Arnold Kling  

Stocks and the Economy, Again

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Every few years, I have this argument with a new round of commenters.

The ratio of stock prices to earnings is P/E.

The ratio of earnings to GDP is E/Y.

The ratio of stock prices to GDP is P/Y, which equals P/E times E/Y.

(Note that the basic math here uses stocks that turn all of their earnings into capital gains, paying none as dividends. Including dividend payouts makes the story more complex, but does not change the economic analysis.)

For stock prices to grow faster than GDP, either prices have to grow faster than earnings or earnings have to grow faster than GDP.

Stock prices certainly can rise faster than GDP for long but finite periods. If the P/E ratio starts at about 5 and gradually rises to about 25, that will do it. Something like that happened in the 20th century. Also, if earnings of shareholder-owned companies start at less than 10 percent of GDP, then they can grow faster than GDP for a long time.

Looking forward from today, which do you think is going to happen? Is the P/E ratio going to go up, because people become more willing to hold stocks? Or is the share of national income that goes to shareholder-owned companies going to go up? If you have a good story for one of those two happening, let me know.

(For example, one story is that U.S. firms will earn increasing profits overseas. I do not think that this will be a big enough effect over a sufficiently long period of time to drive earnings growth much above GDP growth. Still, it is an empirical issue.)

But if you think that stock returns will be higher than GDP growth without either ratio increasing, then one of us is incapable of doing simple algebra, and I am going to guess that it's not me.


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COMMENTS (57 to date)
thruth writes:

I was with you until the last paragraph:

"But if you think that stock returns will be higher than GDP growth without either ratio increasing, then one of us is incapable of doing simple algebra, and I am going to guess that it's not me."

Agree that stock prices cannot grow faster GDP indefinitely, but total stock returns:

  (P' + D)/P
  where
    P' = next period stock prices
    D = aggregate dividends
    P = current stock prices

can be higher than the GDP growth rate indefinitely with no impact on P/E or E/Y. Paying out dividends prevents the size of the stock market (and earnings) from becoming a disproportionate share of GDP.

So I guess it depends on what returns you are talking about...

J Storrs Hall writes:

ummm ... P/E * E/Y = P/Y no matter what E is ... the E's cancel out. The value of E has no effect on the result.
(unless E= 0, in which case the whole expression is undefined).

Floccina writes:
Looking forward from today, which do you think is going to happen? Is the P/E ratio going to go up, because people become more willing to hold stocks? Or is the share of national income that goes to shareholder-owned companies going to go up? If you have a good story for one of those two happening, let me know.

Both

1. I have heard that since the beginning of the industrial revolution yields on saving have been falling. KO, one of worlds safest stocks, has a PE of only 13 and still yields close to 3%. I think that that can continue to fall maybe in 100 a company like KO will only yield 1.5% and have a PE close to 30.

2. It is a 24 7 drag job to run some businesses as a sole proprietor. According to the book "The Millionaire Next Door" most of the Millionaire business owners interviewed prefer that their children go to college and get a good job rather than run their very profitable business because running the business is a drag. So I expect more small businesses to close and their markets to taken over by big public companies.

Hasdrubal writes:

J Storrs Hall:

If P/E is constant, and E/Y is increasing, then P is also increasing relative to Y.

Say P is 50, E is 10 and Y is 20 to start.

P/E is 5, E/Y is 1/2 and P/Y is 5/2

Now, say E grows to 20 but P/E stays at 5, meaning P must grow to 100. If Y stays the same, P/Y will have grown to 5.

So P/Y can change if P/E stays the same and E grows, because that means P will grow as well.

Stephen Dodson writes:

If companies never issued dividends (or repurchased shares), stock market returns would solely be based on earnings growth, which would make it equal to GDP growth over time (assuming the multiple stays constant). Dividend payouts do make the story more complex, and it also changes the economics. In short, the total return of the stock market including dividends (or share repurchases, which makes this even more complicated) is higher than GDP growth by basically the amount of dividends.

Think of a hypothetical small town where economic growth is zero. You're a landlord of an apartment building, and the rents you collect equal 5% of your investment. If rents don't increase (i.e., if economic growth is zero), you see a 5% return every year. The value of the building doesn't change, but including rents (read: dividends), you still see a return on your capital. If the economy did grow and rents increased, you would see an increase in the value of the building along with your rents revenue/dividends.

