Recently there has been a discussion of the so-called ?Fed Model,? with some questioning the validity of model, and others affirming it. Even the venerable John Hussman has commented on models akin to the Fed Model that he dislikes. This piece aims at taking a middle view of the debate, and explain where the Fed Model has validity, and where it does not.

What is the Fed Model?

The Fed Model is a reasonable but imperfect means of comparing the desirability of investing in stocks versus bonds. It can be considered a huge simplification of the dividend discount model, applied to the market as a whole, rather than an individual stock. The dividend discount model states that the value of the stock is equal to the future stream of dividends discounted at the corporation?s cost of equity capital.

What simplifying assumptions get applied to the dividend discount model to create the Fed Model?

1. The market as a whole is considered rather than individual stocks.
2. A constant ratio of earnings is paid out as dividends.
3. The growth rate of earnings is made constant.
4. A Treasury yield (or high/moderate quality corporate bond yield) is substituted for the cost of equity capital.
5. Instead of following a strict discounting method, the equation is rearranged to make an explicit comparison between bond yields and equity yields.

Assuming that the dividend discount model is valid, or at least approximately so, what do these simplifying assumptions do to the accuracy of valuing the market as a whole? The first assumption is more procedural in nature, and does no major harm. The fifth assumption simply reorganizes the equation, and doesn?t affect the outcome, but only the presentation. The real changes come from assumptions 2-4.

Dividends are more stable than earnings, so the payout ratio certainly varies over time. Additionally, corporations have shown less willingness to pay dividends, and investors have shown less inclination to demand dividends, to the payout ratio today is roughly half of what it was in the early 60s.

Earnings don?t grow at a constant rate, either. Over the last 53 years, earnings have grown at a 6.7% rate, but that has included times of shrinkage, and boom times as well.

As for the cost of capital to a corporation, I believe that the Capital Asset Pricing Model is genuinely wrong, and I refer you to Roll?s famous critique for what should have been its burial. Academics need risk to be something simple though, with risk being the same for all investors (not true), so that they can easily calculate their models, and publish. The CAPM provides useful, if mistaken, simplification to financial economists. It is not going away anytime soon.

One day I will write an article to explain my cost of equity capital methods in more depth, which derive corporate bonds and option pricing theory. In basic, for any corporation, the basic idea is to compare the riskiness of the equity to that of a bond. Look at the yield on juniormost debt security of the firm, the cost of equity is higher than that. Examine the implied volatility [IV] on the longest dated at the money options for the firm. How do those implied volatilities compare with other firms? In general the higher the IV, the higher the cost of equity capital.

Practically, when looking at the capital structure of the firms in the S&P 500, I think that the yield on a BBB bond plus a spread could be a good proxy for the weighted average cost of capital for the firms as a group. I?ll get to what that spread might be in a bit. We have BBB yield series going back a long way. Equity risk for the S&P 500 (a high credit quality group) is probably akin to the risk of owning weak BB or strong single-B bonds on average. (My rule of thumb for cost of equity capital in an individual corporation is take the juniormost debt yield and add 3%. For those with access to RealMoney, I have written more on this here.)

To summarize then: there?s not much I can do about assumptions 2 and 3. The only thing I might say is that earnings are a better proxy for value creation than dividends, and that expectations for longer-term earnings growth do not change nearly as much as actual earnings growth does. On assumption 4, a BBB bond yield plus a spread will be a reasonable, though not perfectly accurate proxy for the cost of equity. My view is that spread should be between 2.5%-3.0%.

The Results

With that, the ?Fed Model? boils down to a comparison of BBB bond yields less a spread versus earnings yields. Wait, ?less? a spread? Didn?t I say ?plus? above?

Let?s consider how a stock differs from a bond. With a bond, all that you can hope to get is your principal and interest paid on a timely basis. With equity, particularly in a diversified portfolio, one can expect over the long term growth in the value of the business from a growing dividend stream, and reinvestment of retained earnings. As I mentioned above, that has averaged 6.7%/year earnings growth over the past 53 years.

If I were trying to balance the yield needed from bonds to compete with equities, it would look like this, then:

Earnings Yield + 6.7% = BBB bond yield plus 2.5-3.0%

Or,

Earnings Yield = BBB bond yield – 4% (or so)

Here is how earnings yields and BBB bond yields have compared over the years.

Thus my criteria for investing would be under the ?Fed Model,? when the earnings yield is more than 4% less than the BBB bond yield, invest in bonds. Otherwise, invest in stocks. Following this method, how would a portfolio have done since 1954?

Wow. Pretty good rule, in hindsight. Is the spread of 4% the best spread for simulation purposes?

Pretty close. The optimum value is 3.9%. This chart uses an actuarial smoothing method to give a fairer view of noisy historical results. (Life actuaries use this smoothing method in cash flow testing to calculate required capital, because sometimes small changes in spread produce large differences in the results for a particular scenario.)

