A large-ish number of people have asked me to write this piece.  For those with access to RealMoney, I did an article called The Fundamentals of Market Tops.  For those without access, Barry Ritholtz put a large portion of it at his blog.  (I was honored .) When I wrote the piece, some people who were friends complained, because they thought that I was too bullish.  I don’t know, liking the market from 2004-2006 was a pretty good idea in hindsight.

I then wrote another piece applying the framework to residential housing in mid-2005, and I came to a different conclusion  — yes, residential real estate was near its top.  My friends, being bearish, and grizzly housing bears, heartily approved.

So, a number of people came to me and asked if I would write “The Fundamentals of Market Bottoms.”  Believe me, I have wanted to do so, but some of my pieces at RealMoney were “labor of love” pieces.  They took time to write, and my editor Gretchen would love them to death.  By the way, if I may say so publicly, the editors at RealMoney (particularly Gretchen) are some of their hidden treasures.  They really made my writing sing.  I like to think that I can write, but I am much better when I am edited.

Okay, before I start this piece, I have to deal with the issue of why equity market tops and bottoms are different.  Tops and bottoms are different primarily because of debt and options investors.  At market tops, typically credit spreads are tight, but they have been tight for several years, while seemingly cheap leverage builds up.  Option investors get greedy on calls near tops, and give up on or short puts.  Implied volatility is low and stays low.  There is a sense of invincibility for the equity market, and the bond and option markets reflect that.

Bottoms are more jagged, the way corporate bond spreads are near equity market bottoms.  They spike multiple times before the bottom arrives.  Investors similarly grab for puts multiple times before the bottom arrives.  Implied volatility is high and jumpy.

As a friend of mine once said, “To make a stock go to zero, it has to have a significant slug of debt.”  That is what differentiates tops from bottoms.  At tops, no one cares about debt or balance sheets.  The only insolvencies that happen then are due to fraud.  But at bottoms, the only thing that investors care about is debt or balance sheets.  In many cases, the corporate debt behaves like equity, and the equity is as jumpy as an at-the-money warrant.

I equate bond spreads and option volatility because contingent claims theory views corporate bondholders as having sold a put option to the equityholders.  In other words, the bondholders receive a company when in default, but the equityholders hang onto it in good times.  I described this in greater measure in Changes in Corporate Bonds, Part 1, and Changes in Corporate Bonds, Part 2.

Though this piece is about bottoms, not tops, I am going to use an old CC post of mine on tops to illustrate a point.

		David Merkel
		Housing Bubblettes, Redux
		10/27/2005 4:43 PM EDT

From my piece, “Real Estate’s Top Looms“:

Bubbles are primarily a financing phenomenon. Bubbles pop when financing proves insufficient to finance the assets in question. Or, as I said in another forum: a Ponzi scheme needs an ever-increasing flow of money to survive. The same is true for a market bubble. When the flow’s growth begins to slow, the bubble will wobble. When it stops, it will pop. When it goes negative, it is too late.

As I wrote in the column on market tops: Valuation is rarely a sufficient reason to be long or short a market. Absurdity is like infinity. Twice infinity is still infinity. Twice absurd is still absurd. Absurd valuations, whether high or low, can become even more absurd if the expectations of market participants become momentum-based. Momentum investors do not care about valuation; they buy what is going up, and sell what is going down.

I’m not pounding the table for anyone to short anything here, but I want to point out that the argument for a bubble does not rely on the amount of the price rise, but on the amount and nature of the financing involved. That financing is more extreme today on a balance sheet basis than at any point in modern times. The average maturity of that debt to repricing date is shorter than at any point in modern times.

That’s why I think the hot coastal markets are bubblettes. My position hasn’t changed since I wrote my original piece.

Position: none

I had a shorter way of saying it: Bubbles pop when cash flow is insufficient to finance them.  But what of market bottoms?  What is financing like at market bottoms?

The Investor Base Becomes Fundamentally-Driven

1) Now, by fundamentally-driven, I don’t mean that you are just going to read lots of articles telling how cheap certain companies are. There will be a lot of articles telling you to stay away from all stocks because of the negative macroeconomic environment, and, they will be shrill.

2) Fundamental investors are quiet, and valuation-oriented.  They start quietly buying shares when prices fall beneath their threshold levels, coming up to full positions at prices that they think are bargains for any environment.

