Another take on q-factors and investment CAPM

Standard consumption CAPM applies a constant discount rate across all stocks, but surely that is odd if different companies face different costs of capital, as indeed they do.  Take the companies with a higher cost of capital — in equilibrium they also should have higher rates of return as an offset.  And those are (usually) the small stocks, and indeed we know there is a small stock premium (sometimes better expressed as a lower market to book premium) in the finance literature.

But that premium comes from the supply side arbitrage conditions, not from some odd properties of portfolio risk.

You will note that “the investment CAPM says that controlling for a few characteristics is sufficient to explain the cross section of expected returns.”  Theory advocates claim that investment CAPM indeed passes that test: “…most anomalies turn out to be different manifestations of the investment and profitability effects.”

That is all from this Lu Zhang paper.  Here is my earlier post on q-factors and investment CAPM, still not sure I understand it!


The CAPM fully does not assume constant discount rates for each co. It assumes constant market risk premium and risk free rates over time. It would be utterly useless if it assumed constant discount rates for each co...

There was something potentially lost in translation here. I am certain.

You don't discount a dividend from Apple with a different rate than you discount a dividend from Amazon. End of story. Simple. No mistake.

Amazon has a higher beta than Apple, due to operating leverage.

The abstract is braggadocious: "the investment CAPM succeeds in mounting an efficient markets counterrevolution to behavioral finance in the past 15 years." It looks like the paper just sticks Fama-French characteristics (like size and ROE) into a return equation, and calls them "supply factors".

I think you could benefit from some more reading about asset pricing and what the Consumption CAPM assumes and doesn't assume. See for instance:

It is odd that Tyler didn't acknowledge that stocks with higher risk should have higher returns, i.e., higher discount rates. This is true in the simplest Miller-Modigliani or CAPM contexts.

Agreed - I'm not sure if this is him joking or trolling to see what happens when he emphatically makes an incorrect assertion, but it's hard to imagine anyone who's taken even a single finance course claiming "You don't discount a dividend from Apple with a different rate than you discount a dividend from Amazon. End of story. Simple."

You are confusing the time rate of discount with the (possibly varying) marginal utility of money.

Tyler, macroeconomists use "discount rate" to denote subjective rate of time preference, usually for risk-free investments. But financial economists use that term for (conditional) expected return on a risky investment. Hence, investments with different risks can have different discount rates.

What really matters here is consistency with the paper, which uses the term "discount factor" for a (uniform) subjective rate of time preference. It is true I switched this to "discount rate" but clearly this is the same concept, again no error, not even of terminology.

I see where the confusion lies. The stochastic discount factor, typically denoted "m", does not vary across assets - this is the factor the expresses the relative utility of payoffs in different states of the world: P=E(mx) holds for all assets. "Discount rates" typically denoted "r" refer to the rate at which E(x) is discounted (where x is a stochastic payoff), and will vary across assets, according to the correlation of x with m (that is, how the payoff varies with relative utility of money in different states of the world). It's not correct to use discount rate to refer to the stochastic discount factor (or at least you shouldn't be surprised if people are confused when you conflate the two). See the cochrane link (chapter 1 of his "Asset Pricing") for a clearer discussion of this.

Or it's someone pretending to be Tyler in the comments.

Agreed. At the least, differences in beta and financial leverage would directly cause differences in the discount rate for Amazon and Apple implied by CAPM.

See page 9 of Zhang's paper for a review of the dividend discounting model. The "r_i" variable in the model refers to the individual firm's internal rate of return. That absolutely varies depending on whether the firm is Apple or if it is Amazon. We intuitively expect this because each firm has a different risk profile. To move this away from the ivory tower and into the real world, the discount rate for Huawei under a Trump administration is going to be different from a US based tech company.

“Standard consumption CAPM applies a constant discount rate across all stocks.” No, it doesn’t. Someone just failed Finance 101.

"But that premium comes from the supply side arbitrage conditions, not from some odd properties of portfolio risk."

It has to be both though, right? Otherwise, why wouldn't investors prefer the higher returning stocks? Put another way, why do some firms have higher cost of capital if not because investors view them as (undiversifiably) riskier? In a risk-free world, for example, all stocks do need to have the same return --- to avoid arbitrage --- which, in turn, would lead to the same cost of capital, the risk-free rate, for all firms.

Supply-side arbitrage conditions, such as firms take on all positive NPV projects, are in addition to, not in place of, investor-side no arbitrage conditions.

Think of it this way. Suppose one observes an "anomaly" that high-profitability stocks tend to have higher returns.

The conventional view is that high-profitability must somehow indicate higher systemic, i.e., non-diversifiable, risk and that return premium is compensation for such risk.

An alternative view is that some firms are systemically riskier than others. Investors will demand higher returns to hold those stocks, which raises those firms' cost of capital. Since firms only take on positive-NPV projects, the higher cost of capital will cause those firms to take on only high-profitability projects. Thus, those systemically risky firms will tend to be associated with higher profitability.

Does higher profitability indicate higher risk or does higher risk instead tend to be associated with higher profitability? Yes.

