(Alternative Title: Back to Grade School Arithmetic)

The investing year of 2008 dealt a horrible blow to portfolio values, inspiring the Financial Press to Chicken Little scenarios, sending some retirees back to work and causing many people to cast aspersions on equity investing. As it happened, starting in March 2009, the markets roared back, appeasing investors after a fairly short six months of angst.

Our Fall 2009 article posited a Three Step Strategy for investing peace. In summary, this included a) having a sense of what minimum long term rate-of-return you need to happily get through life and b) tracking your actual long term compound rate-of- return to compare to a).

But first, lets refresh our memories on some grade school math, and remember the old adage “ Lies, damn lies and statistics”. Lets start with “percentage-up” and “percentage-down”. For instance, assume a $1,000 portfolio experiences a 20% decline (“percentage-down), dropping it to $800. It will take an increase next year of 25% (“percentage-up”) to restore it to the $1,000. A 20% increase (the amount of the decline) will only return the portfolio to $960.

Note that for the net-zero pairing over two years, in this case 25% up and 20% down, it doesn’t matter in which order they appear—the loss followed by the gain, or the gain followed by the loss — the two-year net result is still zero.

The formula to determine what return in year 2 offsets the return in year 1 (“R1”) is 1/((1/R1+1).

Another lesson is the impact of off-setting net-zero years on the long term compound return. Two years that offset each other bring you back to where you were, but that means having two years which didn’t get you anywhere! If your required long term rate-of-return is 5%, then you expect $1,000 to become $1,102.50 two years later (that equals two years of returns plus compounding). If, instead, you experienced a calamity year and were then fortunate enough to achieve a net-zero recovery of that in the following year, you only got back to $1,000, and didn’t add the extra $102.50. So, you have fallen behind your goal.

A further lesson is that the punishment of two net-zero years on your long-term attainment varies with the duration of your life-time investing history. The longer that history, the smaller will be the long term impact; and the shorter that history, the greater will be the long term impact. The following table walks you through 2008-9-10 for select client portfolios: (see following commentary)

The first three columns show the simple returns in each of these past three years. The two compound columns on the far right show the portfolios’ long term returns before, and then after, the 2008 calamity/2009 recovery. In each example, you see that the long term return has taken a drop. For long held portfolios, the drop was approx 1%, but for newer portfolios the impact typically was in excess of 3%….. in other words, fewer averaging years were available to fall back on. The shaded column in the middle makes a notional calculation of what recovery rate was required in 2010 to a) recover the 2009 loss AND b) keep the same 2008 long term compound return after 2010. You will see that those notional returns for 2010 typically needed to be in the 40% range, whereas in fact they were only in the 20% range. So, long term compound returns have taken a hit for now.

These kinds of calculations and observations are subject to start-and-end bias… in other words, what range of investing years are counted in your compound return. If you start tracking your compound return through a bull market, your compound return will start high, and subsequent calamity years will cause a large drawback. Further, at what month-end are they determined? Our published monthly Trendlines show how much rolling one-year returns vary month-by-month through the year.

The problem with our Three-Step Strategy is that, even for long term investors, the financial industry tends not to produce the long term compound statistic for the investor. Most investors will never know what their compound return was, starting from the day they first put savings aside and until they pass away! At Trivest, we make these calculations for all of our portfolios, but they can only commence from when you join us. The other problem with following our Three-Step Strategy is that you need to have gone through the formal financial planning process to see what compound return you need to deliver a desired lifestyle and legacy estate for your heirs.


On to another fundamental investing matter to rest comfortably in a stormy world….what is your asset allocation strategy? A healthy proportion of fixed income in your portfolio typically will offset the swings experienced in the equity markets. For instance, the correlation between Canadian bond returns and Canadian equity returns has been only 28% since 1994.

The following table shows one-year rates of return produced by bond portfolios for select client portfolios in 2009 vs 2010. Remember that equity markets were giving serious negative returns in 2009 and serious positive returns in 2010, as shown by the global equity benchmarks in the adjoining columns. Also note the different cut-off points in the far left column—short term interest rate movements in 2010 have had profound effects on the rolling one-year returns, eg. from 6.7% in February to 3.2% in March! The average maturity of the bond portfolio also will have an impact-look at the two February statistics in 2010– 6.7% vs 3.9%.

Article posted August, 2010