Tuesday, January 6, 2009

The Ugly: P/E Multiple

In response to yesterday's EconomPic post detailing the "Good and the Bad" of the equity market, reader "dblwyo" comments:

You should have gone ahead with "The Ugly" on future outlooks to complete the trifecta :) ! You might also want to re-visit Graham-Dodd's valuation formula where PE = (8.5 + 2 x G) x (4.4 / Y), where G = earnings growth and Y = AAA bond yield.
Great idea... for those unfamiliar with the Graham-Dodd P/E formula (or interested in seeing a full matrix), go here. Also, before I dive in... be forewarned that it is just a model. As Paul states over at Infectious Greed:
I don’t buy trough P/E, or recession length, or relative valuation, or interest rate, or sectoral rotation arguments, or… you get the picture. I love data, but I’m increasingly close to being an outright nihilist when it comes to over-reliance on historical financial data without any truly coherent supporting rationale.
Now that I've given proper warning... lets go to what this formula tells us.

Current yields on AAA corporate bonds are a little over 5%, down from over 7% just a few months back as rates and spreads have rallied. This is great for the P/E multiple, as we multiply (4.4% / AAA Bond Yield) against the first component of the formula, thus a lower yield increases the P/E multiple and a higher P/E multiple = a higher price of equities. Why this 4.4% rate? Back to RBCPA:
The original formulation was made at a time when there was very little inflation, and growth could be assumed to be real growth; the AAA corporate bond interest rate prevailing at the time was 4.4%. In later years, the formula was adjusted for higher current interest rates that contained an inflationary component.
Assuming a 5% earnings growth rate for the next five years (I do not think we will have 5% growth for the next five years for reasons detailed later), the current AAA corporate yield predicts a 15x P/E multiple, much lower than the current P/E ratio implied by either backward or forward looking earnings (roughly 19x and 22x each based on S&P earnings estimates).

But what annualized earnings growth should we expect over the next five years? Not 5% according to dblwyo for the following reasons:
If the economic outlook is for 2-2.5% growth on average over the next five years (IMF) at best and we presume a 5% yield a PE multiple of 10-12 becomes appropriate. Given that the markets were held up by leverage applied in one form or another (buybacks, housing ATM,et.al.) consider a go-forward regime where a 15 historical average PE is inappropriately optimistic!
Agreed, but I'll let each of you use any figure you want... the next chart shows what inputs are needed for the model to spit out the "inappropriately optimistic" 15x P/E multiple or the unreal 22x forward P/E .

With the current 5.2% AAA Corporate Bond Yield, earnings need to be at least 5% to justify a 15x P/E multiple (as detailed above), which would still imply equities are currently overvalued by 30%. For current equity valuation (22x), we need 9% growth... FOR EACH OF THE NEXT 5 YEARS. A more likely outcome that gets us to our current market valuation is for AAA corporate bonds to continue the recent rally. However, based on a 2.5% earnings growth rate, the rate needs to approach a measly 2.5% AAA yield. Highly unlikely...


  1. You might enjoy my post here comparing the Graham and Dodd formula to standard DCF calculation.


  2. Nicely done, though ugly indeed. Of course I might be a bit biased :).
    To extend the woefulness, sadly, there was a key quote in your except on the G-D formula on why 4.4 - "back when earnings were real". While inflation looks to be under control with leverage disappearing one might want to consider adjusting the "necessary" yield up a tad,say to 6 or 7%. Then the results are truly depressing.