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Fed model: low yields justify higher P/E

Without any rational reasons, the markets have been conquered by a wave of hysteria. I guess that about 50% of the assets of the TRF readers as a group are held in the form of stocks (that's the percentage for Americans above $1 million) so as a community, we feel it.

What will the stocks do in the near term, medium term, and long term? Should the central banks' policies be adjusted in some minor or radical way to create a better economic system in the U.S., in European countries, or in the world?

The recent days of insanely huge drops of the stock market have been blamed on the uncertainty about the Fed's desire to increase the interest rates. It was generally assumed that the interest rates would start to go up in September 2015 – for the first time since 2006 – but because the conditions weren't spectacular and China slowed down and may be "exporting deflation" and because the Fed minutes were ambiguous, people are uncertain.




Well, if the rate hike is delayed, traders should be enthusiastic, shouldn't they? Well, some of them, or average ones, should be happy. Most others should be indifferent because the rate hike doesn't really matter for almost anyone, especially if it is going to be about multiples of 0.25%.

Just try to realize the absurdity of this whole reaction: the main driver of the dynamics on the Wall Street is the question whether the rates will be increased by 0.00% or 0.25% in September – almost every other answer seems extremely unlikely. And this difference between the two possible values of the increment – which should translate to a much smaller extent in other quantities, perhaps by 0.05% – has already subtracted some 4 percent of all the stocks prices that have almost nothing to do with it. Someone has clearly lost his mind.




The actual reason might be the fear that somewhere in between the lines of the Fed minutes, the omniscient Fed gurus are expressing the opinion that the economy isn't great. Yes, no, should a rational person look for such Da Vinci code? Shouldn't everyone be able to see what the economy is doing by himself and forget about some supernaturally good knowledge in the Federal Reserve? And shouldn't everyone see that the global economy is doing really well, anyway?

But even though most companies aren't really detectably affected by it, the mass hysteria of the ordinary, stupid people creates huge changes in the stock markets. Some of them jumped to the market really recently and expected some 100% certain monotonic growth. So they're getting out because this certainty doesn't seem to work?

Well, under status quo, it may indeed expected that the yields on bonds will be lower over the coming months and years. And that should send the stock exchange indices up, not down. It's been like that most of the time. Lower interests are good for companies, they can borrow, and so on.

Is there some better theory behind this claim? Yes, there is. The Fed model.

A company produces some earnings and when they're reliable and constant enough, the stock price is "roughly derived" from the earnings. The relationship is captured by the so-called P/E ratio. P is the market price of the share while E is the earnings per share.

The P/E ratio may be 10-20 in average. It means that the dividends per share "repay" the share you bought at the beginning in 10-20 years. Now, this is no universal rigorous rule. P/E may be lower or higher. It may be negative – a company may report a loss, hopefully temporarily. It may be much lower than 10 – when the profits were high but expected to decrease in the future. And it may be higher than 20 – usually when the profits are expected to go up quickly in the future or when the latest dividends looked like an exceptional downward fluke.

This is a fun rule-of–thumb. But is there some reason why the "medium" value of P/E is 10-20 and not 5-10 or 30-60, for example? Is P/E=15 just a convention that "kind of" became popular or is there some "calculation of this value from the first principles"? Well, there is one. It's the Fed model – named after the Federal Reserve that issued an equivalent comment by Ed Yardeni, an investment guru, in 1997.

The equation is simple:\[

Y_{10} = \frac{1}{ P/E}

\] The inverted P/E ratio should be pretty much equal to the 10-year treasury (bonds) yields \(Y_{10}\). A "rough" justification of the formula is simple. There is an equilibrium between stocks and bonds. The dividends replace the interests of the bonds. In both cases, you get "something like" the original investment back, plus the interest/dividends (although the stocks value may go up or down, a noise that averages to a fixed number).

If the bonds' real interest rates were much higher than the dividends you get each year, people would sell stocks and go to bonds, and vice versa. This justification sounds perfectly sane but the actual empirical record of the Fed model is a mixed baggage. However, you may construct graphs in such a way that the validity of the formula above is just stunning:



Since 1982, the agreement between S&P yield and the after-tax corporate bond yield (with the average rating of Baa) is just eye-catching. And one may hand-wave the disagreement before 1982 away because the laws were blocking the free repurchasing of shares which made the market ineffective.

What does it mean for the possibly "very different futures"?

Well, if the 10-year yields remain very low – currently close to 2% – or drop even lower, the averaged P/E of the stocks should go up, perhaps to 50 and higher. This may be counterintuitive because low yields may be linked to pessimist opinions about the future – and the people's ability to repay the debt in the future (in the possibly weaker future economy).

But the actual sensible causal relationships say that if the GDP growth stays weak, so will probably the interest rates – perhaps partly because of the central banks' efforts to stimulate the economy. And if the interest rates on bonds stay low, one should expect higher stock prices despite moderate earnings.