3) But at the bottom, even long-term fundamental investors are questioning their sanity.  Investors with short time horizons have long since left the scene, and investor with intermediate time horizons are selling.  In one sense investors with short time horizons tend to predominate at tops, and investors with long time horizons dominate at bottoms.

4) The market pays a lot of attention to shorts, attributing to them powers far beyond the capital that they control.

5) Managers that ignored credit quality have gotten killed, or at least, their asset under management are much reduced.

6) At bottoms, you can take a lot of well financed companies private, and make a lot of money in the process, but no one will offer financing then.  M&A volumes are small.

7) Long-term fundamental investors who have the freedom to go to cash begin deploying cash into equities, at least, those few that haven’t morphed into permabears.

8 ) Value managers tend to outperform growth managers at bottoms, though in today’s context, where financials are doing so badly, I would expect growth managers to do better than value managers.

9) On CNBC, and other media outlets, you tend to hear from the “adults” more often.  By adults, I mean those who say “You should have seen this coming.  Our nation has been irresponsible, yada, yada, yada.”  When you get used to seeing the faces of David Tice and James Grant, we are likely near a bottom.  The “chrome dome count” shows more older investors on the tube is another sign of a bottom.

10) Defined benefit plans are net buyers of stock, as they rebalance to their target weights for equities.

11) Value investors find no lack of promising ideas, only a lack of capital.

12) Well-capitalized investors that rarely borrow, do so to take advantage of bargains.  They also buy sectors that rarely attractive to them, but figure that if they buy and hold for ten years, they will end up with something better.

13) Neophyte investors leave the game, alleging the the stock market is rigged, and put their money in something that they understand that is presently hot — e.g. money market funds, collectibles, gold, real estate — they chase the next trend in search of easy money.

14) Short interest reaches high levels; interest in hedged strategies reaches manic levels.

Changes in Corporate Behavior

1) Primary IPOs don’t get done, and what few that get done are only the highest quality. Secondary IPOs get done to reflate damaged balance sheets, but the degree of dilution is poisonous to the stock prices.

2) Private equity holds onto their deals longer, because the IPO exit door is shut.  Raising new money is hard; returns are low.

3) There are more earnings disappointments, and guidance goes lower for the future.  The bottom is close when disappointments hit, and the stock barely reacts, as if the market were saying “So what else is new?”

4) Leverage reduces, and companies begin talking about how strong their balance sheets are.  Weaker companies talk about how they will make it, and that their banks are on board, committing credit, waiving covenants, etc.  The weakest die.  Default rates spike during a market bottom, and only when prescient investors note that the amount of companies with questionable credit has declined to an amount that no longer poses systemic risk, does the market as a whole start to rally.

5) Accounting tends to get cleaned up, and operating earnings become closer to net earnings.  As business ramps down, free cash flow begins to rise, and becomes a larger proportion of earnings.

6) Cash flow at stronger firms enables them to begin buying bargain assets of weaker and bankrupt firms.

7) Dividends stop getting cut on net, and begin to rise, and the same for buybacks.

8 ) High quality companies keep buying back stock, not aggresssively, but persistently.

Other Indicators

1) Implied volatility is high, as is actual volatility. Investors are pulling their hair, biting their tongues, and retreating from the market. The market gets scared easily, and it is not hard to make the market go up or down a lot.

2)The Fed adds liquidity to the system, and the response is sluggish at best.  By the time the bottom comes, the yield curve has a strong positive slope.

No Bottom Yet

There are some reasons for optimism in the present environment.  Shorts are feared.  Value investors are seeing more and more ideas that are intriguing.  Credit-sensitive names have been hurt.  The yield curve has a positive slope.  Short interest is pretty high.  But a bottom is not with us yet, for the following reasons:

• Implied volatility is low.
• Corporate defaults are not at crisis levels yet.
• Housing prices still have further to fall.
• Bear markets have duration, and this one has been pretty short so far.
• Leverage hasn’t decreased much.  In particular, the investment banks need to de-lever, including the synthetic leverage in their swap books.
• The Fed is not adding liquidity to the system.
• I don’t sense true panic among investors yet.  Not enough neophytes have left the game.

Not all of the indicators that I put forth have to appear for there to be a market bottom. A preponderance of them appearing would make me consider the possibility, and that is not the case now.

Some of my indicators are vague and require subjective judgment. But they’re better than nothing, and kept me in the game in 2001-2002. I hope that I — and you — can achieve the same with them as we near the next bottom.