Or another way of thinking about it is imagine the bond market if interest rates never changed or no one ever defaulted. Bonds would be issued at par and returned at par, but the interest on them would create a return for the bond market as a whole. A bank doesn't need the price of your home to increase to make money on the interest.

Arnold Kling writes:

@thruth:

NO!!!!

Dividends cannot grow faster than GDP forever, either.

To put it another way, earnings cannot grow faster than GDP, whether they are retained or paid out as dividends.

Philo writes:

Even in a steady-state economy, with economic growth = zero, there will be a positive interest rate. On average, the investor will get a positive return for his *abstinence* or *waiting*. This can go on indefinitely, with shareholders achieving returns significantly greater than the (zero) rate of economic growth. (No algebra required.)

Eric Ulm writes:

@Arnold Kling

NO!!!!!!!

Numerical Example of 7% returns (combined Price growth and dividends) indefinitely in an economy where earnings grow at 3% indefinitely. Assume earnings are $1 per share paid annually at the end of the year. Today's stock price is $25.00. In one year, the stock pays its $1 dividend and the price of the stock has risen to 25.00*1.03 = $25.75. Total return: (1+25.75)/25 = 7%. Next year the price is $26.52. Total return (1.03+26.52)/25.75 = 7%. Wash, rinse, repeat. P/E ratio stays constant at 25/1. E/Y stays constant if Y grows at 3%. P/Y stays constant if Y grows at 3%. Price grows at 3% annually. Earnings and dividends grow at 3% annually. Stock returns *7%* year after year.

Eric

AH writes:

Is the problem here that we're assuming that return on stocks is the same as return on capital in the economy. Ie, that debt financing to firms is ignored?

I mean, GDP equals the sum of compensation to workers and compensation to capital. So if the split doesn't change then compensation to capital should grow at the rate of GDP.

However, firms finance with a mixture of debt and equity, so why can't the return on equity be higher than GDP growth so long as the return on debt is lower, such that the growth of return on capital is overall the same as the rate of GDP growth?

Thanks
-AH

ed writes:

This mistake again? Boy this is embarrassing for Arnold. Has he heard of dividends? Does he realize that dividends are part of "stock returns?"

@truth did NOT CLAIM that dividends could grow faster than GDP. If they grow right along with GDP it means that total returns will be above GDP growth with NO CHANGE IN P/E or E/Y. Please, please redo your calculations including dividends and this will be apparent to you.

(Not to mention, with share repurchases, dividends per share CAN grow faster than GDP, although you also have to consider share issues.)

Once again, I am willing to bet Arnold any amount of money that stock market returns will exceed GDP growth over any reasonably long length of time.

ed writes:

Here's an example to make it simpler for Arnold.

Imagine a stock that costs $100 per share and pays a $5 per share dividend for a 5% dividend yield.

Now imagine that the firms earnings fail to grow AT ALL. Furthermore, assume that the P/E doesn't change AT ALL either, so the stock price stays stuck at $100. Imagine GDP growth is 2%, so the firm value and profits are actually shrinking as a share of GDP.

According to Arnold's methods, the return on this stock is zero. I claim that the return is 5%, higher than GDP growth, despite the fact that the value and profits are shrinking as a share of GDP.

Now who agrees with me and who agrees with Arnold?

(I've ignored inflation, so just assume all numbers and growth rates are real.)

thruth writes:

@Arnold. I disagree. Eric Ulm's, AH's and ed's good comments explain why.

In the context of funding retirement benefits, the fundamental reason it's inappropriate to evaluate the adequacy of pension funding by discounting at a rate of return on stocks or other risky asssets is NOT because those rate of return assumptions will be optimistic (though they may be) but because it implies the risk premium on risky assets is a free lunch.

A retirement benefit is (usually) a firm commitment. The correct way to value that commitment is to apply the discount rate imputed from equivalent firm commitments such as long-term Treasuries (or perhaps a AAA rated corporate/municipal obligation in the case of most state pensions). If benefits are indexed in some way then one would use a discount rate imputed from an appropriately index financial instrument (e.g. the rate of return on TIPS for CPI indexed benefits). The fact that the commitment is being "funded" by an investment in stocks or other risky assets is immaterial to the value of the promised benefits. If the assets in the fund don't earn the returns required to meet the obligations, then someone else will be footing the tab (the value of that someone else's exposure, essentially in the role of guarantor, is the difference between the current value of the assets and the APPROPRIATELY discounted value of the benefits).

