fedmodel_updatejan05

I spent the last few days looking back at my Fed Funds Model analysis. I plan to update this with new insights and want to share some early thoughts and provoke some discussion.

- The "fair value" of the S&P is at 1722 (using the avg. 2005 earning prediction of analysts and strategists) - This implies a discount (or "under" valuation) of -31.73% (as calculated in my model)

- Since 1979 there has been a strong tendency for over/under valuation to return to the mean (-3%)

- Since 1979 there has been a extremely strong tendency for the S&P to be doing most of the moving to bring back to the mean.

- Since 1979 there has never been a period where the index spends more than 2 years in an extreme situation (1979-1980 -- extreme undervaluation, 1999-2000 extreme overvaluation, 2003-2004 extreme undervaluation)

- Since 1979 the 12 and 18 months prognosis for the type of under-valuation like today (i.e. more than 20% undervalued) is very good (12 month S&P return:

- the S&P is not going to go to fair value (1722) anytime soon -- there are two other variables that can and will move: 10yr i% and forward earnings - It is theoretically possible to reach the mean by the other variables moving (roughly earnings/10-yr note: 50e/4.25%, 55e/4.75%, 60e/5.25%, 65e/5.75%, 70e/6%, 75e/6.50%) - it is likely that if the 10yr note starts to move to 6% (as suggested by mr. e on Jan 3rd) that the return to the mean will be delayed. So even though the S&P is "pricing in" 6% 10yr-note acc. to the Fed funds model, it could take a 20-30% hit before it returns to the mean (and bring us back where we are now BTW so not a pretty sight at all) -- maybe this is what mr. e is predicting for April-May this year ????.

- The Fed Funds model cannot be used for trading in most periods: 75% of the time because it is near its mean. In extreme overvaluation (8% of the time), it is very dangerous to short because the short term performance can be very (very) high (cf. 1999) - It can be used today because the prognosis is good and statistically relevant - The best way to use the model is -- during extreme under valuation situation only -- to go long S&P while shorting ten-year notes using the forward earning number to adjust the proportions dynamically (very tricky though so not really usable for small players). - Just going long the S&P (based on the model) is flawed because the possibility always exist (although it never happened this way since 1979) that the ten year note and the earnings number does the work required to return to the mean while the undervalued situation remains.

NOTHING -- the number that comes out of the equation does not mean that the snp should be there (the Jan 1979 Fair value -- 33under so +/- like today - was only reached 4 years later). The difference between where the S&P is and where the fair value says it is, is in fact a quantified reflection of the premium/discount required by investors to hold equities vs. bonds. So in that sense, it is a contrarian indicator (and a good one at that). The problem is the following one: Today it says that S&P holder are very risk averse (in relation to the 1981-2002 period) and bond holders are much too complacent -- basically as in may 80 where the bond holders were about the see yields go from 10% to 15% in one year). This is interesting because it seems that the consensus says that equities are again in a mini bubble (and at best fairly valued) and that bonds yield will increase slow enough for holders to make money holding them.

In any case, I'll try to work on the idea of buying the S&P with dynamic hedging with bonds to see whether this is something that will reduce the numbers of outliers (overvalued/undervalued) if done on a large scale and also look at whether a traded futures on forward S&P earnings could be interesting

The Fed Model might be nice and easy to use, but even for a simple model it is not robust enough and omits to many important variables:

1. It assumes the P/E or earnings yield is a function of the 10-year bond ONLY. What about earnings growth (as someone mentioned earlier), earnings stability/quality, a risk premium for equities and dividend policy?

If one goes back to the Gordon model (not to say it's worth much anyway) and then divide both the numerator and denominator by earnings you get an equation for the market forward P/E. If you expand it you can get

The Fed model is then a special case where the payout ratio is 1 (vs. current 30% or so) and the RP = LT Growth. LT Growth is often pegged at 7.5%. RP is generally less (i.e., RP of equities over Treasuries. I think more like 4-5pc but not sue)

2. The rate used is the 10-year, which can get distorted by world events. If there is a major world event and a flight to quality -- to U.S. paper -- the yield goes down and all of sudden the S&P is "theoretically worth more"?

