## How have different kinds of investments performed in the past? Let’s take a look, because history, even though it doesn’t predict the future, is still a good basis for adding to our understanding of investments.

In Post #15 (http://donezra.com/15-how-to-think-about-different-kinds-of-investments/) we used games to learn about investing. In this post, let’s consider a calendar year as constituting a play of each game – not because there’s any magic to calendar years, but just because it’s convenient. Figure 1 below shows returns from investing in a pool of large US companies (specifically, it reflects the S&P 500 index returns) from 1928 through 2015. Each year’s return is placed in the appropriate 10-percentage-point range, from -50% (meaning the investment lost half its value) to +60% (meaning it gained more than half of its value from the start of that year).

*Figure 1: Annual returns for S&P 500 Index, 1928-2015*

Notice that the middle portion of the range occurs with the greatest frequency, and the frequency fades away as the returns become more extreme on both the left and the right. If you think that the average annual return over the period is somewhere in the 10%-20% range, you’d be right: it’s actually 11.4%.

There’s a statistic called the “standard deviation” that is often used for distributions with this sort of shape. It leaves out the extremes on the two sides, and searches for the range that covers roughly the middle two-thirds of the results. In this case the standard deviation is 19.8%. (Never mind how it’s calculated.) This is a neat way of saying that roughly two-thirds of the outcomes were in the range from 11.4%+19.8% (which adds up to roughly 30%) to 11.4%-19.8% (adding up to roughly -10%). Check it out: yes, most of the annual returns are indeed between -10% and 30%.

Another interesting result is that 64 of the 88 years resulted in a positive return (that is, 73% or roughly three-quarters of the time).

The same source (pages.stern.nyu.edu, retrieved on May 14, 2016) also gave me the numbers for inflation each year, and I calculated the “real” returns, which is a jargon expression meaning the excess of each annual return over that year’s inflation. The average real return was 8.2%, and since the shape of the distribution is pretty much identical, it’s not a surprise that the standard deviation is an almost identical 19.7%. But the proportion of positive years shrinks a little, to 67%. That is, roughly two-thirds of the time the annual return exceeded the year’s inflation.

In fact, most of the time it’s the real return we’re interested in, because for a return to be really useful, it ought to exceed inflation, so that the investment enables us to purchase more at the end of the year than we could at the start. That’s why we invest. So from now on I’ll discuss only real returns.

How about if we look not at individual years, but at chunks of 5 or 10 consecutive years? Some of the interesting results are shown in Table 1.

__Table 1: Summary statistics, S&P 500 real returns, 1928-2015__

Best single year 53.7% (1954)

Worst single year -38.0% (1931)

Average return[1] 8.2%

Standard deviation 19.7%

Proportion of positive single years 67%

Best 5 consecutive years (annualized)[2] 25.3% (1995-1999)

Worst 5 consecutive years (annualized) -10.3% (1937-1941)

Proportion of positive periods of 5 consec years 76%

Best 10 consecutive years (annualized) 17.9% (1949-1958)

Worst 10 consecutive years (annualized) -3.8% (1999-2008)

Proportion of positive periods of 10 consec years 88%

With 5 and 10 year chunks, the best and worst aren’t nearly so extreme as the one-year numbers. The proportion of positive periods increases – but still doesn’t reach 100%. I even tried 15-year periods, and the positive proportion goes up to 96% – but that’s still not 100%.

Observe that, if you think of investing in US equities as a good strategy, you find that the longer you play, the more likely you are to win (that is, achieve a positive average real return), but even a good strategy can have bad outcomes – and to find, after 10 or (worse) 15 years that your returns still haven’t matched inflation will undoubtedly result in a very bad feeling. Yes, there are no guarantees, and no easy money. (Remember those lessons from Post #15?)

