Many people think that uncertainty washes out when you buy and hold for a long period of time. Not so, that is the fallacy of time diversification. Although the average return becomes more certain with more periods you don’t get the average return you get the total payoff and that becomes more uncertain with more periods.
To illustrate I ran 100,000 simulations of a 30 year stock market investment with a 7% return and a 20% standard deviation. The mean payoff across all 100,000 runs was $759.58 (recall the theoretical mean is $761.23 so we are spot on). But now consider the following. What percentage of returns would you guess lost money, i.e. had a total payoff after 30 years of less than $100?
After 30 years, 8.9% of all returns lost money!!! In terms of recent debates, (average) r>g does not mean that wealth accumulates automatically. Fortunes can be lost even when the averages are in your favor.
Perhaps even more surprisingly what percentage of investors would you guess earned less than the average payoff of $761.23? An amazing, 69.2% of investors earned less than the average. The median payoff in my simulation was only $446.85, so the median return was not 7% but 5.1%. The average investor earned less than the average return.
Human behavior is economic behavior. The particulars may vary, but competition for limited resources remains a constant.
- CEO Nwabudike Morgan
Along the same lines, I saw a figure today that I had been wondering about for quite some time. I always wondered what kind of returns the average stock investor got over time, figuring that it would be way below the 9% or 10% that is usually considered the "historic norm." The figure I saw was for a 20-year period up until some point in 2010 (it was a book on retirement investing and I believe it was quoting a study from some point in 1990 to some point in 2010). The figures given were an average annual return of 8.3% for the stock market but only 4.2% for the average investor who was oftentimes buying high and selling low. Ouch!
The PP performance should be a lot more predictable, primarily because of the low standard deviation but also because of the fundamental diversification across economic conditions. Shifts in the four asset classes are generally uncorrelated over time, but not random (the money has to go somewhere, so stocks or bonds generally rise when stocks fall). So the statistical probability of all four buckets moving way up or down in tandem (skewing the averages) is very low compared to any concentrated bet.
Also, the larger problem (as barrett points out) for the average investor is not mathematical distribution of a Monte Carlo situation (which still assumes 100,000 investors don't touch their investments) but pure investment psychology. The percentage of people who don't panic when stocks fall (and ignore the impulse to sell low) is extremely small, it seems. That's why I roll my eyes on other investment forums when people ask "what's your risk tolerance?" Young people will always say "high!" by default (with the implicit assumption that "if it breaks, I have time to fix it"), which leads to recommendations of very high percentages of stocks and the inevitable panic sell at the first big fall in the markets. The better question is "what's the risk you will reallocate your investments at the wrong time when they don't do what you'd like?" IMHO, an honest answer to that question would lead many to more balanced strategies.
Last edited by Tyler on Wed Jul 23, 2014 1:17 pm, edited 1 time in total.
Tyler wrote:
The percentage of people who don't panic when stocks fall (and ignore the impulse to sell low) is extremely small, it seems. That's why I roll my eyes on other investment forums when people ask "what's your risk tolerance?" Young people will always say "high!" by default (with the implicit assumption that "if it breaks, I have time to fix it
Quite true. A better way to phrase the risk problem to young folks is ask them how many thousands of dollars they can risk losing in a slump, instead of a percentage of the stock market. Thinking in dollars instead of a percentage focuses your attention real fast, in my experience.
Which raises the question of how many PPers cut and run when one or more of the 4x25 portfolio segments declines sharply. Last year was a test, and I think I did fairly well in holding steady (although I do confess to changing my planned rebalancing band in a hurry) But my excuse was that 2013 was my first year in the PP and I was extra cautious during the sharp gold downturn.
I would imagine that the PP would fare better due to its lower standard deviation cutting the size of the extremes. So the median PP return is probably still smaller than the mean PP return, but it's probably smaller than the difference between the median and mean 100% stock return.
In other words, reducing volatility isn't just for suckers with no risk tolerance.
Human behavior is economic behavior. The particulars may vary, but competition for limited resources remains a constant.