For the shorts, you have more time to play, but time is running out till we get back to more ordinary markets, where the shorts have it tough.  Exacerbating that will be all of the neophyte shorts that have piled on in this bear market.  This includes retail, but also institutional (130/30 strategies, market neutral hedge and mutual funds, credit hedge funds, and more).  There is a limit to how much shorting can go on before it becomes crowded, and technicals start dominating market fundamentals.  In most cases, (i.e. companies with moderately strong balance sheets) shorting has no impact on the ultimate outcome for the company — it is just a side bet that will eventually wash out, following the fundamental prospects of the firm.

As for asset allocators, time to begin edging back into equities, but I would still be below target weight.

The current market environment is not as overvalued as it was a year ago, and there are some reasonably valued companies with seemingly clean accounting to buy at present.  That said, long investors must be willing to endure pain for a while longer, and take defensive measures in terms of the quality of companies that they buy, as well as the industries in question.  Long only investors must play defense here, and there will be a reward when the bottom comes.

For my readers, particularly my Canadian readers, you can read an article that I wrote on risk control in portfolio management for MoneySense magazine.  In the process of writing the piece for MoneySense, I got to read a number of back issues, and found it to be a good quality publication, of most use to Canadians.  Having passed the Life Actuarial exams, I know enough about Canadian tax law and financial services to be a danger to myself, and those who listen to me.  Fortunately, the piece I wrote was generic, and can benefit investors anywhere.

Notes on Stocks and the Fed

On a side note, why didn’t the stock market fall more today? For me, it boils down to two things: the FOMC surprise move, which ratcheted up total rate cut expectations for January, and seller exhaustion.  It’s hard for the market to fall hard when you have already had a high level of down volume net of up volume, and huge amounts of 52-week lows net of 52-week highs.  This wasn’t just true of the US, but of most global equity markets.

So, if we are going down further, the market will have to rest a while.  That said, valuations are more compelling than they were, especially compared to Treasuries.  Compared to BBB corporate yields, they are still attractive.  I think I would need to see 10-year BBB corporates at yields of 7% or so before I would begin edging in there.

One other note, the forward TIPS curve is showing some life again; perhaps that will be another fake-out, as in August, but there is certainly more oomph in the inflationary effort now than when the stimulus effort was grudging and fitful as it was back then.

Finishing off the presentation proved to be harder than I estimated, together with all of my other duties.  Well, it’s done now, and available for your review here.  For those looking at one of the non-PDF versions, you might be able to see the notes for my talk as well.

I’m writing this before I give the talk.  If I had it to do all over again, I would have made the talk less ambitious.  Then again, of the four topics that I offered them, they picked the most ambitious one.  When you look at the talk, you’ll see that it is a summary of the macroeconomic views that frame my investment decisions.  The presentation will run 40 minutes or so, plus Q&A.  Reading it is faster.

Enjoy it, give me feedback, and I’ll be back to normal blogging Monday evening.

Recently Bill Rempel posed the following question to me:

Could you compare the total return of a 10-yr Treasury bought fresh and new anywhere from 1976-1980, and held to maturity (sending the coupons to cash) — to the total return from an equal-sized basket of stocks or residential real estate over the same time period? Please use “risk-adjusted returns” in the previous comment, re: returns on bonds. As a non-institutional investor who doesn’t care as much about the “mark to model” on any bonds I would hold, I would view double-digit Treasuries as free money, especially in light of long-term returns on stocks barely cracking the DD with divvies included …

He also made this recent post to further elucidate his views. So, let’s do a thought experiment. Suppose you knew where real interest rates and inflation would be ten years from now. How would that affect your investment policy?

The easy answer would be that you would know what to do with bonds. After all if rates are higher in the future, you would shorten your bond holdings to preserve your capital, and vice-versa if rates were lower.

But what do you do with your stocks? How is their performance impacted by future real interest rates and inflation rates? Before I answer that, let’s consider the difference between the yield of a bond, and its realized return from reinvesting the coupons. The following graph shows the coupon rate on a ten year Treasury note, and the realized return from investing the coupons at money market rates until the bond matured. The realized return is higher than the coupon when the average money market rate was higher than the coupon, and vice versa. But the difference is rarely very large. Most bond income comes from coupons.

