No, the stock market doesn't really earn 10% per year
Matthew Martin
1/19/2014 05:54:00 PM
Tweetable
First things first: even if the only analysis you are interested in is the average returns, you should know that the average is actually only 7.3% (nominal) per year, not 10%. To get the 10% figure, you have to surreptitiously exclude data from both before 1975 and after 2007. We have a word for an oft repeated claim that excludes contrary data: derp.
Ok, so the actual average return is 7.3%, not 10%. We can just use the new number right? Actually, no, it's highly misleading to say that the average return is 7.3%--even though that is literally the number you get when you calculate the mean, that is not a valid calculation at all:
The graph above shows three different trend forecasts. The solid line is the "actual" time trend as estimated by OLS. The blue dashed line is a trend forecast by assuming the average annual growth rate will continue from today on, while the yellow dashed line is the trend we would have forecast back in 2007 by assuming a 7.3% average growth rate from then on. On the graph, the difference between these forecasts may not seem so significant, but they are. As a thought experiment, consider a person investing his retirement portfolio in the stock market today, for a predicted retirement in 2050. The blue line would overstate his returns by more than 215 percentage points.
The reality might even be worse than that. The estimated trend in the graph above may not be stationary. In a stationary model, R tells me that the "actual" trend is only 5.92% returns per year, barely half the advertised rate. (R code after the jump). That means that using the average would overstate the returns on his portfolio by a whopping 463 percentage points!
Bottom line is that if you take all the financial advice at face value--that you'll earn 10% per year--then chances are you'll end up scraping by on woefully inadequate savings in your golden years.
The data is here https://drive.google.com/file/d/0B8-nvwPMR6AyVzBGaHg1VXRXVjQ/edit?usp=sharing you may have to download the data and change the filepath to get this to work though. Data is the log levels of the DJIA from Fred
R code (requires forecast library):
dowJones<-scan("dowJones<-scan("https://drive.google.com/file/d/0B8-nvwPMR6AyVzBGaHg1VXRXVjQ/edit?usp=sharing",skip=0)
dow<-ts(dowJones,frequency=1,start=1959)",skip=0)
dow<-ts(dowJones,frequency=1,start=1959)
library(forecast)
dowArima=auto.arima(dow,ic="bic")
dowForecast<- forecast.Arima(dowArima,h=100)
dowForecast
dowArima

Max
1/20/2014 02:53:00 AM
Aside from the behavior of the market, we don't actually know how well the typical stock market investor does. It might be significantly worse than the indexes (and the average investor). There's some evidence of this, but we lack the data to really know.

Matthew Martin
1/21/2014 03:08:00 PM
That's very true, but any investor could theoretically earn the market average by investing in index funds rather than actually maintain in a portfolio of stocks.

J Marshall
1/24/2014 12:38:00 PM
Theoretically yes. But most index funds have a management fee, trading fee, or some other variable to separate that theory from reality, and the investor from his money.