# Fed Model Update, from Alex Castaldo

The Fed Model postulates that if the forward earnings yield of the S&P Index is higher than the 10-year treasury yield, stocks are “undervalued“, and vice versa. As of December 31, the S&P was at 1468.36 and expected forward S&P 500 earnings for the next 12 months were 101.86, making the forward earnings yield 6.94 percent (101.86/1468.36). The yield on the 10-year T-note was 4.02 percent.

Historically, subsequent market returns have been correlated with the differential between the S&P forward earnings yield (estimated 12 months earnings divided by the S&P 500 level) and the 10-year treasury yield. On the 10 occasions when this differential has been greater than 1 percent, the S&P 500 has risen ten out of ten times for an average of 13.5 percent in the subsequent 12 months. (This differential currently stands at 2.92 percent, which the highest it has ever been at year end).

We have found that the best way to specify the Fed model relationship for forecasting purposes is with a linear regression in the form:

S&P Return[t+1] = a + b * ( Forward Earnings Yield[t+1] - 10 Year Yield[t] )

Estimating this regression using yearly data since 1980, we obtained the following equation:

```S&P Return[t+1] = 0.082 + 4.172 * ( Forward Earnings Yield[t+1]  -   10 Year Yield[t] )

t-stat     2.66      1.85

p-values   1.32%     7.53%```

The R-Squared of 0.12 is quite high for a predictive regression in the financial markets and indicates that 12 percent of variation in subsequent returns was explained by the independent variable over the time period studied.

To determine current Fed Model forecast:
Current S&P (as of 12/31/07) stands at 1468.36
Forward Earnings = 12 months consensus forward earnings for the S&P 500 = 101.86
Forward Earnings Yield = Forward Earnings / S&P = 101.86/1468.36 = 6.94 percent
10.Year.Yield = The Current Yield on 10-Year government note is 4.02 percent
The Differential (Earnings Yield - 10.Year) = 2.92 percent
Substituting these numbers into the regression formula :
0.082 + 4.172 * (0.0694 – 0.0402 ) = 0.203
Therefore, Fed Model yields a forecast of 20.3 percent for next 12 months.

## Jason Humbert asks:

How does Dr. Castaldo counter the failings of the Fed model in other G10 countries? Japan has been horrible under that model. Germany has been OK, barely statistically significant. UK has been good, like the US.

## Alex Castaldo replies:

I believe Mr.Humbert is referring to the paper "The Fed Model: A Note" FRL (2006) by Javier Estrada who tested the Fed model in a number of foreign markets.   I have exchanged Emails with the professor but neither one of us was convinced by the other's arguments; we will just have to disagree.

# Where Do I Fit In? from Jason Humbert

When I took Goldman's Where Do I Fit In? quiz , I got "Credit Risk Management" and "Investment Banking." I was hoping for "Committee to Run U.S. Monetary System" or "Shadow U.S. Government," but apparently they don't advertise those…

# Ten Hours on an Airplane, from Jason Humbert

August 14, 2007 | 2 Comments

Spending hours on an airplane with nobody you know can make you crazy, enable you to do some serious thinking, or some combination of both. As I fly over the California coast I have been going over in my mind for the past five hours what the market possibilities are going forward.

I have been involved in investing and trading the global markets for 18 years now. I've really never done anything else, never wanted to do anything else, and through thick and thin, which included more than one trip to the welfare line and some really cool sports cars, never tried to do anything else. For at least seven of those 18 years the money I have been trading has been 100% my own, and for many of those years nearly all the money I had. This has given me a different approach from most, since trading other people's money while earning a 2% management fee or while taking in a nice salary while you hope something good happens can give a level of comfort I was not blessed with coming out of the gate. Whenever someone asks me how to learn to trade my response is that it's easy to learn — take every dollar you have, put it in a brokerage account, put it all on the line, and I promise you will learn very quickly how it works. I don't mean to be glib. It's just that this is exactly how I did it so I know of no other way.

I have spent these years reading hundreds of books on trading, investing, economics, economic history, statistics, psychology, philosophy, systems development and countless other subjects all with the hope that I could develop some kind of long term edge in the markets. Have I been successful? Only a lot more time will tell.

The largest position I have right now is long stock futures in the US. The method I use to manage money takes into account the current positions in the US futures markets to help establish risk/reward for me on individual positions. The belief is that when participants get skewed towards one side, the chance that a market will have a big move the other way increased substantially. This does not work every time, which is why I use stop losses on every position. This also gives me no edge on determining the path of a given move, which can be anything from a quick straight line move that lasts a few weeks before the participants react, to a multi-year choppy move before adjustments are made. I have had positions work that have had a path where they were initially very profitable, then pulled back 15-20%, only to resume the profitable path. These moves were not fun, but ultimately made a lot of money from entry to exit.

In mid-February I was getting indications that participants were way too long on the stock indices to be sustainable and I was expecting a sharp drop because of that. Surprisingly, after a two week drop in the market in late February/early March the participants went from very net long to very net short, which is the quickest I have ever witnessed this in 15 years of monitoring these data across 40 markets. My systems got long on March 14 and have remained that way since. Has this trade worked? Sure, so far. Does this mean I won't get stopped out? Not at all. This is by no means a magic system, but I stick to it because it works very well over time.