Now, let’s consider how the ten year Treasury yield, inflation and real rates have varied over my study period, 1954-1997.

And look at how the ten year Treasury yield, the real rate of interest, and the inflation rate would change over the next ten years.

Looking at these graphs, you can guess that future equity returns are affected by changes in inflation and real interest rates, but here’s proof:

Or, another way of looking at it, future equity returns depend on future real interest rates and inflation rates. Note that bonds only beat stocks for ten-year investments beginning during the period 1964-1973, and not all of the time even then.

I ran a regression on the difference between ten-year stock returns and ten-year realized Treasury note returns, with the regressors being the current inflation and real interest rate, and the inflation and real interest rates 10 years from then. The R-squared was 57% (good in my opinion), and the coefficients were:

• Current inflation: +22%
• Current real interest rate: -12%
• Inflation 10 years from then: -121%
• Real interest rates 10 years from then: -46%

There was some autocorrelation of the residuals, indicating that periods of under- and out-performance of equities over bonds tends to persist:

All were statistically significant at a 95% two-sided level. What the regression tells us is that of the four variables considered, the most important one is future inflation rates. If future inflation rises, the value of future cash flow declines. It gets even worse if the Federal Reserve tries to squeeze out inflation by raising real interest rates high enough to overcome the inflation. Oddly, higher current inflation is a modest plus — maybe that indicates pricing power? Perhaps it is useful to think of equities as ultra-long bonds, with rising coupons. Rising rates would hurt those considerably.

Upshots

1. Note that it was a bullish period, and that stocks did not lose nominal money over a ten-year period to any appreciable extent.
2. Stocks almost always beat bonds over a ten-year period, except when inflation and real interest rates 10 years from now are high.
3. Investing in stocks during low interest rate environments can be hazardous to your wealth.
4. Watch for inflation pressures to protect your portfolio. Stocks get hurt worse than bonds from rising inflation.
5. Inflation and real rate cycles tend to persist, so when you see a change, be willing to act. Buy stocks when inflation is cresting, and buy short-term bonds when inflation is rising.

The relationship of the VIX to the S&P 500 is an interesting one, one that I have studied for the past nine years. Over that time, I have used the relationships to:

• Design investment strategies for insurance companies selling Equity Indexed Annuities.
• Estimate the betas of common stocks. (Not that I believe in MPT…)
• Trade corporate bonds.
• Gauge the overall risk cycle, in concert with other indicators.

If there is interest on the part of readers, I can go into the details of any of the above. Perhaps that could be the basis for future articles in this series. Today’s article is on the following relationships:

• The relationship of percentage changes in the old VIX to percentage changes in the S&P 500.
• The relationship of the old VIX to the new VIX.
• How quickly does the VIX mean revert, and
• The relationship of the VIX to price levels of the S&P 500.
• Maybe there will even be some hints at profitable trading rules.

The relationship of percentage changes in the old VIX to percentage changes in the S&P 500

I have a rule of thumb that I calculated a long time ago that the percentage change in the old VIX (and the new VIX, almost) is usually about ten times the percentage change in the S&P 500, and with the opposite sign. Well, I went and re-estimated the relationships. What do they look like?

The best fit line almost goes through the origin, and the slope is –0.0993. Inverting that, the value for my rule of thumb is 10.07. (Hey, that’s pretty close!) The best fit line explains about 50% of the variation in changes in the S&P 500.

I used the Old VIX because the data goes all the way back to the beginning of 1986, versus the new VIX, which starts at the beginning of 1990.

The relationship of the old VIX to the new VIX

I think differences in the two measures can be overstated. The two measures are 98.6% correlated. This equation describes the relationship:

New VIX = 2.04 + (Old VIX * 0.86)

The relationship is tighter when the VIXs are low, and gets a touch looser when the VIXs gets higher (no surprise, many relationships get strained in volatile times. That also implies that percentage changes in the new VIX should be about 86% of the changes in the old VIX, so my rule of thumb applied to the new VIX would be, “The percentage change in the new VIX is usually about 8.6 times the percentage change in the S&P 500, and with the opposite sign.” Still close to 10. I can live with that.

How quickly does the VIX mean revert?

Back in 1998, when I was developing my first generation old VIX / S&P 500 models, I came up with a statistic that said that the VIX mean-reverted to a level of 16, and it would tend to return at the rate of 20%/month, while being jolted by random disturbances pushing it to and away from the mean. The jolts are more powerful in the short run, but the mean-reversion is like gravity, inexorably pulling.

