Making the Fed Model Work

Includes: DIA, QQQ, SPY
by: Marc Gerstein

The Fed Model, actually named by Dr. Edward Yardeni rather than by anyone at the Fed, suggests that stocks are undervalued when the earnings yield exceeds the yield on 10-year Treasuries and vice versa. So far, its limitations have made it more useful as a discussion topic than a tool for market timing or asset allocation. Actually, though, the constraints are quite manageable. By treating the key inputs as we would any other financial parameter, developed a timing model for general market analysis and to trigger equity buy-sell rules.

The Basic Model

It can't get any easier than this: 

  • Stocks are undervalued if the S&P 500 Earnings Yield is greater than the 10-year Treasure Yield
  • Stocks are overvalued if the S&P 500 Earnings Yield is less than the 10-year Treasury Yield

Unfortunately, this clear, crisp formulation falls prey to the if-it-sounds-too-good-to-be-true adage.


We cannot really consider stocks and bonds to be in equilibrium just because these yields are equal. Assuming no changes in credit conditions, bond income would be fixed. But for corporations, a static income stream would be a rare exception, rather than a rule.

Therefore, in equilibrium, earnings yields should differ from treasury yields. If the corporate profit stream is expected to grow over time (as is assumed by most stock valuation models), it would be fair to accept a day-one earnings yield that is less than the Treasury yield. But even this is not clear cut. It is possible that growth expectations may not be met; earnings may even fall. That forces us to consider the notion of a risk premium. The capital asset pricing model (which applies to overall security returns rather than income streams per se) and its progeny introduce the additional notion of a premium or discount to compensate for greater or lesser uncertainty (quantified through volatility).

So from the standpoint of financial theory, we can't really make any hard-and-fast good-for-all-time pronouncement regarding how earnings and treasury yields ought to relate to one another.

An expanded view of the Fed Model

Theory aside, if earnings yields exceed treasury yields, we may not have a perfect case for equities, but we do at least have a pretty good head start.

We'd know we have some sort of risk premium. Arguments can always be made as to whether a particular premium is sufficient. But at the very least, having a premium we can argue about puts us in a better position than we'd be in if treasury yields exceeded earnings yields. So as noted, we have a pretty good head start.

Given the normal assumption that corporate earnings grow over time, situations wherein the earnings yield exceed the treasury yield at the outset (before we experience any actual benefits from growth) make for a nice bonus or, stated again, a pretty good head start.

The top portion of Figure 1 shows how the pretty good head start has fared over time in signaling the direction of the S&P 500. The dark blue line represents the S&P 500; the black line is the risk premium (the S&P 500 earnings yield minus the 10-year Treasury yield).

Figure 1

From early-2001 through mid-2002, the risk premium was negative or very modest (below 1 percentage point) and stocks struggled. From mid-2002 through mid-2007, the risk premium was better, above 1.00, and the stock market did well on the whole. But after mid-2007, the relationship between stock prices and risk premium faltered badly; the risk premium remained above 1.00, but stocks performed poorly. For almost a year, it looked like we could have simply said 1.00 wasn't enough of a risk premium. But by the start of 2008, it seemed that no increase in risk premium would be sufficient to halt the market decline.

To bridge the gap from pretty good head start to actionable buy-sell signal, we need to look at the other charts in Figure 1, especially the red line which represents the consensus current-fiscal year EPS estimate for the S&P 500. Uptrends in the estimate were often present at times when stock prices rose even in the face of positive-but-lackluster risk premiums. And declining estimates in the more recent past correspond reasonably well with weak stock prices, trumping the increase in risk premium.

Putting the red and black lines together, it seems more reasonable to say that rising stock prices are associated with positive risk premiums and favorable investment-community views regarding the earnings that go into the earnings yield calculation.

Making the Fed Model actionable

The present situation is especially interesting. Figure 1 reflects data through October 8, 2008. We see that the risk premium shot up as stock prices plummeted. Obviously, at that time, stocks were a screaming buy — if one believed in the estimates.