Many pension actuaries are a complete disaster on this point despite the significant economic literature on the subject such as this and this.

Gregor Bush writes:

Arnold,
If the initial ex ante equity risk premium were 0%, I think you would be correct.

But if the initial equity ex ante equity premium is greater than zero, the total return index can rise faster than GDP indefinitely if with no change in P/E or E/Y.

Think of the difference between a risk free Treasury bond and a BBB rated bond. Suppose the interest rate on the risk free bond were equal to the growth rate of the economy as in the neoclassical growth model. To compensate investors for the risk of holding the BBB bond, its yield will be higher. Therefore the total return index on the BBB bond will grow faster than a similar index on the Treasury bond, which will grow at the same rate as GDP.

The reason this is possible is because the initial price at which the BBB bond was purchased was lower (its ex ante risk premium was higher) than the Treasury bond.

ed writes:

Don't complicate things by worrying about the equity risk premium. Arnold's error is much more basic than that, independent of any assumptions about risk.

It should be obvious that investment can have a positive return even with no economic growth at all. If you prefer macro to finance, think of a simple non-stochastic Solow growth model in steady state with zero growth in total factor productivity. GDP growth will be zero, but the return to capital will not be zero.

You know, people saved corn for planting as seed even before the industrial revolution.

kebko writes:

Arnold's turning the old joke on its head. Everybody is saying, "Here. I have a can opener." And, Arnold keeps yelling, "No! If we assume there is no can opener, then we're all going to starve!"

Arnold, (1) the ratio of capital and earnings to GDP is totally irrelevant to the mistake you are making and (2) imagine that dividends never existed and that all profits are paid to owners through share buybacks. How does this change your analysis?

Gregor Bush writes:

ed,

I fully agree. But if GDP growth and the risk-free rate are zero and the return to capital is positive, the risk premium is greater than zero.

All I was saying was that for Arnold to be correct, the risk premium on equity (or capital) would have to be zero. If it's above zero, his assertion that stock returns cannot be greater than GDP growth unless P/E or E/Y are rising is incorrect.

Arnold Kling writes:

Folks,
You are giving me examples in which dividends are paid out of thin air. But a firm can only pay dividends if it has earnings. And earnings are a component of GDP.

If a stock earns $2 and pays out $5 in dividends, then the shares lose $3 in value. Unless you keep track of that in your examples, they are not going to persuade me.

A separate issue is how to think of government as a financial intermediary. "thruth" is worried about the government choosing a discount rate when it has a riskless liability funded by a risky asset. AH is thinking that the government might increase its returns on investment by holding more of the risky asset and less of the risk-free asset.

That raises the question of how I react as a "shareholder" in government when it changes its portfolio. Do I act as if I have a share of the government's assets and liabilities in my portfolio (a sort of Modigliani-Miller story) and, if so, where does that lead?

Jamie_NYC writes:

Arnold, can you please address the zero-growth toy model that ed and others mentioned. That would be the cleanest case: no growth, company/building earns 5%, pays out 5% in dividend.

Thanks.

Gregor Bush writes:

GDP=100
GDP growth = 0%
Earnings growth = 0%
E/Y = 5%
E=5
P/E=20
P=100
dividend payout ratio = 100%

P/GDP = 1

Annual Equity return = 5%

Every year I receive a 5% return on my investment, which is the share of total earnings to GDP in this simple example. Is my wealth not growing faster than GDP despite the fact that P/E and E/Y are constant?

Would the result not be the same if the dividend payout ratio were 0%? Either way, the total return index will rise relative to GDP.

ed writes:

Well, this is going from bad to worse. I never claimed that dividends are paid "out of thin air."

So fine, in my example add the assumption that earnings yield is 5%, which is all paid out as dividends (as in Gregor's example).

Or, if you think that the 5% earnings yield in my example is unrealistically high (it's higher than that right now for the S&P500, but whatever). Then go ahead and change the earnings and dividend yields in my example to 2%. Then the stock return is 2%, which in my example is still above GDP growth, which is exactly what you claim is impossible as a matter of algebra.

