Friday, September 22, 2006

Acorn Clarification

In my previous post regarding the effect of demographics on asset prices, I asserted that “a stock does not represent an infinite stream of dividends subject to the market’s valuation; it represents a finite stream of physical returns.” In the comments section, Gabriel Mihalache appropriately asks for clarification:
…could you please expand on your comment regarding shares? I thought that shares entitle you to dividends in perpetuity, or at least as long as the company exists. When the company sells more, their value depreciates, but ignoring this, I don't understand what you mean by finite stream of physical returns.
It’s certainly true that dividends are what shareholders actually get, for as long as the company keeps paying them, which in the case of successful companies, is usually in perpetuity. However, the payment of those dividends represents the productivity of the underlying assets (e.g. plant and equipment), and any particular asset will typically tend to depreciate (become less productive) over time (or at least, will tend to have a finite useful life). The critical question is what happens when those underlying assets depreciate.

A corporation has a choice about what to do with its cash flow as its current assets approach the end of their useful life. It can invest in new assets, or it can return money to shareholders by means of dividends and stock buybacks. Since corporate managers generally seem to be very concerned about their stock prices, it seems likely that they will tend to make this decision based on maximizing the stock price. When there are a lot of working-age people who want to invest, there will be a lot of demand for companies that invest in productive assets, and the stock market will presumably favor stocks of companies that reinvest their cash flow. If you can say, “Look, we’ve invested in this great new project that is going to produce great returns in the coming years,” people will want to buy your stock.

On the other hand, when most of the population consists of retirees, there won’t be a lot of demand for companies that invest in new productive assets. Rather, stockholders will want to take what the company produces and just consume that product, while allowing the assets to live out their limited useful life. In that case, the stock market will favor companies that pay high dividends and use their excess cash to buy back stock. If you expect to live only another, say, 15 years, you’ll be willing to pay a premium for a stock that promises good payouts over those 15 years even if it will start to become worthless afterward. So even though the transactions are financial and involve things like dividends, the investors ultimately control whether a company reinvests the proceeds from its physical assets, and it is roughly as if those investors owned pieces of those assets directly.

Thus when Prof. Siegel imagines seemingly perpetual financial assets that depend on market demand for their value, he is creating an artificial construct. Ultimately, a stock represents part of (for example) a factory, and a factory really is like an acorn. The squirrels who own it can choose when to consume its output.

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18 Comments:

Blogger Gabriel Mihalache said...

A lot of stuff to consider, as always.

Is your analysis here based on a particular model/steady state equation? It would save me a lot of time if you could suggest something!

In most dynamic models of the firm I've seen the firm maximizes an actualized flow of dividends, where "actualized" means the usual geometric discounting: beta^1, beta^2, beta^3 and so on. (with beta the time preference or discount rate, < 1)

But if you're right then there are people that value long-term dividends more than short-terms ones and there are people who value the opposite (Maybe I'm reading you wrong.) in which case beta discounting doesn't make sense. (Doesn't this open up the possibility for arbitrage, in a world with well-behaved interest rates?)

Does this mean that firms oscillate between periods of investment/little or no dividends and periods with little investment/large dividends? (You make it sound as if there are 2 "regimes" with 2 distinct "target investors".)

I'm confused. Hopefully this will look more tractable in the morning!

Fri Sep 22, 06:55:00 PM EDT  
Blogger Economunculus said...

"The squirrels who own it can choose when to consume its output."

Well, not really for our system. The firm's managers make the decisions in practice, and they are more influenced by institutional than individual investors. But, if we assume that institutional managers reflect the needs of their investors, I'll grant that it's feasible to imagine that if you accept that boomers want dividends over capital gains, this could make it's way into manager behavior. You have to assume away a lot, including that they aren't interested in giving their nest egg to their kids, and they won't just switch sectors to derive income vs that boomers can drive a sea change in how equity markets work (from mainly capital gain expectations to mainly short run dividend expectations).

I'd also question the assertion that it's only stock price that motivates corporate managers. While that is certainly the single biggest factor, I think you'd be hard pressed to find more than a few CEO's that believe their only responsibility is to their shareholders. They also believe they have at least some responsibility to employees and customers, and taking a view of zero capital investment in order to squeeze short term cash flow and dividends is something I think few CEO's would put in practice if they are interested in keeping their jobs.

So while I don't think the scenario of slowing firm capital investment is likely due to boomers wanting dividends over capital gains, I do think it's a very interesting concept and not impossible. I also think there are several good arguments for the equity market falling off a cliff due to boomer retirement, and added in with this possibility, it's yet another reason to be wary.

PS. I agree that in practice, we should view single firm dividends as a finite time stream. PV vanishes fairly quickly, and even the biggest firms face a substantially non-zero probabilty of failure/business technology change/etc.

Sat Sep 23, 12:45:00 PM EDT  
Anonymous happyjuggler0 said...

I'm inclined to think that when most of the population consists of retirees, they won't be investing in stocks, at least not to the extent they used to. They will move into bonds for the reasons you outlined.

