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    June 2012
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    Average, Mean/Median and Compound Annual Growth Rate – what is the difference?

    Ian Whiting

    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

    The MONEY® Network