Eric Ulm writes:

@Arnold Kling

In my example, dividends aren't coming from thin air. They are 100% of the firms earnings. The firm is 1/1,000,000 of an economy that has $1,000,000 in GDP in year 1, $1,030,000 in GDP in year 2 etc. The market participants demanded a 7% return in order to invest in the stock, and therefore supply and demand sets the price of the stock at $25. If they had demanded an 8% return, supply and demand would have set the price at $20. If they had demanded a 4% return, supply and demand would have set the price at $100. In none of these cases are dividends magically created. They are always $1, $1.03 etc because that's what the firms underlying business process produces in the economy.

Eric

Eric Ulm writes:

By the way, my example isn't any different if you include pre- and post-dividend prices. The $25 stock grows to $26.75 after one year, pays out a $1 dividend and immediately drops in price to $25.75. So what? The stock price is set by supply and demand. Investors demanding 7% and knowing the $1, $1.03 ... dividend stream will set the price at $25 at time 0, $26.75 at time 1- and $25.75 at time 1+. As many people want to sell the stock to other investors at those prices as want to buy it as those prices. I feel like I'm in a parallel universe where nobody won a Nobel Prize for the CAPM.

Eric

thruth writes:

To strip this back to its bare bones, take a neoclassical, representative agent, endowment economy with no uncertainty (ergo no risk premiums). The endowment grows at rate g and is consumed immediately. The representative agent has time separable utility over consumption (c_t) with subjective discount factor "b" (0

u(c_0) + b u(c_1) + b^2 u(c_2) + ...

Agents can choose to consume or save in a bond earning rate of return "r" and bonds are in zero net supply. This setup implies that the equilibrium price of bonds is given by the standard Euler condition (the standard asset pricing result):

bu'(c_{t+1})/u'(c_t)(1+r) = 1

Assuming u(c) = ln (c) and c_{t+1}/c_t = 1+g we get

1+r = (1+g)/b

Which tells you that the risk-free rate of return depends on endowment growth (or, more generally, consumption growth) and the subjective discount factor. So rates of return can deviate from gdp growth... Generalizing this doesn't change the basic implication that returns aren't necessarily tied to growth rates. Preferences matter. (NB: I know this model completely fails to price assets in the real world a la Mehra and Prescott, but nonetheless it illustrates the principle.)

On the question of govt as financial intermediary, I like M&M as a first approximation. I'm agnostic whether govts or pension managers should to fund safe liabilities with risk assets, but I think an honest accounting would use market prices to value the assets and liabilities. (But I'm wary of tying bank capital requirements to market prices)

Eric Ulm writes:

Thanks thruth. I've avoided posting that derivation of how market interest rates are (typically) higher than growth rates until I was able to post a link to the original academic paper but you're absolutely right. Straight out of Cochrane or Duffie's asset pricing textbooks. Dr, Kling, have you read these? Do you disagree with their derivations or is there something subtly different about what they (and I and thruth and others) are trying to say and what you are trying to say?

Jason writes:

Gordon Growth Model, no risk, constant growth rate of dividends.

R=D/P+G

The rate of return equals the dividend yield plus the growth rate of dividends. G equals the growth rate of real GDP. d/p can be anything, it is a function of a flexible asset price. Therefore R can be anything.

P and D both growth at the constant rate of real GDP growth. The return is a function of the asset price. Although it has to grow at the rate of GDP growth, its level determines the return on stocks. The return on stocks can be high forever even as the price is always the same multiple of GDP.

Less Antman writes:

@Arnold

GDP / Value of Nation = Total Return of Country

Earnings / Value of Stock = Total Return of Stock

This is what you are asserting must, over time, have a close relationship. True, BUT:

(GDP - Previous Year GDP) / Previous Year GDP = Growth Rate in GDP

which is NOT GDP / Value of Nation!

Gregor Bush's excellent example should prove the point, but might be clearer if I add one more figure: the implied value of the nation based on a 5% capitalization of his 100 GDP would be 2,000.

So you keep insisting that the return on stocks cannot exceed 5% over the long term, which is correct, BUT THE GROWTH RATE IN GDP ISN'T 5%, IT IS 0%, since it is 100 every year. You keep insisting that 5% equals 5%, while we're all trying to explain to you that 5% does exceed 0%, which is what a comparison of stock returns with GDP growth rate involves.

There is no way earnings equals the growth rate in earnings unless there is no consumption, in which case we all drop dead from starvation and exposure. CONSUMPTION explains why stock total returns MUST exceed the growth rate in GDP for eternity.