How about if you invested more broadly than the US equity market: in the developed markets of the world, including the US? I analyzed the results of investing in the MSCI World Index from 1970 (when the index was first compiled — source: Wikipedia). The results are shown in Table 2. Of course, this is a shorter period. But two things make the numbers worth showing. One is that they’re not dramatically different from the US numbers over the same period. (Take my word for it, even though I haven’t shown the US results for that period.) The other is that they’re not dramatically different from the US numbers over the longer period starting in 1928.[3]

__Table 2: Summary statistics, MSCI World real returns, 1970-2015__

Best single year 31.3% (2003)

Worst single year -40.5% (2008)

Average return 6.8%

Standard deviation 17.7%

Proportion of positive single years 70%

Best 5 consecutive years (annualized) 23.5% (1985-1989)

Worst 5 consecutive years (annualized) -7.0% (1970-1974)

Proportion of positive periods of 5 consec years 71%

Best 10 consecutive years (annualized) 14.1% (1980-1989)

Worst 10 consecutive years (annualized) -2.7% (1999-2008)

Proportion of positive periods of 10 consec years 86%

OK, we’ve looked at investing in equities (growth assets) in some detail. How about the supposedly safe assets, Treasury bills?

It won’t surprise you to know that the equivalent of Figure 1 for Treasury bills is just two columns. The mammoth one is the range 0%-10%, and there are also a number of years in the 10%-20% range, reflecting years in which inflation was high. Again, let’s focus on real returns, that is, the extent to which Treasury bills produced returns that outpaced inflation. The results are shown in Table 3.

__Table 3: Summary statistics, Treasury bills real returns, 1928-2015__

Best single year 12.8% (1931)

Worst single year -8.9% (1941)

Average return 0.5%

Standard deviation 3.9%

Proportion of positive single years 61%

Best 5 consecutive years (annualized) 8.7% (1928-1932)

Worst 5 consecutive years (annualized) -6.0% (1942-1946)

Proportion of positive periods of 5 consec years 61%

Best 10 consecutive years (annualized) 3.8% (1981-1990)

Worst 10 consecutive years (annualized) -5.0% (1941-1950)

Proportion of positive periods of 10 consec years 60%

Let’s interpret these results.

Treasury bill real returns (for annual, 5-year and 10-year periods) are all in a much narrower range than those of equities, and their standard deviation is also very much smaller. Both of those observations demonstrate that they have been more predictable (and in that sense, safer) than equity real returns. To compensate for that, their average return has been very much smaller than that of equities. In fact, on average T-bill returns are close to zero, relative to inflation.

This shouldn’t be a surprise. Given how much greater is the scope of equity investing to produce a serious loss, why on earth would you invest in equities unless the compensation is a potential gain that’s very much greater than for T-bills? And that too is one of the principles we derived in Post #15: the higher the potential loss, the higher the potential gain that investors demand in order to be willing to invest in equities.

Two final thoughts.

One is that I’ve said nothing about bonds. That’s because in a sense they’re an in-between asset class, neither particularly growthy nor particularly safe. You therefore wouldn’t be astonished to learn that their statistics are in between those of T-bills and equities.

The other is that there’s actually a fifth lesson (in addition to the four in Post #15) that we should see in the numbers. *The past has not always been a reliable guide to the future*.

Here’s something you can try yourself. In Figure 1, find the year of your birth, or the year of a parent’s birth, if it’s no earlier than 1928. See which column it appears in. Then check the following year, and the one after, and so on for 20 years or so. You won’t find a pattern appearing, of good years routinely following bad years (or the reverse), or of two good years followed by two bad ones (or the reverse), or anything that offers a formula for predictability. Too bad. It’s almost as if the pattern is random.

***

## Takeaway

*Historically, equities have behaved like a good growth-oriented strategy, Treasury bills like a good safety-oriented strategy. But neither strategy is absolutely safe. And the past hasn’t been a good predictor of the near-term future.*

***

[1] This is the arithmetic average, not the geometric average. Most people don’t understand the difference, and it isn’t necessary for our purposes. I mention the difference only for the techies.