The Fed model isn't rigorous and one may present an argument with the opposite conclusion. If the general GDP growth is expected to be high in the next 10 years, then the total profit you expect from the stock will be higher (because of the exponential growth) which should imply a higher P/E. However, the Fed model says the opposite. In this scenario, people will demand higher interest rates, so the bonds will become more attractive than stocks, and stocks' logical P/E may actually be lower despite the expected growth.

As you can see, nothing is unambiguous here. It's a piece of black magic. With so many conflicting arguments "what should happen" with P/E under different scenarios, you could say that it is a supernatural quantity whose value is not dictated by anything reasonable in the market and that could very well be frozen to a predetermined function of time so that it would improve the economy.

Central banks: buy stocks

I have defended a similar point – a kind of stock exchange index targeting – in the 2008 blog post about the Dow Jones money. We could pay with banknotes that are effectively covered by a mixture of the stocks from the stock market. The evolution of the Dow Jones index could be made predetermined.

My algorithms to achieve this goal – a monetary system in which "everyone" effectively owns a mixture of stocks all the time – weren't terribly clear. One could adjust the interest rates and wait that the stocks react accordingly, and so on.

At the end, I think that the only reliable way to keep the value of stock indices in terms of "abstract banknotes" at a prescribed (accurate enough) value is to allow the central banks to buy and sell stocks. Should it be allowed? Is it anti-market? Would it be helpful or harmful or immoral?

The government of China has already purchased some stocks while trying to stop the decline of their stock market. It may look like a communist policy but it's just another, slightly different form of "quantitative easing". The main "moral" problem is that the government may pick the winners and losers and selectively help some particular stocks' price. This shouldn't be allowed, so they should uniformly buy at least whole sectors or filter according to some predetermined, canonically looking mechanistic criteria.

However, in principle, the inclusion of stocks into "quantitative easing" – which only involves the purchasing of bonds, and only selected types – would be natural and more effective. Why?

Because whether you like it or not, bonds are just a different form of cash. Their value doesn't fluctuate much. You may sell them and then buy your bread in the supermarket. People own a mixture of cash and bonds – which are just "two types" of banknotes. It's just slightly easier to buy bread for the normal cash – you need one step instead of two. But it's not so fundamentally different.

Quantitative easing as we know it in the U.S. and Europe means just the central banks' purchasing of the bonds for the newly printed banknotes. In effect, this only exchanges one type of payment papers that is already out there, the bonds (which are then "liquidated", pretty much), by another type, the regular banknotes (which must be printed). When doing so, the bonds are being eliminated and people get the normal cash instead – which is arguably "more tempting" to be spent. And when the bonds are being purchased for the newly printed cash, the price of bonds goes up (and the yields go down) while the value of the regular cash goes down (the quantitative easing positively contributes to inflation, or reduction of deflation, which is really the goal). The old owners of bonds and future owners of cash are being rewarded while the old owners of cash and new owners of bonds are being punished.

But because bonds are so similar to cash – their price ratio doesn't change by too many percent a year – this operation is rather innocent and inconsequential.

Stocks are different. They fluctuate more wildly, perhaps by dozens of percent a year per stock. And it's really the stocks whose crash starts Great Depressions and similar epochs. Even though the leftists love to claim otherwise, the real tragedy with a lasting impact occurs when the rich and courageous people – the entrepreneurs and those who own stocks – get much poorer and less capable to do things they're good at. Then, the level of investment and hiring and similar things go down. Try to appreciate that the investment is the rich man's spending and the average rich man has 50% of his assets in stocks. So when stocks (indices) drop by 20%, the average rich man gets 10% poorer and you may expect something like a 10% reduction of the investment, perhaps a bigger one because he becomes terrified that this may get worse and he may start to behave as a poor man. This may easily translate to (not quite) 10% drop in the GDP over a few coming years.

Isn't there a way to avoid it? Sure, there is. The central banks may protect stock indices against excessive collapses.

I understand that the libertarians may view it as a huge intervention to the free markets, perhaps the ultimate one. But it may also be viewed as a semi-automatic innocent policy that eliminates a useless, frivolous degree of freedom. And it may be viewed as a method to back the money – by the stocks.

The major central banks could very well decide to buy 5% of the publicly traded companies in the next year or two. Or some percentage. Perhaps, the percentage could be made sector-dependent. Perhaps, the number determining how much they buy could be dictated by the price increase caused by this operation, not by a fixed percentage, and so on. I can tell you lots of details about the actual algorithms when and how the stocks could be bought for that recipe not to create an easy opportunity for profit via arbitrage etc.