That last clause is not to be taken lightly. If estimates fall further, stocks would remain undesirable.

So what are we to make of the little uptick in the latest estimate revisions? Is this the start of something beautiful?

Monday October 13 witnessed an upside explosion, consistent with the notion of extreme undervaluation. But going forward, the key issue remains the same: Will the estimates rise or at least hold stable, or is fallout from the financial crisis likely to push them lower? Figure 2 is a close-up of the estimates trend, reflecting data through 10/13.

Figure 2

Obviously, a pronouncement of increase or decrease lies in the eye of the beholder. Bulls can point to a clear, upturned hook-like pattern. Bears can hang their hats on what looks to be an abrupt reversal. Bulls can respond that the very latest data point seems to again suggest upward movement.

Hence definitive answers remain elusive. This shouldn't be a surprise: If the questions were easy, we'd all be gazillionaires.

The good news is that we've come a long way form the ivory tower and that the questions we now face, while not simple, are not materially different form the sorts of issues investors and strategists deal with all the time. While we can't necessarily peer into a crystal ball, we can make sensible assumptions, test them, reconsider and refine them, test them again, and so forth; again, things many of us do all the time.

And like many problems, this is one for which there can be many solutions. The Portfolio123 SP500 Market Timing Model created by Marco reflects a solution that gives a green light to stocks if the following two conditions are met:

  1. The current risk premium must be above 1 percentage point
  2. The five-week moving average of the current-fiscal-year S&P 500 EPS estimate must be above its 21-week moving average

The uptick in the estimates we saw in Figure 1 is not yet sufficient to satisfy the second requirement, so at this moment and notwithstanding Monday's super-rally, the Portfolio123 model is in cash.

Back-testing the Portfolio123 SP500 Market Timing Model

In fact, this is more than just a market-timing model. It represents a set of market-timing signals layered on top of a pre-existing Value-Momentum ranking system. Once the timing signal turns favorable, the model buys the top rated 15 stocks, subject to a rule that no industry can comprise more than 15 percent of the portfolio. Individual stocks will be sold and replaced if their rank falls below 85. The model will switch to all-cash if the 5-week moving average of the EPS estimate drops below the 21-week moving average (the cash-out occurs regardless of where the risk premium is).

Figure 2 shows graphically simulated portfolio performance with rebalancing every four weeks, an assumed $10-per-trade commission, and assumed 0.25% price slippage on each buy and sell.

Figure 3

Figure 3 shows the back-tested performance of that same value-momentum ranking system with the market-timing parameters factors omitted (all of other simulation parameters remain the same).

Figure 4

For the most part, the value-momentum system performed fairly well on its own. The market timing features — simple factors based on an expanded, pragmatic, approach to the Fed Model — served to get the model portfolio off to a decent low-stress start back in the early tumultuous 2001-02 period, and to prevent the portfolio from giving back most of its gains during the vicious downturns we experienced this year.

Clearly, the model was pretty much on target with the big calls.

At first glance, the smaller signals seemed less impressive.

Figure 5 presents a close-up of 2004.

Figure 5

Figure 6 zeros in on the 7/1/05-9/30/05 period.

Figure 6

The verdict

We clearly see some signals that, in retrospect, were not especially helpful. But closer examination of the big picture indicates that the model actually served us reasonably well. Getting us out of bear markets is one function; in this, the model worked. But there's another side to the coin. We also want a timing signal that prevents us from missing too much of rallies. From 2003 through late-2007, the model did a reasonably good job of keeping us in stocks and allowing us to profit from a prolonged upturn. Figures 5 and 6 show that it failed to do this with perfection. But let's be realistic. when it comes to investment strategy, perfection is a rarity. On the whole, the model did a pretty good job in preventing us from hiding in the spectator section as a major multi-year bull market unfolded, notwithstanding scares here and there (example: mid- to late-2004).

All in all, it looks like the Portfolio123 SP500 Market Timing Model gives us what we'd want from a market timing model.