There is also the issue that no one really knows they'll live another 15 years, or whatever, if they are perhaps 65. As such growth may well continue to be part of their investment strategy. It is only when you get much closer to the demographic end of life (90, 100?) that asset growth ceases to be a concern. It would suck to be 65 and plan on dying at 80 only to wake up as a healthy 81 year old and be broke.

Sat Sep 23, 02:56:00 PM EDT  
Anonymous Anonymous said...

On the other hand, when most of the population consists of retirees, there won’t be a lot of demand for companies that invest in new productive assets. Rather, stockholders will want to take what the company produces and just consume that product, while allowing the assets to live out their limited useful life. In that case, the stock market will favor companies that pay high dividends and use their excess cash to buy back stock.

Wrong. Intertemporal consumption is mediated by interest rates. When most people are of working age (i.e. they are net savers), interest rates are low. When they start to retire, interest rates rise. See Modigliani & Friedman's life-cycle model.

Sat Sep 23, 05:48:00 PM EDT  
Anonymous Anonymous said...

By the way, I agree that people are not saving enough and that interest rates should be lower. Blame Social Security and other Ponzi-as-you-go schemes.

Sat Sep 23, 06:02:00 PM EDT  
Blogger knzn said...

Ragazzi, There’s basically two things that have to be true in order for my basic argument to be right: (1) labor and capital are reasonably good substitutes (Cobb-Douglas is good enough, I think), and (2) asset markets are smart enough to carve out for people the assets that they really want rather than forcing them to accept cookie-cutter assets like stocks that maximize the PV of dividends. As long as capital can be substituted for labor, it can generate enough real product to provide for future retirees. (Not that it necessarily will, because in actual fact, they probably aren’t accumulating enough capital, but that also means there won’t be a huge amount to be liquidated, so it is not a reason to expect a crash in prices.) Siegel’s argument has to be based on either lack of substitutability or capital market imperfections. And I’m trying to argue that capital markets are not as imperfect as he seems to think.

If I get a chance, I’ll deal with some of the details of the comments later.

Sat Sep 23, 08:12:00 PM EDT  
Blogger Gabriel Mihalache said...

I don't see how Cobb-Douglas is required... Where's the connection?

Firms face a trade-off between investing their income and paying dividends... it's not either/or but rather a continuum.

You're saying that a shift in demographics will lead to a shift in this ratio, away from investment and towards pay-outs, economy-wide. What we need is a transmission mechanism for this.

I've looked into a few dynamic models of the firm but since they all maximized either a expected sum of discounted utilities or dividends. I don't think we can replicate your hypothesis without overlapping generations...

But I was unable to write such a model and "make it stick", no phun intended. It turns out writing DGE models is harder than reading them. Who knew!

Anyway, in the unlikely case that someone is "into this" enough to help me, I'd love to see how one would go about modeling this. (We can assume firms don't have access to credit and that the representative consumer can't save other than by stocks.)

Mon Sep 25, 02:08:00 PM EDT  
Blogger knzn said...

The production function certainly matters. In the extreme case, with a Leontief production function, an insufficient rate of productivity growth, and goods that are non-storable, there just won’t be enough to go around if there aren’t enough working people. In that case, there is no way you could structure assets to provide adequate real returns during that period, because the real output just wouldn’t be there. At the other extreme, where labor and capital are perfect substitutes, it is purely a question of the transmission mechanism. Cobb-Douglas is somewhere inbetween, but my guess is that, for practical purposes, it is close enough to the perfect substitutes case given that total factor productivity is growing and some goods are storable.

This is a very interesting and important topic, but unfortunately I don’t have the time or the resources to do real work on it.

Tue Sep 26, 12:12:00 PM EDT  
Blogger knzn said...

anonymous (Sep 23, 05:48:31 PM), Interest rates ultimately depend on the marginal product of capital. If interest rates are low but the marginal product of capital is high, then there will be a capital spending boom, which will absorb quite a lot of capital, possibly at a reasonably high return. It all depends on the production function. In the extreme case where capital and labor are perfect substitutes, there will be no persistent changes in real interest rates no matter what the demographics; all the adjustment will be by quantities (capital spending) rather than prices (interest rates). With a more reasonable production function, there will be some changes in interest rates, but these depend on the specific shape of the function.

Tue Sep 26, 12:23:00 PM EDT  
Anonymous Anonymous said...

AFAICT, perfect substitability doesn't come into it. What matters is diminishing returns to capital, which the Cobb-Douglas function certainly exhibits.

Tue Sep 26, 02:27:00 PM EDT  
Blogger knzn said...

Assuming constant returns to scale (which is a reasonable enough assumption at the macro level), the rate at which returns to capital diminish is determined (inversely) by the degree of substitutability between capital and labor (also assuming there are no other factors). The question is how quickly those returns diminish, which is equivalent to asking how much substitutability there is between capital and labor. It’s an empirical question, but I don’t think we are seeing signs of significantly diminishing returns to capital today.

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