So You Didn't Get A 63% Return On Your Investments Last Year? The Mathematical Wonders Of Diversification

by: Matthew Salter, CFA

What?!! You didn't get a 63% return on your investments last year?! (With thoughts from King Solomon and Warren Buffett)

Just before we close the door shut on 2012, I thought it would be informative to make a quick review of the returns we saw over the last year in the major asset classes and see how holders of a typical portfolio may have fared. (We'll get to the 63% shortly.)

For the purpose of this exercise I've taken the following eight asset classes as representative of the typical asset classes a mainstream dollar-orientated investor may have included in a portfolio. The table also shows the overall return for each of the asset classes for the year with the corresponding volatility.

Asset Class Return / % Volatility / %
S&P 500 13.4 10.6
DAX 29.1 14.8
MSCI EM 15.2 19.9
Gold 7.3 16.0
Cash 0.1 0.0
US Gov 2.1 2.1
US Credit 7.8 2.3
US High Yield 13.8 4.8

An impressive set of returns!

So before moving on, let's spend a brief second kicking ourselves for not holding 100% of our investments in the DAX.

Now, given that most of the investment world was apparently scared stiff of risk last year, and fled to cash or the short end of the curve where a paltry 0.1% or so was on offer, I thought it would be interesting to look at how some reasonable alternative low-risk strategies would have fared over the last 12 months.

Distribute portions to seven, or even to eight, for you never know what calamity will strike the land.

Ecclesiastes, 11:2

As we all know from our portfolio-theory basics, diversification theory was set out by King Solomon in Ecclesiastes around two thousand years ago. More recently, Markowitz added a few equations and got a Nobel Prize. But as shown in the quote above, 2000 year-old advice is to diversify. And as King Solomon suggests, we could start by simply splitting our investment equally between the eight asset classes.

Some portfolio outcomes to show your investment advisor

So, if at the beginning of 2012 we would have equally split our investments between the eight asset classes, we would have seen a rather impressive return of just over 11% with a respectable volatility of 7.3% (beats cash at 0.1%).

But I thought we could do better than that and I ran a couple of scenario optimizations (I hope your holiday break was more exciting). I wanted to take the volatility (7.3%) that we see in an equally weighted portfolio and calculate the maximum return we could have obtained.

Even adding the additional constraint that no asset class has a less than 5% allocation, it turns out we could have achieved the same volatility as an equally weighted portfolio but returned a rather staggering 16%. To put this in perspective - it's a return higher than all but one of the asset classes, achieved by diversifying through all eight asset classes, and still with volatility in single digits.

Impressive, huh? All brought to you by the mathematical wonders of diversification.

In one other optimization scenario, I checked to see how much return we could have achieved if we'd been more risk averse and held as much as 25% in cash - with the same low volatility.

Turns out, with the same volatility target as the equally weighted portfolio we could still have obtained a staggeringly impressive 14%! - so, impressive returns and low volatility, even with a large 25% cash allocation.

So how about that 63%?

Well if your investment advisor had perfect foresight (don't they all?), he or she would have rotated all your investments into the number one performing asset of the coming month, at the beginning of each month. The investment classes you would have chosen are shown in the able below, and would have resulted in a very nice return of 63%.

Month Top Performing Asset Class
Jan Gold
Mar S&P 500
Apr US Gov
May US Gov
Jun S&P 500
Aug Gold
Oct US High Yield

I thought it was interesting to note the 'variety' of the top performing asset class each month and the fact that there was a large degree of rotation for the monthly outperformer.

But before you go and vent your frustrations at your investment advisor for not spotting the obvious winning asset class every month (even more so if your investment advisor is yourself), it's worth bearing in mind at this stage the words of the great Warren Buffett:

I know people who have a lot of money and they get testimonial dinners and they get hospital wings named after them. But the truth is that nobody in the world loves them. If you get to my age in life and nobody thinks well of you, I don't care how big your bank account is, your life is a disaster.

So, with those words from King Solomon, Warren Buffett and myself, here's wishing you a great 2013!

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.

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