## Thursday, May 27, 2010

### Equity Valuation Matters...

Step 1) Take the S&P 500 Index (lots of data here) and divide that level by the current level of nominal GDP (you can find that here).

Below is a chart of just that going back to 1950 and the corresponding 60 year average.

Step 2) Take that 60 year average (8.2184%) to normalize the first year of your 'Fair Value S&P 500' "FV" Index by taking nominal GDP at the starting date (in this case June 1950 = \$284.5 billion) and multiplying by the percent (x 8.2184% = 23.83). In this case 23.83 = the FV Index level.

Step 3) Using that 23.83 (or calculated value using a different time frame) as the FV Index starting value, at each interval increase the index by the change in nominal GDP (note... in the chart below, I estimated the S&P value for Q2 end at today's closing level and Q2 GDP at 4.0% annualized). Why nominal GDP? Go here.

The below chart shows this FV Index against the actual S&P 500 index.

Step 4)
Calculate the percent the S&P 500 Index is over or under valued relative to the FV Index.

Proof....

Note 1: under this methodology, the S&P 500 is currently slightly below fair value
Note 2: a change in the starting value of the FV Index would simply shift the x-axis to the right or left (i.e. it would not change the relationship between the two)

Source: Irrational Exuberance

1. Very good. Thanks :)

2. Very pretty, elegant almost.

3. Neat post, but did you use real, inflation adjusted, return for the last chart? It doesn't look like it, if the data points from the early 1970s are there.

It really needs to be using real return, otherwise it's pretty meaningless.

4. it is not real. the fact is that equities over the long term returnvery close to nominal GDP + dividend rate.

nominal is relevant as it is how you need to compare expected equity returns to nominal bonds (which have coupons in nominal, not real terms).

real is obviously what matters to an investor and analyses can easily be done with the same methodology using real returns and real GDP growth.

5. That the 1970s was a horrible time to be long bonds doesn't mean it was a good time to be long stocks. The fact is that, contrary to common wisdom, during the one period where we had protracted inflation, stocks performed abysmally.

Since our graphs have so few data points, it is highly relevant.

6. bob- i'm not in disagreement. my assumption is 1970-1980 would have been horrendous as a bit after 1980 appears to be when the S&P 500 was literally at the cheapest its been since 1950.

that said the ten year period returns for the S&P 500 1974-1984 (hits the heart of the inflationary pressures as well - and more importantly is the earliest decade i can easily get S&P total return figures), the S&P 500 returns 14.77% annualized vs. 7.4% annualized inflation.

real return in exccess of 7% is pretty f'n solid.

7. Bob- I'll re-run tomorrow (or next week) in real terms.

Enjoy the long w/e

8. Jake,

I'm looking at Schiller's spreadsheet of S&P500 data and he show's the real S&P500 price level at 417 in 1974 and in 1984 330, and real dividend for those eleven years of about 150, so 417 to 480.

That's about 1.4% annualized real return. That's much better than the Treasuries, but a lot worse than buying a vacant lot just about anywhere in the country.

I don't mean to sound anal, but inflation is a real killer. And one of my pet peeves is the blanket assumption that equities perform well in inflationary environments. Over the last 15 years, with average inflation of 2-3%, they've performed much, much worse than Treasuries.

9. Jake --

(1) This is essentially equivalent to your 26 April post, isn't it? Are you using total returns here, rather than capital increase? I think the earlier algorithm is actually a tad better, with less cumulative rounding error than the current step 3.

(2) While it is hard to argue with the practical results, it would be nice to also have a theoretical justification. The closest I can come is a recent post by David Merkel: http://alephblog.com/2010/04/30/the-rules-part-xii; have you thought about this?

(3) Shiller's CAPE suggests, of course, overvaluation. Do you have a story to tell about why one measure or the other might be right (again, from an explanatory viewpoint, in addition to results)?

10. Perhaps this post at FT Alphaville gives a way of reconciling the Jake view and the CAPE view. CAPE might say that Jake gives too much emphasis to the excessively high dot com valuations. Jake might say that CAPE is too theoretical; high valuations have occurred before and can occur again.

11. Bob- the 1970's were highly inflationary times, so you need to reinvest that dividend over the 10 years at that higher rate (which included the 7.4% inflation rate). The figure I pulled is from a Bloomberg TR Index, so I'm pretty confident with my results. All that said, I completely hear you about inflation not necessarily being a driver of equities. If inflation hits the price of a firms goods and not input prices = good. If inflation hits the price of expenses = bad.

Jim- you completely figured me out. Same (exact) concept as the 4/26 post, but trying to put it all in "relative value" terms vs. a simple percent of GDP.

To answer your #3 "Shiller's CAPE suggests, of course, overvaluation. Do you have a story to tell about why one measure or the other might be right (again, from an explanatory viewpoint, in addition to results)?"

The simple answer is I used S&P 500 / Nominal GDP to "normalize" a starting point. Had I used the actual starting point of the S&P 500 in June 1950 (~25% lower than my starting point) then the "model" would have shown valuation ~25% lower than it did. In other words, it was a qualitative starting point. The key is the relationship, between rich and cheap, not the exact valuation.

In a nutshell, there are no easy solutions to investing and no models should be trusted in absolute. It is only when markets are in extreme dislocations (i.e. late 2008 / early 2009) that "screaming buys" exist. Otherwise, no model will spit out a perfect result and everything takes interpretation...