[2] These “annualized” (that is, annual average) numbers are geometric averages.

[3] For the global investments I used the returns in US dollars and adjusted for US inflation.

### 4 Comments

I have written about retirement planning before and some of that material also relates to topics or issues that are being discussed here. Where relevant I draw on material from three sources: The Retirement Plan Solution (co-authored with Bob Collie and Matt Smith, published by John Wiley & Sons, Inc., 2009), my foreword to Someday Rich (by Timothy Noonan and Matt Smith, also published by Wiley, 2012), and my occasional column The Art of Investment in the FT Money supplement of The Financial Times, published in the UK. I am grateful to the other authors and to The Financial Times for permission to use the material here.

Don, you know how much I like statistics and history, and when you put them both together in a chart, my mouth starts to water.

Very nice, if you happen to be an American, or investing in the U.S. market. For your readers, here are the same statistics for Canada (here I start with 1924 — thanks to the Canadian Institute of Actuaries — and go to 2017; as a result, I have 94 observations): the number of positive years is 69 — resulting in the percentage of “positive” years of 73.4%. Exactly, and probably not surprising, what you had for the U.S. However, decade-by-decade, the results are quite different.

1930s. 1940s. 1950s. 1960s. 1970s. 1980s. 1990s. 2000s

Canada. 0.9. 9.1. 15.6. 10.0. 10.4. 12.2. 10.6. 6.6

U.S. -0.1. 9.2. 19.5. 7.8. 5.7. 17.5. 18.2. 1.4.

For five decades in a row, Canada had delivered consecutive double-digit returns. The U.S., only two decades of back-to-back double digits. As well, the Eighties and Nineties in the U.S. was the high-tech era — which Canada really didn’t participate in.

These are nominal numbers, didn’t have time to do “real”.

Encore, JJ, encore! I can’t wait for further details — particularly if they follow the format of the tables of real returns in this post, so that Canadian returns will be directly comparable with US returns. There’s no magic about US returns, it’s just that they come from the world’s largest national equity market. In fact, in showing results for the world index, my hope is that that will become the natural reference point, rather than US returns. But the more I can encourage readers to show their own individual country returns, the happier I’ll be. In addition, your reference to the Canadian Institute of Actuaries stats reminds me that (approaching 40 years ago, if my fallible memory serves) Colin Carlton, Keith Sharp and I wrote an early paper analyzing Canadian market returns, after a paper by James Patterson; and those papers, I believe, were part of the prompting for the Institute to start gathering and publishing market return stats in a disciplined, formal way.

You and J.J. have illustrated the benefit of diversification. For instance, in your three examples there is no consistency of best or worst five years and no overlap of a best five and a worst five. The main issue I have is the composition of some indices, such as the Canadian index. With its significant overweight in three sectors, the Canadian index does not represent a prudent benchmark for a retirement portfolio – another argument for diversification.

For those of us now in retirement, our time frame for the public equity portion of our investments is not necessarily compatible with the rewards accruing to the patient investor. As history rhymes, I wonder if there are (statistical) indicators for tweaking asset mix.

Thanks, you make a couple of very important points.

One is the need for geographical diversification. There tend to be, I think, three reasons why we tend to focus on our own country. (A) We know it best. (B) There are sometimes tax disadvantages to foreign investment. (C) There are sometimes laws or regulations limiting foreign investment. In the absence of these, the default ought to be something global, with (A), (B) and (C) then helping us to decide if some countries should be excluded from our portfolio. Of course, going global exposes us to currency risk — but that can be dealt with separately.

The other great point is that we retirees have a time horizon somewhat short of “indefinite,” and it gets shorter as we age. Yes, I think this has important consequences for our asset allocation, but they’re too involved for a quick response here, so I’ll devote a number of posts to that crucial issue. You’ve laid the groundwork!