I have nine years more data now. Much of that time was a higher VIX era, so it is no surprise that the mean reversion target is 18.94. What is more interesting is that the reversion happens a little faster, at a rate of 28.2%/month, which means absent other disturbances, it closes half of the gap to the mean reversion target over 44 days. (Hey, pretty close to 50 days… could that be significant?)

This helps to show that snapback rallies after crises are so reliable in their appearance. Given the strength of the mean reversion effect in volatility, for the VIX to stay elevated for a long period of time requires a series of crises akin to what we had in 1998-2002.

I experienced the pain of that firsthand managing mortgage and then corporate bonds. Bond yield spreads are very highly correlated with the implied volatilities of stocks, and the yield spreads on bond indexes are highly correlated with the implied volatility on broad market equity indexes, like the VIX.

(Note for wonks: I estimated the mean reversion level (which is very close to the historic mean, no surprise) by regressing the one-day lagged Old VIX on the Old VIX itself. If you want how the math works on that, I can provide it, but it will make most readers go “huh?”)

The relationship of the VIX to price levels of the S&P 500

Finally, the most controversial bit. The S&P 500 tends to be lower than trend when the VIX is high, and higher than trend when the VIX is low. In equation form, it would look like this. (S_n is the S&P 500 at time n, and the same for V, the Old VIX. The V with a bar over it is the mean reversion target for the VIX.

In other words, the S&P tends to rise at a constant rate r, over time n, unless the VIX is above or below its long run average. Now, this is an oversimplification. I am using a very simple function form to allow me to come up with a result for now. There is probably some better functional form our there based off of Black-Sholes, or something like that, that wil do a better job. This is what I have for now.

Taking logs and simplifying, I get:

I know the S&P 500 and the old VIX over time, so I can estimate the parameters a, r, and e. The regression explains 88% of the variation in the S&P 500. a works out to be 4.94, which implies an S₀ of 263.42, which is not far off from the actual starting value of 242.17. The rate of growth for the S&P 500, r, is 9.30% which is consistent with the actual result of 9.45% (not counting dividends, and running from 1987 to the present). Finally, e, the shape parameter on the old VIX is 21.5%. What this means is when the old VIX is double its mean-reversion target, the S&P 500 should be 16% above trend, and when the old VIX is half its mean-reversion target, the S&P 500 should be 14% below trend.

Wait, isn’t that backwards? How can a high VIX be associated a high price for the S&P 500, and vice versa for a low VIX? (I blinked when I first saw this, but the coefficients are statistically significant at a very high level.) This is my explanation: when the VIX is high, the equation anticipates mean-reversion, and so gives a value that reflects what the S&P will be worth once volatility mean reverts. Vice-versa for when the VIX is low.

What does that imply for today? Putting the old VIX closing value of 25.18 into the equation would predict an S&P 500 price of 1898.90, a little more than 30% above the current quote. Time to buy!

Limitations

Well, not so fast. This is a deliberately simplified model compared to the realities of the market. Does the S&P 500 go up 9.3% annually? No, but over a long period, it seems to. Do I have the right functional form for the effect of the VIX? No, but this equation will be right to a first approximation. What about interest rates? Couldn’t they be included as a valuation parameter? Sure, maybe in the next round. They certainly helped in the “Fed Model.”

Don’t I have lookback bias here? If I were back in early 1987, would I think that the mean reversion target for the VIX should be 18.94? Maybe back then, but one would scratch his head in 1994, 2002, and 2006. The data fits very well inside the sample, but how well it will work in the future is always open to question. Every economic era is special, and blindly applying old parameters when the game might be changing is dangerous.

Possible trading rules

All that said, here are a number of trading rules that can be concocted from this study, and many work in hindsight. They boil down to buy when the VIX is high (panic), and sell when it is low (complacency). In future posts, I can work through a few of them, subject to the warning that data-mining can be hazardous to your financial health. (I have tried to pass through the data as few times as possible, but I have doubts…) I have found that being picky can generate big gains, but with few signals over long time periods (wait, isn’t that just the rise in the market?), and shorter-term systems generate many signals, but over short time spans, for small gains.

As an example of a system, you can look at Babak’s method using distance of the VIX from its 50-day moving average. 50 days? Close to the half-life mean reversion time. Looks like it can generate some good trades. Anyway, more later; hope you enjoyed this article.