By the way, real US stock returns were around 7% in the 20th century, and even a tripling of PE over that century would have only explained 1% of it. And real stock returns were also around 7% in the 19th century. So even if you assert that PE ratios have gone from 2 to 18 over the past 200 Years, which is ridiculous, you'd have to argue that either real GDP growth has averaged around 6% over US history or you need another explanation for stock returns (Jeremy Siegel of the Wharton School at the University of Pennsylvania is the source for my stock return numbers).

J Storrs Hall writes:

I think that a lot of the confusion here has to do with whether we are talking about the numbers P, E, and Y, (technically not numbers but functions of time), or their growth rates dP/dt, dE/dt, and dY/dt.

Showing something about P, E, and Y says nothing about their derivatives (or those of their ratios).

In particular,

d((P/E)(E/Y))/dt
is NOT
d(P/E)/dt * d(E/Y)/dt
but rather
(E/Y) d(P/E)/dt + (P/E) d(E/Y)/dt

So, does "stock returns" mean P, E, P/E, or d(P/E)/dt?

Let's take a simple example: P=E=Y=exp(t). This makes all the numbers and their growth rates equal to each other -- but all the ratios (P/E, etc) are a constant 1 and all the growth rates of the ratios are 0. It clearly doesn't make any sense to compare the growth rate of P/E (i.e, 0) to the growth rate of Y (exponential).

If "stock returns" means P/E or d(P/E)/dt, a simple counter-example to the post is P=E=Y=exp(-t). Then "stock returns" are respectively 1 or 0, and GDP growth (= dY/dt) is -exp(-t), which is uniformly negative and thus less.

Shayne Cook writes:

@ Arnold:

A couple of things that may be indicative of an over-simplification (and lack of utility) of your algebra ...

"But a firm can only pay dividends if it has earnings. And earnings are a component of GDP."

Both statements are wrong, or at least wrong-headed. A firm can pay dividends from either past or anticipated future earnings. Your first statement implies firms can only pay current dividends from current earnings.

The second statement is wrong. Earnings are NOT a component of (U.S.) GDP - (I)nvestment spending inside the U.S. is a component of U.S. GDP. Multi-national firms' investment spending outside of the U.S. is NOT counted in U.S. GDP calculations. And that foreign investment spending has become decidedly more non-trivial in recent years - and has generated extraordinary returns (earnings growth, NOT counted in U.S. GDP) to multi-national firms.

Also, Earnings (or Net Earnings, or 'Profits'), irrespective of source, are an accounting fiction, not an absolute measure of the profitability/viability of a firm. Spending, on the other hand, is current, tangible, measurable, and not subject to accounting rules (depreciation, depletion, etc.) that distort 'bottom-line earnings'. That is why (I)nvestment spending, not earnings, is counted in GDP.

To address your main question, I refer to the 'aside' comment in your original post on "... increasing profits overseas ..." You indicate you suspect foreign earnings influence is over-estimated. I suspect you may be under-estimating foreign earnings influence - now and for the future. A current indicator of the magnitude of that phenomena is the often-bemoaned amount of money U.S. firms (such as Microsoft) are holding on their books, and not re-investing in the U.S. economy. That 'cash-on-hand' is estimated to be well in excess of $1 Trillion. But for the most part, that cash (past earnings) is foreign derived and the owning firms would have to pay 35% taxes to 'repatriate' it to spend in the U.S. That's in addition to foreign taxes already paid in the country of origin. That U.S. 'repatriation' tax rate is being debated in Congress right now, by the way.

Given the rather distorted nature of the 'Earnings' component of Price/Earnings (P/E) ratio, either for an individual stock, or for some arbitrary aggregation/index of stocks, P/E is solely indicative of the market's current risk tolerance or optimism. But P/E does not lend itself at all to the rigorous algebraic application you've posed. At least not to formulate any sort of reliable conclusions regards stock market returns to capital in correlation to U.S. GDP. And as you already know, the measured/published GDP number has its own distortions.

Charles R. Williams writes:

Capital cannot grow faster than gdp forever. If you fix the debt/equity ratio then equity cannot grow faster than gdp forever. But the return on equity in aggregate is largely consumed. So a 7% return on equity is consistent with a 3% growth rate in gdp as long as 4% is consumed and 3% is reinvested. This is accomplished at the company level through share repurchases and dividends. At the individual level dividends can be reinvested or shares can be sold. Through the life cycle young workers accumulate equity, and old workers consume equity. Obviously, changes in demographic mix can affect the desired level of capital/equity.

