In my previous post I described the stock and bond markets by analogy with a casino, but you might reasonably question the validity of that analogy. Are market returns really as unpredictable as coin flips? The real payoff probability distributions obviously aren’t binary; what do they actually look like?
Math != Truth
But first, another word of warning, especially if you come from a background in the physical sciences. In social science (including finance and economics) and more generally in complex systems (like biology, and climate modeling) math plays a somewhat different role than in does in physics and its scientific progeny. We are fortunate to live in a universe which seems to behave in mathematically elegant ways at a very basic level. Our mathematical constructs appear capable, in many cases, of corresponding pretty much exactly to the underlying physics of the world. Because of this, we in the physical sciences often think of our (experimentally validated) mathematical descriptions of phenomena as Truth. Sometimes we turn out to have been overconfident, and we end up wrong, but often we’re close enough that it just doesn’t matter that much in a practical sense. The Voyager, Galileo and Cassini spacecraft, which have explored the outer solar system, have been guided by Newtonian physics, long after Einstein had shown Newton to be wrong. We knew this was okay, because we knew under what circumstances Newton’s approximation of reality broke down, and we knew that none of these spacecraft were going to be experiencing such circumstances.
In naturally occurring complex systems, like ecologies or markets, the situation is somewhat different. Here, math is often used as a descriptive language, to say explicitly what it is we have observed. Making the leap to assuming that such an empirical description really encapsulates the entire space of underlying dynamics and possibilities is risky at best, and occasionally catastrophically wrong, as Long Term Capital Management discovered in 1997… and everyone else discovered in late 2008 and early 2009. This isn’t to say that math is a useless tool here, but rather that it’s somewhat less sacred in this domain than in the realm of James Clerk Maxwell.
History as a guide
With the above in mind, we can look at historical broad-market returns to get some idea of the games actually on offer in our grand casino. Vanguard actually has a wonderful little interactive info-graphic with which you can explore this data available online (and from which I painstakingly cribbed the data I’ll play with below… as it’s mostly proprietary). The time series we’ve got for the period 1926-2009 are broad US stocks (e.g. the e S&P 500 index), high credit quality US corporate bonds, and “cash”, as represented by virtually zero (credit) risk US Treasury bills. Also included for comparison is inflation, as represented by the (admittedly imperfect) CPI-U. Yes, these are all incredibly US-centric data to look at. Unfortunately international data isn’t as easy to come by. All this data is already adjusted for inflation (except of course the inflation data itself…).
So, in place of binary coin tosses, what we’ve really got is the following:
Stocks are pretty wildly variable. The value g=0.0668 (or 6.68%) in the upper left is the geometric mean of the distribution, i.e. it’s the constant interest rate you’d have to be earning to end up with the same returns, on average, as if you were drawing from this distribution. The “inter-quartile range” (iqr) is just the distance between the 25th and 75th percentiles of the distribution, a measure of its dispersion, which works well for non-Gaussian distributions with central tendencies. It’s 24.6%. So stock returns over the last century were something like 7% +/- 25%, which makes for a pretty wild ride. Bonds by comparison were downright chill:
Notice that the x-axis is only half as wide here, so this is really a much more focused pile of returns, something like 2.5% +/- 10%. The real returns on cash were pretty much indistinguishably from zero:
Inflation is, ironically, probably the only one of these four distributions you’d be willing to say might constitute a non-zero measurement if you found it in lab. Maybe that’s not too surprising, since it’s actually something the government has relatively direct control over (printing presses, etc.), and at least recently, a target for (2-3% no less).
Now of course, these asynchronous distributions aren’t the whole story. The one financial history we actually have to learn from experienced these distributions in a particular order, and the order matters. Knowing that on average over 85 years stocks have made 6.6% is nice, but it’s only really helpful in planning for retirement if you can be pretty confident that you’ll also be able to get something resembling that rate of return over your own personal time frame… which unless Aubrey de Grey has his way, will most likely not be 80 years.
This plot shows the growth of a dollar, from 1926 to 2009. Note that the y-axis is a log scale (and don’t freak out, these returns have already been adjusted for inflation, so the fact that inflation ends up above bonds doesn’t mean bonds don’t beat inflation). Based on this particular history, the only really reliable growth seems to have come from stocks, though certainly not without some headaches and stomach acid. Bonds and cash on the other hand seem to have had something like 40 years in the desert between WWII and 1980 (when inflation also picked up). Just looking at this time series, it certainly seems possible that there are secular changes in market behavior over long time periods. However, confidently attributing those changes to any particular cause is pretty difficult (this is the stuff that Finance and Economics PhDs are sometimes made of…). Was the change in 1980 the fact that the dollar de-pegged from gold? Or was it the beginning of a new wave of globalization? Or a change in securities regulations? Or a change in the way the CPI is calculated?
The problem here is that we don’t get to re-run the experiment, so it’s ultimately very hard to control for all the possible variables. We can see in retrospect that something changed, but we may never know exactly what (people still fight about what caused the Great Depression). Realizing that something was in fact changing, at the time, would be even more difficult. It’s often said that the four most expensive words in investing are “This time it’s different.”, which isn’t to suggest that things are never different, but rather that it’s way too easy to fall for that as an explanation, when the glitter and gold seems within reach, and you’ve got a great storyline telling you how to make a grab for them. It’s supremely boring, but the safest (and most often correct) thing to do is just assume that things are the same as they ever were. You will very occasionally be wrong, but oh well.
This is especially frustrating to anyone with a physical sciences background, where you can run and re-run and re-design experiments, where knowing that some interesting underlying structure exists means picking it apart and seeing how it works, and in the fullness of time, being able to predict its behavior. In messy non-repeating systems like history and markets, it often doesn’t work that way.
For instance, much ink and many bits have been spilled on the subject of whether markets are truly efficient. The efficient market hypothesis states that all available information has already been taken into account in the prices you see in the (e.g.) stock and bond markets. Behavioral economists counter that there are many observable cognitive biases in our economic transactions, which are out of step with reality and which render our markets inefficient and in theory create arbitrage opportunities for more rational actors. However, I think it’s worth noting that it is possible for a market to be inefficient without creating arbitrage opportunities because we can also be wrong in many different unpredictable ways.
From our point of view as individual investors, who ends up being right about the underlying theory is a little bit irrelevant. What we care about is optimizing for high return and low risk, using investment vehicles which are actually available to us on the market today. In practice, this generally means mutual funds. A mutual fund is just a collection of stocks and/or bonds, of which you may buy a share. In my next post… I’ll talk more about how they work and why you might want to use them, instead of just buying your own individual stocks and bonds.
However, since I’m heading to Canyonlands in Utah for 10 days here pretty soon… if you need something to entertain yourself with in the meantime, I recommend Fama and French on Luck vs. Skill in Mutual Fund Performance, and if you want more background on their simple but functional parameterization of expected portfolio returns, see the Wikipedia articles on financial beta, and the Fama-French three factor model (or even their blockbuster 1992 paper “The Cross-section of Expected Stock Returns“).