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.

I debated on whether to post on this topic or not. I try to be a gentleman, so I don’t want to be too rough on those I criticize. Let me start out by saying that those I criticize have honorable intentions. They want to make investing simple for investors. Noble and laudable; the trouble comes when one over-simplifies, and errors get introduced as a result.

I am both a quantitative and a qualitative analyst, which makes me a little unusual. It also means that I am not as good as the best qualitative or quantitative analysts. To be the best, it takes dedication that would squeeze out spending too much time on the other skill. I have always tried to stay balanced, which helps me as a businessman, actuary and investor. Good problem solving requires looking at a problem from many angles, and then choosing the right analogy/tool to do the job.

One of my readers, Steve Milos, forwarded to me a piece from Merrill Lynch’s life insurance analyst suggesting that Price-to-Book — Return on Equity [PB-ROE] analyses were simply low P/E investing in disguise. I tossed back a comment “The Merrill analyst doesn’t understand what he is talking about. PB-ROE analyses are richer than low PE, though in a few environments, like the present, they are similar.”, prompting Steve to say, “LOL, I love that – now tell me what you really think!”

I decided to let the matter drop until Zach Maxfield, one of the analysts from Bankstocks.com, posted a laudatory article on Ed Spehar’s piece. I didn’t learn what I am about to write in a day, so let me take you on a journey explaining how I came to learn that PB-ROE analyses are valuable.

Back in 1982, I was a graduate teaching assistant at UC-Davis. The professor that I worked for used regression analysis in financial analysis to try to separate out effects that might be more complex than current modeling would admit. I did not get a chance to use the idea though, until 1992, when I began value investing, after my Mom gave me a copy of Ben Graham’s “The Intelligent Investor.” As I began investing, I noted that some stocks seemed better valued using book, others by earnings, and some by other metrics. Initially I began doing rule-of-thumb tradeoffs like Price to (book plus 5 times earnings). Eventually I wondered whether I had the right tradeoff or not, and how I might work in other metrics like dividends, sales, cash from operations [CFO], and free cash flow [FCF].

I’m not sure when it hit me, but I decided to run a regression of price versus earnings, book, sales, FCF, and CFO. Reasoning that sectors have different economic models, I did separate runs by sector. Truly, I should have done it by industry, or subindustry, as I do it today, but my initial attempts still found promising inexpensive stocks.

It was not until 1998 that I ran into PB-ROE analysis for the first time. Morgan Stanley was marketing a derivative instrument that would reduce book, turn it into earnings, and reduce taxes at the same time. I became the external expert on that derivative instrument, while hating its sliminess. (The whole story is a hoot, but it would take too long, and isn’t relevant here. Suffice it to say that the EITF and the IRS killed it six months after the first transaction got done.)

For those who believed PB-ROE analysis, the derivative was a godsend — less book, more earnings. With my more general model, I said, “So what, give up book, get “earnings,” which come back to book value anyway. These are just accounting shenanigans.” I didn’t see the value of PB-ROE then.

By 2001, I was a corporate bond manager. The Society of Actuaries Investment Section recommended the book, “Investing by the Numbers” by Jarrod Wilcox. An excellent book, I learned a lot from it, and he explained the PB-ROE model to me for the first time. To the best of my knowledge, it is the only place where I have seen it explained.

Where does the PB-ROE model come from? It is a simplification of the dividend discount model. In 2004, I gave a talk to the Southeastern Actuaries Conference. The relevant pages are 5-11, where I go through an example of a PB-ROE analysis, and give the limitations of the analysis. There are several limitations, here they are:

1. Encourages maximization of ROE in the short run, rather than the long run
2. Revenue growth is often equated with earnings growth in practice
3. “Run rate earnings” is adjusted (operating) GAAP earnings, versus distributable earnings (free cash flow)
4. Implicit assumption of constant earnings growth, required return, and dividend policy in the Price to Book versus ROE metric
5. The model assumes that capital is the scarce resource needed to produce more earnings.
6. ROA is more critical than ROE; it’s harder to achieve. In bull markets, anyone can add leverage.

Items 4 & 5 are the only problems intrinsic to the PB-ROE model; the rest are problems with how the model gets abused by practitioners. I don’t think that any industry fits those conditions perfectly, but I usually think that the are good enough for a first pass, and after that I make adjustments for different expected growth rates, excess capital, earnings quality and more.