Shayne Cook writes:

@ Charles R. Williams:

"Capital cannot grow faster than gdp forever."

Which/whose GDP? For that matter, which/whose capital?

Again, capital, and returns to capital (RTC), can and does grow faster than any individual nation's GDP - particularly current U.S. GDP - and can theoretically do so forever. Capital, and returns to capital are GLOBAL, not bounded by national borders as is any individual nation's GDP.

I suspect quite a few folks in the U.S. dramatically underestimate the concept of globalization. There's a good reason for that. From 1945 through about 1990, the U.S. economy was the vast majority of global economy. As such, it was viable to consider only U.S. returns to capital in correlation to U.S. GDP. Globally (outside the U.S.) derived RTC was "in the noise", for lack of a better term. That is no longer the case and will decreasingly be the case in the future.

Chris Kerns writes:

"If a company grew faster than the economy forever, it would eventually overtake the entire world economy"
-Value: The Four Cornerstones of Corporate Finance. 2011. McKinsey & Co., p.19

Arnold, I believe you are just expressing one of the core assumptions of business valuation. The other comments, to me, seem to be missing the forest because of the trees.

Shayne Cook's post, I believe, points to one argument that could support a sustained increase in either P/E or E/Y, that being an inflow of capital (thus increasing P) or earnings from outside the national economy (assuming you were drawing an imaginary line around the U.S. economy, which you may not have). To Shayne's point, the U.S. economy is not a closed system.

I find it interesting that some obviously very intelligent and educated people are arguing that P/E and E/Y can remain constant while P/Y can change. I think J Storrs Hall second post (regarding the derivatives) explains the mistake some are making.

@ J Storr Halls: to your first post, even though the "E" cancels out, there are many times where separating out component ratios is a useful (and commonly practiced) exercise. For example, looking at

ROE = NetIncome/Assets * Assets/Equity

can be more insightful to a firm's financial performance than just looking at NetIncome/Equity

Scott Sumner writes:

I agree with this post.

kebko writes:

Chris Kerns,

A company doesn't have to have positive growth in order to provide a return on investment.

ed writes:

Yikes, is that the real Scott Sumner? He hasn't heard of dividends either? What is going on here?

Thanks Jason for a succinct explanation:

R=D/P+G

Joe W writes:

Try thinking that the entire economy is a closed system (the world) and is made up of one business.

Less Antman writes:

2010 GDP $14,256 Billion
2009 GDP $14,093 Billion

Now, quick, what was GDP in 2010?

Correct Answer: $14,256 billion
Arnold's Answer: $163 billion

And anyone who thinks GDP can be $14,256 billion when it only increased by $163 billion obviously doesn't understand algebra. ;)

Total stock returns cannot exceed GDP. True.

Growth in stock returns cannot indefinitely exceed growth in GDP. True.

Total stock returns cannot indefinitely exceed growth in GDP. False.

Please, Arnold, stop assuming we're all weak in algebra and consider that you may be making the wrong comparison. You want algebra? Here is your argument (once we allow for the possibility of increases in corporate share of earnings until it is all of it):

A = B (roughly, total corporate earnings is limited to GDP)

A' = B' (growth in corporate earnings is limited to growth in GDP)

Therefore,

A = B' (total corporate earnings is limited to growth in GDP)

THE CONCLUSION DOES NOT FOLLOW. Either compare A to B or the derivative (slope) of A to the derivative (slope) of B, but stop comparing A to the derivative of B.

Or look at Gregor Bush' clear example with an open mind and you'll see that 5% indeed exceeds 0%.

Eric Ulm writes:


@Charles R. WIlliams - July 8, 10:09 AM

Exactly.

J Storrs Hall writes:

A lot of this is based on the intuition that a component of a total can't grow faster than the total indefinitely. This isn't true: it can increase asymptotically to the total, always growing faster, never exceeding. People's intuitions re infinite series are notoriously unreliable, going back to Xeno.

Chris Kerns writes:

Kebko,
I understand that. A firm can have 0% earnings growth but maintain a ROIC in excess of WACC, thus generating real and excess returns to investors. Although that position is typically hard to maintain in a free economy as others will just copy you and eat away your ROIC without some higher barriers to entry (e.g., utility companies). I would typically expect a reversion to the mean where ROIC = WACC in this case.

But I don't get what point you are trying to make?