But the point is that the cash could be pumped to the real economy through the stocks. At some moment, the rules of this "new quantitative easing" could say that the central banks are obliged to sell the stocks again, once they grew by a certain percentage, or something like that.

At the same moment, this policy could protect the stock indices from dropping e.g. by more than 20% each 12 months. It could protect individual sectors of the economy – defined by their separate indices – from drops exceeding a percentage that depends on the sector.

One might say that it would be "unfair" for the central bank to insure the holders of the stock in this way. But the broader point you should see is that it is in the interest of the whole economy – almost all the people who live in it – to protect them against the worse collapses simply because difficult years almost always follow after such collapses.

Needless to say, with this kind of insurance, stocks would be getting more attractive and their average P/E would have another reason to increase. The volatility of the inclusive enough stock indices would go down – and ever greater groups of people would be keeping increasing percentages of their assets in the stocks (or stock funds tracking the indices).

As you must have understood, I actually consider the complete elimination of the "normal" money to be a goal. At the end, the old cash would become almost worthless and irrelevant and the de facto main cash used by pretty much all the people would be expressing a fixed portion of the traded companies.

Have you tried to ask "how big a portion of the world you own if you have $100,000, for example?" It is a very difficult question because there are different kinds of assets. Cash, bonds, corporate bonds, easy-to-sell real estate or cars, hard-to-sell real estate or land, and so on. One of them is the regular cash – in different currencies. The relative value of the cash and things like stocks oscillates and creates (or follows from?) all kinds of crises. But these wiggles could be eliminated.

The final result of the operations pumping P/E to ever greater values and leading people to replace the "old cash" by "new cash" would de facto be the money in which the "most inclusive relevant index" grows monotonically by a certain rate. How big the rate should be?

You could think that there is a freedom here but there mustn't be a freedom. If this rate were too high, people would prefer to buy the "basket of stocks" instead of the cash – moving in one direction – or vice versa for the opposite inequality.

The new cash – linked to the stock exchange index – wouldn't bring its owners dividends, so the dividends are exactly the difference between "holding the new cash" and "holding the corresponding mixture of the stocks". So to achieve equilibrium, the centrally prescribed growth rate of the relevant index expressed in the "new cash" would pretty much agree with the weighted average of the dividends (expressed as a percentage of the capitalization).

A funny detail is that you don't know how big the average dividends will be next year or later in this year. But that doesn't really matter. You can prescribe a value. The current S&P 500 dividend yield is just slightly above 2%. It has been as small as 1.1% in 2000 and 14% during the Great Depression. If the rule were that this yield is preprogrammed to be 2%, you would especially avoid the insane peaks such as those in the Great Depression.

What would actually be going on in 1929 if they had this "new cash" system? Well, they clearly had overly pessimistic ideas about the future which is why the stock prices went down so much – and the yields were a much higher fraction of those stock prices. But the "new cash" is linked to the average stocks. You have almost nothing else to "buy" if you don't like the stock underneath your "new cash". If you think that the intrinsic value of the companies will go down in the future, it's easier to borrow (because it seems easier to repay) the "new cash" because the "new cash" is basically the "dwindling stocks". So even the pure market interest rates would automatically go down and stimulate the economy. If you were afraid that your cash (linked to the stocks) is becoming worthless, you could start to buy cars and things for that, and that would stimulate the economy.

I haven't quite decided whether the interest rates would still have to be derived from an independent value dictated by the central bank or whether it could work more independently.

The fiat money have some extra freedom. They are an abstract unit whose magnitude is being given by all the long-term contracts and commitments in the economy – but whose value may be continuously driven up or down by changing policies. The question is what is the optimum way to do so.

In the medieval past, the money was linked to the price of gold. So the price of a particular commodity was being "targeted". That's clearly a highly unsophisticated choice. Many central banks are supposed to target the inflation rate today (the change of a basket of goods, something that the most "needy" people actually need to buy for their money). One may include many other things in the basket. And I've defended the nominal GDP targeting which automatically stimulates the economy when the real GDP growth seems slow.

But at the end, I do think that some stock market index targeting of one form or another would be more helpful in the fight against unjustified "cyclical" phenomena and unnecessary crises. Before we start to develop a significantly different monetary system in the whole world, the inclusion of the stocks into a quantitative easing program is also a straightforward extension of existing methods to pump more cash into the economy.

It's a method such that the central bank is never likely to run out of the bullets. All the bonds out there may be "sucked" by the normal quantitative easing program. But by the moment when the central banks start to own a significant portion of the stocks and offer newly printed money for the remaining stocks, it will become clear that the money is losing value and inflation is guaranteed to occur. So the remaining owners of the stocks will demand more money for their stocks, making the stocks purchasing program more effective (probably an infinite firing power is hiding there). Most importantly, there is nothing such as the "zero interest rate threshold" at which the regular quantitative easing has to stop.

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