!

These charts (and other following competitor versions) also included the “average” rates of return for the various market segments for various time periods. While interesting to see the changes over time, I feel these “averages” actually took away from the validity of the material – which was to show that segments of the markets move randomly and that while “average” projections were interesting, they weren’t overly valuable for making long-term projections. These charts also provided all of the necessary proof that GICs and savings bonds were neither adequate on their own and that in order for a client to enjoy any reasonable probability of achieving their goals, other assets and products had to be considered.

Having received a great amount of both theoretical and experiencial education in this phenomenon, I have come to the conclusion – despite having been guilty (along with the rest of our industry) of using average growth rates in everything from growth in universal life policies, estimating future values for investments and planning for both retirement and estate distributions – sometimes 40 years into the future – this practice is now foolhardy in the extreme!

Stay tuned for the next collection of wandering thoughts as I explore this further using some actual numbers!

Welcome to my bog and some random thoughts!

As the newst blogger here, I would like to say that I am looking forward to sharing some thoughts and opinions (most of which are politically correct but some aren’t!) that will challenge a lot of conventional wisdom within the financial community and the industry at large. I welcome comments (pro and con) as well as suggestions for future commentary.

For my next blog, I will offer some opinions on “traditional” financial planning using average interest/growth rate assumptions and the move along to Monte Carlo simulations – are they really a major improvement? If anyone wants a “sneak preview” on those thoughts, I refer you to Jim Otar’s excellent website as noted under TAGS. As a follow-on, I next plan to look at what a reasonable rate (if you must use a fixed rate), makes sense and will stand the test of time!

Remember, I did say I was going to challenge some long-held beliefes and principals – to get us all thinking about how we work with our clients and their future plans!

Cheers Boom Boom

Brenda Hiscock – You and Your Money – Financial Blogger – coming soon!

I am a Certified Financial Planner (CFP), and have also completed my Registered Health Underwriter (RHU) designation, which provides me with a specialty in the areas of Disability, Critical Illness and Long Term Care Insurance. I also teach part time at Seneca College, where I teach Investments, and I also teach a Life Insurance Licensing prep program from time to time. This ensures that my knowledge is always current and up to date.

View my recent articles and profile page.