Coupon_Clipper writes:

Thanks to Less Antman for chiming in. He's straightened out my intuition about this and related topics a number of times.

kebko writes:

Chris, I think the last paragraph of Les Antman''s comment makes my point the best. Some part of the return is not growth based.

Chris Kerns writes:

I'm starting to think you all agree with Arnold but just haven't figured it out yet, probably because you think he is saying something he is not.

First, Arnold is not saying that TRS cannot increase faster than GDP, he's just saying that when that happens, one of the ratios is changing. The algebra makes it pretty hard to dispute.

Gregor Bush's "excellent example" actually supports Arnold's claim when you observe Arnold's constraint that all earnings are converted into capital gains, which is the same as saying that the dividend payout ratio is 0%, not the 100% that Gregor used. So, using that same excellent example:

Start:
P=100
E=5
Y=100
Therefore P/Y=1, P/E=20, E/Y=5%

End:
P=105 (100 + 5% return; if it helps to think of this in terms of a 100% dividend payout, just think of the price the day before the dividend is issued)
E=5
Y=100
Then P/Y=1.05, P/E=21, E/Y=5%

So, yes, returns to stock holders grew faster than GDP (P/Y increased), which, to Arnold's point, drove a higher P/E ratio. Why? Because the firm now has more cash on its balance sheet and investors are surprisingly good at valuing cash.

If two companies, "A" and "B", are identical except that "A" holds more cash than "B", A will have a higher P/E ratio.

I don't see where Arnold ever states that "total corporate earnings is limited to growth in GDP"

I recommend the McKinsey book on "Value". Quote: "the long term growth rate in corporate earnings is the same as the long-term growth rate in GDP"

Eric Ulm writes:

@Chris Kerns

I think you misunderstand me. I don't disagree that ""the long term growth rate in corporate earnings is the same as the long-term growth rate in GDP", I disagree that this implies that stocks cannot return in excess of GDP indefinitely. Reread my example. In it, ""the long term growth rate in corporate earnings is the same as the long-term growth rate in GDP" yet the stock returns a much higher rate than the long-term growth rate in GDP. I recommend reading Dynamic Fiscal Policy by Auerbach and Kotlikoff and programming some examples in Excel to convince yourself that the returns on both fixed and stochastic assets are determined by supply and demand and can easily be higher than the long-term growth rate in GDP.

Eric

Gregor Bush writes:

Chris Kerns,

In the case where the firm pays the 5 percent as a dividend it's clear that my return was greater than GDP growth without any change to PE or EY.

The case where thefirm pays no dividend and buys back shares is no different. P and E per share rise as the number of shares outstanding delines by 5 percent. The PE ratio need not rise.

Scott, where have I made a mistake?

Eric Ulm writes:

@Chris Kearns

"I find it interesting that some obviously very intelligent and educated people are arguing that P/E and E/Y can remain constant while P/Y can change. I think J Storrs Hall second post (regarding the derivatives) explains the mistake some are making."

Please reread our examples. We are claiming P/E, E/Y and P/Y can remain constant while stocks earn a rate of return higher than GDP growth. The change in P/Y is *not* the same as the return on assets.

kebko writes:

Let me guess, in a few years, when Arnold explains that there are no returns to capital in a no-growth economy, he's going to have to have to go through this whole argument again with a new set of algebra mocking naifs.

Eric Ulm writes:

Wow, Arnold. Are there really no returns to capital in a no-growth economy? Put that simply it sounds really silly, doesn't it?

Eric Ulm writes:

@Joe W

I can't tell if you're on Arnold's side or not, but imagining the economy as a single company may be part of Arnold's problem. See the comment by Charles R. Williams July 9, 2011 10:09 AM. The procedures in "Dynamic Fiscal Policy" require companies that compete for business and overlapping generations, some of which prefer to buy assets and consume less and some of which prefer to sell (or borrow) assets and consume more. Normally, Arnold criticizes the idea of people who work at the GDP factory and get paid in GDP which they take to the GDP store to buy the GDP they made. I hope that's not the issue here.

Joe W writes:

Imagining that there is only one business in an entire economy is not a "problem". It is a simplifying assumption -- assume that all of the businesses merged into (or got bought out by) a single entity. And if your arguments do not work in that case, your arguments need to be reworked.

Joe W writes:

Or, if you prefer, imagine that there are only two businesses in the world economy. One pays a dividend, and one does not.