PB-ROE is equivalent to low P/E investing when the regression line comes close to going through the origin (0,0). From my experience, that rarely happens. For my nine insurance subgroups (bigger than Mr. Spehar’s analysis — I cover them all), almost all of the intercept terms are different than zero with statistical significance. Or, as a colleague of mine said to me recently, “Thanks for teaching me how to do PB-ROE analysis,it really helped with my analyses on Japanese banks and US investment banks.”

Now, there is a seventh problem with PB-ROE, but it is more complex. So you run he regression and get the tradeoff of P/B versus ROE that the market is currently pricing. Is that the right tradeoff in the intermediate term, or are investors overvaluing or undervaluing ROE? Hard to tell, but when the regression line is flat or downward sloping (it happens every now and then), one has to question whether the market’s judgment is right or not.

In some environments, PB-ROE and low P/E investing will be similar, but that will not always be true. Do not accept a false simplification, even though it may be true at present. The PB-ROE model is richer, and works in more environments, after adjusting for the limitations listed above. PB-ROE is a very useful tool, and not “gobbledygook.”

Time for my most recent portfolio changes. The reshaping is complete, here is the data file and here are the qualitative details:

Buys

1. Arkansas Best [ABFS] — Inexpensive, and trucking is out of favor. Trucking should pick up with the economy in the second half of 2007, and as the dollar cheapens, trucking is needed to get the exports to the ports.
2. Deutsche Bank [DB] — Cheap major European bank. I’m light on financials (though if I lost my restrictions you would see a lot of insurance in my portfolio). 9-10x earnings for the next two years seems too cheap for me. Can they have that much exposure to the same problems faced by Bear Stearns? Maybe, but the valuation compensates for that.
3. Gruma SA [GMK] — Inexpensive, and a play on the growing middle class in Mexico. Also a play on the growing popularity of Mexican food in the world. I don’t have a lot in consumer staples, so this helps.
4. Mylan Labs [MYL] — returning to a name I last owned in 1988. Inexpensive generic drugmaker. I have nothing in healthcare, so this diversifies me a little. Generics are unlikely to fare badly as the branded pharmaceuticals should the Democrats win in 2008.

Sales

1. Sold Komag [KOMG] because of the merger, and the arb premium (amount of incremental gains from holding on until deal consummation) was less than what I could earn in cash.
2. Sold St. Joe [JOE], and I wish I had sold when one of my colleagues explained their likely troubles to me one month ago. St. Joe is going to have it tough for a while because they don’t have a lot of ways to generate cash, without selling property, and the land market is not as good as it was two years ago.
3. Sold Sappi [SPP]. The glossy paper market, like other fiber markets faces their share of challenges. Demand is sluggish, and likely to stay that way for a while.
4. Sold a little of Lafarge [LR]. Still have a position there. It’s had a nice run, so I rebalanced down to my normal target weight.

With these moves, I am back to 35 positions, up from 34. I am running with 16% cash, which is high for me. At the beginning of the year, I reinvested and brought cash down to 5% of the portfolio, but good investment results, combined with rebalancing has brought the cash back, and then some. If the cash hits 20%, I will raise my normal portfolio position size, and move cash to 10% or so. Maybe we get a pullback?

What I did not sell

1. SPX Corp — the turnaround continues. For now, honor the momentum.
2. Noble Corp — Hey, I just bought this last during the reshaping; I am not kicking it out so soon, no matter how well it has done.
3. Sara Lee — the turnaround continues. No momentum here; maybe management will succeed. A few of their ideas seem to be on target.

What I did not buy

Many more entries here. As I worked down my list, I kept saying, “Cheap for a reason… cheap for a reason…”

1. Too small: Charles and Colvard, PAM Transportation
2. Don’t care for the industry: Chipmos Technologies, Finish Line, Foot Locker, Encore Wire, First Consulting, Freightcar America, Korea Electric, and Metrogas
3. Already own something that I like better in its industry, and don’t want to increase exposure: Crystal River and MVC Capital (both interesting, though I like Deerfield better)
4. Irregular operating history: Optimal Group and Northgate Minerals
5. Tyco International is not as cheap as the data would indicate because of the recent spinoffs.

