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    July 2012
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    What happens to Average and CAGR when deposits are made every year?

    Ian Whiting

    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

    The MONEY® Network