The strategy produces a return roughly 2.0%/year higher than investing in stocks only, with a standard deviation roughly 1.5%/year lower. At least in a backtest, my version of the ?Fed Model? works.

Limitations

Okay, given the above, I endorse my version of the ?Fed Model? as being useful, but with five caveats:

The first thing to remember is that the ?Fed Model? doesn?t tell you whether stocks are absolutely cheap, but whether they are cheap versus bonds. There may be other more desirable asset classes to choose from: cash, commodities, international bonds or equities, etc.

The second thing to remember is that when interest rates get low, yields do not reflect the true riskiness of bonds ? a slightly superior model would be 107% of BBB yields less 4.7%. But that could just be an artifact of backtesting. To its credit though, the slightly superior model behaves the way that it should in theory, in term of how credit spreads move.

Number three, ideally, all models would not use trailing earnings yields, but expected earnings yields. That said, trailing yields are objective, and expected yields have often proiven wrong at turning points.

The fourth limitation: a high earnings yield might reflect low earnings quality or profit margins higher than sustainable. No doubt that is possible, and particularly in the current era. On the flip side, there may be times when a low earnings yield might reflect high earnings quality or profit margins lower than sustainable. A rule is a rule, and a model is only a model; they don?t reflect all aspects of reality, they are just tools to guide us.

What P/E ratio would the current BBB bond yield (6.74%) support? I am surprised to say that it would support a P/E in the high 30s; 39.8 for the simple model, and 35.2 for the ?slightly superior? one. With the current trailing P/E at 18.1, that would indicate that on an unadjusted basis, the market could be twice as high as it is presently.

That thought makes me queasy, but here three other ways to look at it:

• How inflated are profit margins? If they are going to regress by less than half, then stocks are still a bargain.
• Are bond yields/spreads too low? The recycling of the current account deficit into US debt instruments keeps yields low, and the speculation in the credit markets keeps spreads low. What should be the normalized BBB yield?
• Will earnings growth slow beneath the 6.7% average? If so, the spread needs to come down.

Fifth, this is simply a backtest, albeit one that conforms to my theories. The future may not resemble the past.

Conclusion

My version of the Fed Model provides us with a way of comparing corporate bond yields with earnings yields, giving credit for growth that happens in capitalist economies that are free from war on their home soil. There are reasons to think that current profit margins are overstated, and perhaps that corporate bond yields will rise. All of that said, there is a large provision for adverse deviation in the present environment.

I would rather be a moderate bull on stocks versus bonds in this environment as a result. Don?t go hog wild, but current bond yields are no competition for stocks at present. If you think bond yields will normalize higher, perhaps cash is the place you would rather be for now.

As part of my 2-part project on the Fed Model, I want to give you the results of my recent investigation. This is the simpler of the two projects. A little while ago, Bespoke Investment Group published two little pieces on the relationship between the yield curve and the absolute level of the S&P 500 over short time periods. (You can see my comments below what they wrote.)

My data went from April 1954 to the present on a monthly basis. I regressed the yields on the three and ten-year treasuries, and a triple-B corporate bond spread series on twelve month trailing earnings yields for the S&P 500. The regression as a whole is highly statistically significant. Except for the t-statistic on the 10-year Treasury yield, the other regressors have t-statistics that are significant at a 95% level. I only did two passes on the data, because I didn’t realize until later that I had the spread series… in the first pass that did not have the spread series, the ten-year yield was significant.

Anyway, here are the statistics. What this says is that in the past trailing earnings yields tended to:

1. decline when BBB spreads rose
2. rise when three-year treasury yields rose
3. rise when parallel shifts of the yield curve up
4. rise when the yield curve flattens, with no adjustment in the overall height of the curve

The last three observations make sense, while the first one does not, at least not on first blush. Typically, I associate higher credit spreads with higher E/Ps, and thus lower P/Es, because tighter financing is associated with a lower willingness for equity investments to receive high valuations. I’m not sure what to do with that last observation; perhaps it is that my practical experience exists over the last 20 years which have been different than the whole data sample. Or, perhaps my readers will have a few ideas? 🙂

As for the main current upshot from this admittedly limited model is that current trailing E/Ps, and thus P/Es, are fairly valued against current treasury yields and bond spreads. Here are two graphs that illustrate this:

The nice thing about these graphs is that they easily point out the stock market undervaluation relative to bonds in 1954, 1958, 1962, 1974, 1980, 1982, and September 2002, and overvaluation relative to bonds in 1969, early 1973, 1987, and March 2000 and March 2002. Now this model might have suggested staying in bonds for most of the 90s, but the 90s were a relatively good decade to be in bonds, though not as good as equities.

This is the first time I have done a post like this, and so I put it out for your consideration. Comments?