- CEO Nwabudike Morgan
TennPaGa wrote:
Isn't there a website where you put in such information (i.e. average annual return and standard deviation) and it runs a bunch of simulations?
Here's an example $100,000 PP portfolio, assumed to have 8.86% CAGR and 6.67% standard deviation (data from http://www.peaktotrough.com/hbpp.cgi). To generate the kind of simulation used in the stock example given in the article, no withdrawals are made from the portfolio during the 30 years, and inflation is assumed to be zero (hah). Not one simulation resulted in a loss.
The "ideal" CAGR of 8.86% should result in a $1.27m portfolio after 30 years. In this run, the median ending value was around $1.16m, for an imputed median CAGR of 8.51%.
Last edited by Pointedstick on Wed Jul 23, 2014 5:00 pm, edited 1 time in total.
Human behavior is economic behavior. The particulars may vary, but competition for limited resources remains a constant.
- CEO Nwabudike Morgan
7% CAGR/20% SD is a bit pessimistic for the stock market. Equal weight S&P500 stocks returned around 13.5% from 1972-2014, but the SD was still north of 19.
iwealth wrote:
7% CAGR/20% SD is a bit pessimistic for the stock market. Equal weight S&P500 stocks returned around 13.5% from 1972-2014, but the SD was still north of 19.
http://www.peaktotrough.com/hbpp.cgi says that the CAGR of a 100% SP500 portfolio from 1972-2014 was 9.55%, with an SD of 14%. 13.5% seems way high to me.
Human behavior is economic behavior. The particulars may vary, but competition for limited resources remains a constant.
- CEO Nwabudike Morgan
I'm guessing the calculation was done using a market-cap weighted estimation. Equal-weight provides quite an uplift by giving more weight to the smaller-cap members.
Pointedstick wrote:
I would imagine that the PP would fare better due to its lower standard deviation cutting the size of the extremes. So the median PP return is probably still smaller than the mean PP return, but it's probably smaller than the difference between the median and mean 100% stock return.
In other words, reducing volatility isn't just for suckers with no risk tolerance.
Exactly.
FWIW, the phenomenon of the median return being lower than the average return is simply a matter of statistics.
I believe investment return distribution for a group looks like a skewed bell curve fixed at zero at one end (assuming no margin, once you're broke you're broke). The higher the standard deviation, the greater the returns for the very lucky few at the right end of the curve (who may roll 30 straight years of gains). This increases the spread between the mean and median numbers, enticing investors with a higher average return than they'll likely ever see while understating the risk of running out of money at the low end.
With a low standard deviation, the mean and median numbers for the PP should be much closer, and I imagine the risk of bottoming out is also lower.
Perhaps someone with a statistics degree can correct me.
You can quantify this without running that many sims..
The phenomina is called Volatility drag, and its the difference between arithmetic and geometric mean..
geometric return = arithmetic return - sigma^2/2 , where sigma is the volatility
With 20% vol (typical for the stock market as a whole), sigma^2/2 = 2%, and so with an arithmetic return of 7%, you'd expect a geometric return of 5%, which is what was measured..
If you change the volatility, and re-run the simulations, you'll see the results track this formula quite closely..
The cause of this is basically that mulitplying returns (ie. annual returns over a series of years) is not additive. Over a 2 year period, starting with $100, if you go up 10%, and then down 10%, you end at $99, not $100 (the volatility did extra damage).. The formula above quantifies this effect.
This is my main attraction to PP investing, is the very low volatility in annual results, minimizes this effect, and makes order of returns for retirement savings much less of a problem (when I first encountered the issue of order of returns and its effect on investing, I was at first really depressed, and then did 6 months of research reading everything I could about low vol investing, until I discovered the PP. If you want to depress yourself, and your not in the PP, read up on it)
Last edited by Spectre on Fri Jul 25, 2014 10:37 am, edited 1 time in total.
I don't know about anyone else but I personally didn't have much trouble holding my asset allocation during a very significant drawdown of my portfolio (in 2013). My wife, on the other hand, needed a lot of reassurance that we were still okay.
But my excuse was that 2013 was my first year in the PP and I was extra cautious during the sharp gold downturn.