3. Dividend taxation changes - for high-payout companies like utilities you can make an argument a higher P/E is warranted for a given Treasury yield today since a portion of taxpaying investors will pay more since the net after-tax yield to them changed after the recent changes.

I could go on and on about other reasons why this model is insufficient at best but I think enough flaws have been identified.

I do not actually disagree with what you are saying. That is why I said that the "fair value" number that comes out of the formula has no actual meaning (in the sense that it does not really mean that the S&P is going to go there). The only thing that the model seems to imply based on available data is that if the two numbers (forward earnings and 10-year yield) which are supposed to include all known information about the market get far out of whack with the actual S&P cash value, there is a very strong tendency to return to the mean (the mean implying a small equity risk premium -- about 3%).

So when the equity risk premium becomes very large (like today), the model implies that the variables will converge back to the mean. Historically, the S&P has been the variable most likely to do most of the work (it seems to be slower) but it could conceivably be done by the other two. The maximum variations are (none likely to happen since the variables are not independent) :

1. If the forward earnings number does all the work: FY earnings: 50 (-30% from today)

The truth being somewhere between all these numbers with a high probability of S&P doing +17% (9% std dev) over the next 12 months. (This implies BTW that if forward earning remain where they are or grow according to trend, that the 10-year will be between 5%-5.25% a year from now -- actually not completely unlikely.)

Jordan Neumann comments: I would like to add a small amount of wine to what is already a full cellar. Yardeni's File uses what appear to be average values of the S&P and Ten-Year Bond for a given month. Working from year-end prices and yields on www.economagic.com, I come to a similar conclusion. My Pearson correlation is .42; multiply by the 25 occurrences barely breaks your 10 threshold. But if you add the performance of the T-Bond Future, i.e., inputting S&P price performance less T-Bond appreciation, yields a Pearson number of .59. So it would seem that adding a short bond element to the Fed Model regression adds to our knowledge. As an aside, the T-Bond touched but closed below the all-time constant future closing high of 6/13/03. By my reckoning that would be 114 & 27 on the March Future. Bonds are funny. Who knew we were at an historical high? I guess someone counting his losses, right?

1/25/2005
Fed Model Update, by Tom Downing

As of Friday, Jan 21, the S&P was at 1167, expected forward S&P 500 earnings for the next 12 months were 73.32, and the yield on the 10-year T-note was 4.14 percent.

From these numbers, one can calculate a Fair Value of the S&P 500 by dividing expected forward earnings by the yield on the 10-year note, which results in a reading of 1771 ( 73.32/.0414)

This implies that the S&P 500 is 43 percent undervalued at these levels (1771/1167-1).

As Schmetz has indicated, one cannot really interpret this as an expected return for the market, because 'equilibrium' may also be brought about through adjustments to interest rates and expected earnings, not just stock prices themselves. Nevertheless, the only previous time that the Fed Model was this 'undervalued' was at the end of 2002, just prior to a 26 percent return for the S&P in 2003.

We prefer to base our forecasts on the spread between the forward earnings yield (consensus estimated 12 months earnings divided by the S&P 500 level) on the S&P 500 and the yield on the 10-year Treasury note. The forward earnings yield is currently at a 2.1 percent premium to the 10-year note yield. On the seven occasions when this differential has been greater than 1 percent, the S&P 500 has risen seven out of seven times for an average of 16.5 percent in the subsequent 12 months. Our regression model (which is based on the aforementioned differential) currently forecasts a 20.8 percent return for the next 12 months.

See full details.

Jean-Paul Schmetz brings to Daily Speculations an interesting mix of philosophy (not afraid of real thinking), econometrics (measure, quantify, test...) and media (understanding of mass behavior).

Mr. Schmetz holds degrees in Philosophy (M.A. magna cum laude) and Economics (econometrics) from the University of Louvain (Belgium). He ran the digital division of a large global media firm based in Germany until the end of 2002. In 2003, he switched out of operations to focus on a hedge fund he created in 1998. He continues to sit on the media firm's supervisory board and is a special advisor to the owner.

He was born in Belgium and raised in Belgium and Boston, Massachusetts. He is married with four children, and lives with his family in Munich, Germany.