Earlier this week, EconomPic detailed the relationship between the S&P 500 and nominal GDP and asked "Is the S&P 500 at Fair Value?"

Below is additional detail of those results by decade. Pretty interesting to start in the 1920's (the only data point is 1929) and work through the decades. Definitely shows how we got to the point where we were so extended at the earlier part of last decade.

Source: BEA / Irrational Exuberance

## Wednesday, April 28, 2010

### More on the S&P 500 Relative Value

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Without disputing the conclusion, I think the analysis is a little misleading. Perhaps a statistician could weigh in. The reason the scatter plot looks so good is that 10-year returns are serially correlated and the denominator is relatively fixed. I.e., a good portion of the variation in returns is simply due to the variation in price at the starting point of the 10-year period.

ReplyDeleteBut isn't part of this entirely the point (although I would love a statistician to weigh in). Equity returns are almost solely based on change in valuation, rather than underlying economic performance.

ReplyDeleteIn other words, the main driver of equity performance is P/E multiple expansion / contraction as underlying economic growth is relatively constant as compared to the P/E multiple (nominal GDP may swing from 5-8% growth, but multiples may swing from 5x - 30x).

Actually, my point is slightly different. Say from Year 0 to Year 1, the S&P drops 10% and GDP doesn't change. Then the return from Year 1 to Year 11 is probably close to 10% higher than the return from Year 0 to Year 10, because the second period cuts off the drop. This is why the data clusters so nicely around the regression line. This observation is strictly about price, not valuation, although (to your point) there are many studies which show that P/E is inversely correlated to multi-year forward returns.

ReplyDeleteit may explain why two data points (i.e. years 1-11 and 2-12) are close, but i don't see how this would explain why periods from the 1930's and 1980's (or 1950's and 1970's) all regress closely to the same line.

ReplyDeleteNamazu actually brought up the same point I had in mind. Try running the same a regression without the GDP in the denominator. If the R-squared is roughly the same, then we know most of the explanatory power came from the price alone.

ReplyDeleteIf the slope of the line formed by any two adjacent data points is roughly -1, then the slope between any two points should be roughly -1. The deviation from the line will have to do with the relative values of the first and last years between periods. If you don't mind posting the raw data, I think there may be some good ways to illustrate this.

ReplyDeleteHenry Bee / Namazu-

ReplyDeleteHappy to run additional analysis, but isn't the S&P 500 / Nominal GDP Ratio what I am regressing S&P 500 performance against? If GDP isn't in the denominator, then I am not sure what I should replace it with. Regressing S&P 500 performance against just the index doesn't seem to make much sense.

Jake, the easiest way to think about it is to replace the GDP data with a "constant GDP" such as 100 throughout. You don't have to change anything else.

ReplyDeleteSince the data points aren't truly independent, the graph overstates the strength of the correlation. Notice how some decades are clustered. A histogram of S&P returns by quintile would be more robust, i.e., look more like what you'd get taking random samples of the data set. Since the data points are serially correlated,if you don't adjust for time, you need to find a way to make sure its not biasing the outcome. Except for part of the Great Depression, yoy variations have a minor effect on yoy changes in the ratio, so don't let that confuse matters.

ReplyDeleteWow. The issue just clicked...will try to post a follow up this weekend.

ReplyDelete