Eric Ulm writes:

@Joe W. You know what, you're right in this instance[1]. I'm rereading Auerbach and Kotlikoff (pg. 17-18)and there is only one production sector in the (model) economy. Competitive business are later additions. This model still produces asset returns larger than GDP growth. Table 2.1 (pg 24) clearly shows an economy with zero-GDP-growth that contains positive returns on assets. Apparently only the overlapping generations are necessary.

[1] That doesn't mean that simplifying away (ignoring) the competition in real economies will always produce correct results. Clearly an economy with one monopoly produces a higher price for its good that one with an number of competitive firms so if you were attempting to model "price", you can't simplify away competition.

Joe W writes:

It would be better if you could concentrate on the issue at hand.

I think what many are objecting to is Arnold's statement at the end of his post:

"But if you think that stock returns will be higher than GDP growth without either ratio increasing, then one of us is incapable of doing simple algebra".

The common objection I see to this is that if stocks pay dividends, then an investor's return on a stock investment can be higher than GDP growth.

If earnings are not passed back to the investors, then Arnold's statement is obviously correct -- simple math, as he says. But Arnold further claims that the same result holds if dividends are paid.

So to explore the disagreement, you need to concentrate on what happens when earnings are paid out as dividends, which Arnold says is complicated.

Hence my suggestion to simplify by making an assumption of only one business. Or, if you prefer, two businesses, one that pays dividends and one that does not. Follow the money. Where do the dividends go, and how does that affect investor returns?

Eric Ulm writes:

I agree it is complicated. See Auerbach and Kotlikoff, "Dynamic Fiscal Policy" 1987. Pg. 24 specifically. This is a graduate level textbook and I'm surprised it had to get this far. Pgs. 17-18 make exactly your assumption (only one business). I can't photocopy the pages and post them here and don't have the time to type out the argument and equations by hand, along with the accompanying excel spreadsheets and/or matlab code to solve the optimization problem. Charles R. Williams mentioned what happens to the dividends. Some people reinvest them, some people consume them, and others sell stock to fund their additional consumption. Net capital stock stays a constant percentage of GDP. Assets return in excess of GDP indefinitely. I don't plan to comment further unless Dr. Kling responds to some of the questions since July 8, 2011 5:47 PM or someone else posts the "complicated" analysis *including* dividends and shows that Arnold is correct in his claim that this "complicated" analysis supports the idea that asset returns cannot exceed GDP indefinitely. I think the burden of proof is now on him.

Joe W writes:

On page 24 of the "Dynamic Fiscal Policy" edition I am looking at, I see "Table 2.1, The transition arising from a one-period tax cut". Does not seem relevant to the current discussion.

Can you provide a more specific reference to what you are talking about? Perhaps with section numbers or figure references?

Eric Ulm writes:

Look at table 2.1, (pg 24 in the book, pg. 14 in the pdf). The “Capital” column is the equivalent of “Stock Price”. Its longterm growth is 0 (see 10, 20, infinity all having the same value). The column labeled “Income” is the equivalent of what we’ve been calling “corporate income”. Its growth rate also levels off at 0 (see 10, 20, infinity) and, since there is one company, this is a GDP growth of “0”. Equation 2.8’, page 18, shows an “r_t” that represents the return to capital, defined this way in the 4th to last sentence of the paragraph just below equation 2.7. The “Interest Rate” column in Table 2.1 shows a positive value of “r_t”, the returns to capital, despite GDP growth being zero. It’s an odd looking number because the “generations” are 30 years. If you take the 30th root of 1.540 and subtract 1, you get a quite reasonable 1.45% “interest rate” or return to capital. This is a risk-free return, since the production function is a fully predictable Cobb-Douglas one. I’ve done up excel sheets (several years ago working through the book) that reproduce this table.

Eric Ulm writes:

Oops, forgot to carry the 1. The interest rate is (1+1.540)^(1/30)-1 = 3.16%, which I'd know if I read pg. 24 :-).

Dan Carroll writes:

This has probably been covered, but I didn't read all of the comments:

The return on a stock = change in price + div yield. If P/E is constant, then change in price = change in earnings. Alternatively, return = div yield + div growth. Again, div growth = EPS growth if payout is constant.

In aggregate, E can't grow faster than NGDP on a sustainable basis. For S&P 500 companies, I would use World NGDP for a yardstick, not US.

If E does not grow, but yield = 8%, then your return is 8% +/- P/E change.

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