After I finish this, I will adjust the portfolio over at Stockpickr.com.
Full Disclosure: Long SPW NE SLE LR GMK DB ABFS MYL

The Efficient Markets Hypothesis in its semi-strong form says that the current market price of an asset incorporates all available information about the security in question. Coming from a family where my Mom was a successful investor, I had an impossible time swallowing the EMH, except perhaps as a limiting concept — i.e., the markets tend to be that way, but never get there fully.

I’m a value investor, and generally, over the past fourteen years, my value investing has enabled me to earn superior returns than the indexes. A large part of that is being willing to run a portfolio that differs significantly from the indexes. Now, not everyone can do that; in aggregate, we all earn the market return, less fees. The market is definitely efficient for all of us as a group. But how can you explain persistently clever subgroups?

Behavioral finance has been the leading challenger to the efficient markets hypothesis, but the academics reply that behavioral anomalies are not an integrated theory that can explain everything, like the EMH, and its offspring like mean variance analysis, the capital asset pricing model, and their cousins.

Though it is kind of a hodgepodge, the adaptive markets hypothesis offers an opportunity for behavioral finance to become an integrated theory. First, behavioral finance is a series of observations about how most investors systemically misinterpret investment data, allowing for value investors and momentum investors to make money, among others. The adaptive markets hypothesis says that all of the market inefficiencies exist in a tension with the efficient markets, and that market players make the market more efficient by looking for the inefficiencies, and profiting from them until they disappear, or atleast, until they get so small that it’s not worth the search costs any more.

Consider risk arbitrage strategies for a moment. Arbitrage strategies earned superior returns through 2001 or so, until a combination of deals falling through, and too much money chasing the space (powered by hedge fund of funds wanting smooth returns) made it less worthwhile to be a risk arb. It is like there were too many fishermen in that part of the investment ocean, and the fish were depleted. After years of poor returns money exited the space. Today with more deals to go around, and fewer players, risk arbitrage is attractive again. No good strategy is ever permanently out of favor; after a strategy is overplayed to where the prospects of the assets are overdiscounted, a period of underperformance ensues, and it gets exacerbated by money leaving the strategy. Eventually, enough money leaves the the strategy is attractive again, but market players are slow to react to that, becaue they have been burned recently.

Strategies go in and out of favor, competing for scarce above-market returns in much the same way that ordinary businesses try to achieve above market ROEs. Nothing works permanently in the short run, though as a friend of mine is prone to say, “There’s always a bull market somewhere.” Trouble is, it is often hard to find, so I stick with the one anomaly that usually works, the value anomaly, and augment it with sector rotation and the remainder of my eight rules.

Now, I’m not a funny guy, so my kids tell me, but I’ll try to end this piece with an illustration. Here goes:

Scene One — Efficient Markets Hypothesis

An economics professor and a grad student are walking along the sidewalk, and the grad student spots a twenty dollar bill on the sidewalk. He says, “Hey professor, look, a twenty dollar bill.” The professor says, “Nonsense. If there were a twenty dollar bill on the street, someone would have picked it up already.” They walk past, and a little kid walking behind them pockets the bill.
Scene Two — Adaptive Markets Hypothesis, Part 1
An economics professor and a grad student are walking along the sidewalk, and the grad student spots a twenty dollar bill on the sidewalk. He says, “Hey professor, look, a twenty dollar bill.” The professor says, “Really?” and stoops to look. A little kid walking behind them runs in front of them, grabs the bill and pockets it.

Scene Three — Adaptive Markets Hypothesis, Part 2
An economics professor and a grad student are walking along the sidewalk, and the grad student spots a twenty dollar bill on the sidewalk. He says quietly, “Tsst. Hey professor, look, a twenty dollar bill.” The professor says, “Really?” and stoops to look. He grabs the bill and pockets it. The little kid doesn’t notice.
Scene Four — Adaptive Markets Hypothesis, Part 3
An economics professor and a grad student are walking along the sidewalk, and the grad student spots a twenty dollar bill on the sidewalk. He grabs the bill and pockets it. No one is the wiser.
Scene Five — Adaptive Markets Hypothesis, Part 4
An economics professor and a grad student are walking along the sidewalk, and the grad student is looking for a twenty dollar bill lying around. There aren’t any, but in the process of looking, he misses the point that the professor was trying to teach him. The professor makes a mental note to not take him on as a TA for the next semester. The little kid looks for the twenty dollar bill as well, but as he listens to the professor drone on decides not to take economics when he gets older.