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!

Cheers

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

S (and) P/TSX INDEX VERSUS DOWJONES INDUSTRIAL AVERAGE AND LET’S ADD INFLATION!

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.

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!

“Value for Money” with KIA – Looks and Loyalty Locked-in

KIA Optima
KIA Optima

Cars with the most brand-loyal buyers

Forbes – Jim Gorzelany | Forbes
Keeping existing customers is a hallmark to success in any business, and it’s especially important in the automotive industry, where the average product costs well over $30,000 and the typical ownership cycle is five or more years.

While automakers in the luxury segment are often thought of as enjoying among the most loyal customers in the business, the top names in this regard are all mainstream makes, according to a just-released report based on second-quarter 2011 sales compiled by Experian Automotive in Schaumburg, Ill.

Data shows that Kia currently boasts the most loyal owner body, with nearly 48 per cent of buyers returning to the brand this year. Ford is second highest with 46.5 per cent repeat business. Chevrolet, Hyundai, Toyota and Honda all registered around 40 per cent brand loyalty, with Subaru bringing back buyers at the rate of around 36 per cent.

Among luxury automakers, the highest-ranking brands were Mercedes-Benz with 34.8 per cent repeat buyers, BMW at 31.7 per cent, Porsche at 23 per cent and Jaguar at 16 per cent.

Kia’s parent company Hyundai Motor Group posted a corporate loyalty rate of 49.6 per cent, according to Experian’s data, just edging out Ford Motor Co. at 48.1 per cent and General Motors at 47.6 per cent.

“According to our latest market report, Hyundai Motor Group has been making strides in customer loyalty for several years,” says Jeffrey Anderson, director of consulting and analytics for Experian Automotive. “In North America, both Kia and Hyundai have made improvements in vehicle styling and quality among both brands. This has clearly helped them gain and maintain a strong and loyal customer base.”

Three Kia models ranked among the top 10 vehicles having the most brand loyalty in Experian’s report, including the list-leading Kia Forte compact sedan at 68 per cent, along with the Soul compact wagon and the two-door compact Forte Koup.

Seven out of 10 of the models in Experian’s list were comprised of mainstream domestic-brand models, topped by the Chevrolet Cruze in second place with 64 per cent brand loyalty. The remainder were Ford models, including the subcompact Fiesta, the midsize Fusion sedan, the seven-passenger Flex crossover SUV, the Taurus full-size sedan and the compact Focus.

Experian’s study also concluded that among automotive segments, full-size truck owners were the most likely to purchase another big pickup, registering 58.6 repeat business during the second quarter of 2011. Owners of hybrid cars trade in for other hybrids at the rate of 43 per cent, as do those buying premium crossover SUVs. The least brand-loyal were found to sports car owners, with just 21 per cent buying another equally racy model, and those driving mid-range SUVs – a segment that been steadily losing traction to car-based crossovers in recent years – at 21 per cent.