At his first blog post on this study I commented about globalization and its effect on pricing, both of the goods firms sell and their stock, using Apple to make my point. Here, I would mention Amazon, which priced goods below the competition in order to gain market share even though doing so generated either losses or zero earnings, yet Amazon's stock soared and the company grew by leaps and bounds (increasing market share) until Amazon discovered the cloud and began generating profits which caused its stock to soar to new heights. Indeed, Amazon's stock price continued to rise even during the great recession. How does a firm's stock price soar when its own business plan shows no profits long into the future? And Amazon is not alone. Uber's IPO went well enough and its stock price held steady for six months even though Uber priced its services (ride hailing) below cost with no plan other than to grow and increase market share. Then there's Google and Facebook, which price their services at zero in order to dominate the market. What market? The market in selling their customers' data. My point is that today's most successful businesses are not your grandfather's or father's successful businesses. I applaud the author of this study for his unconventional approach to pricing, an approach, whether right or wrong, is at least a departure from convention. The comments (at this blog post and Cowen's first blog post) demonstrate that departure from convention is not well received, heresy even. That Cowen is willing to look at an unconventional approach to pricing is to be commended. But I would expect nothing less from Cowen.

Is it really different? In the 19th century they rather openly used the word "scheme." Google, Amazon, Uber, WeWork, and all had a scheme to make money at some point. Now we might call it a "story" for investors.

But you are right, a lot of today's biggest companies did not achieve low cost of capital by past returns. TSLA p/e -, div -

Continuing that thought,

“the investment CAPM says that controlling for a few characteristics is sufficient to explain the cross section of expected returns.”

What could this mean? Not that burn rate startups are correctly catagorized, nor that black swans like the 737 Max are anticipated. It must only mean that a subset of companies with a certain history might have better than "expected" (under conventional CAPM) returns in aggregate. That's the exploitable anomaly, no guarantee against black swans, until it is arbitraged away.

Sure, if you have a billion dollar war chest, take a chance.

I don't see that it has much implication for the political economy though, for financial regulations, or industrial policy.

Cowen in a comment refers to discounting a dividend from Amazon vs. discounting a dividend from Apple. Simple. No mistake. Amazon has never, as in never, as in never ever, has paid a dividend. We aren't in Kansas anymore.

Any suggestions would be greatly appreciated.

The post just makes the theoretical assumption that term risk is buried in the balance sheet under debt insurance and money is a no arbitration condition. Under this assumption, shares can be ignored and the whole problem transferred to deposits,m loans and credit risk.

What are shares? A derivative from standard accounting practices and liquid market. It is a simple transform of the problem unde no arb conditions.

The comments cannot get the idea because we were taught that time risk is part of currency banking. No, time risk is a nominal arbitrage inserted by central banks which must then be removed bu shadow banking. It should not even be part of share evaluation but central banking, as we know it, is deliberately deceptive.

The error is in central banking, it is not arb free and cycles.

A more obvious shot at what is going on.
Finance 101 is wrong, it assumes the central bank is no arbitrage, it is not.
The stock market was created to allow a liquid exchange that can hedge the central bank when we send the central bank off equilibrium, which we do all the time because Finance 101 is wrong.

Finance 101 missed out on the Baumol process, the ability o households and firms to rescale operations in response to economic innovations. A common discount rate is the assumption of constant returns to scale which was never true.

The post is saying we have had a bad central banking model from the beginning, and Finance 101 is clueless. Shadow banking puts the clues we missed back into the term structure with debt insurance and does not assume constant returns to scale.

Some of these comments are too horrible, I am taking another shot.

Bad central banking is associated with bad Finance 101 education causing a bunch of unnecessary errors in evaluating firms. So we need the stock market because we all have this horrible model in Finance 101. There is no safe rate, what we think is a safe rate is really a 8, 30, 120 year central bank arbitrage moments which have to be adjusted sooner or later.

Real central banking happens during the generation MMT adjustments, the ineviitable partial defaults and an upgrading of the central banking model to have smaller arbitrage cycles. Shadow banking actually bets these hedges for us, it is there along with the stock market, to correct the boneheads in Finance 101.

Other arbitrage forces missing in Finance 101.
The 14th amendment on the sacredness fd debt, followed by the Supremes deciding the legality of federal default. Built into the central bank, as is the land speculation war that created the rump state of Vermont. That latter issue embedded into central banking by Hamilton.

Finance 1012 make a huge error, these are self sampled system, thee is no Episcapalian Godot to make grid marks. Finance 101 fooled us well enough when Black-Scholes came about, but the next step was double sided futures betting, sellf sampling systems. Took another 30 years to nail that one. Throw away you old Finance 101.

Alright! A paper I can access! Took one read through let me take a swing at it for those as confused as I have been. I recommend reading this paper in nearly reverse order as the "Introduction" is the most inscrutable part.

Basically what this is saying is that firm behavior responds to asset prices, and you need to account for this in your asset pricing models.

More or less, firms with low costs of capital will invest more and more at weaker and weaker expected returns, until their cost of capital rises to meet expected returns (and vice versa for firms with high cost of capital).

So if you're a growthy company with lots of access to capital, returns will be high over the near terms as you invest that capital in awesome stuff, but will converge over the long term as you start to make dumber investments due to all that capital you have.

The paper does a whole bunch of math and shows that this accounts for some of what look like asset pricing anomolies in traditional frameworks (such as momentum).

The claims are a bit grandiose but it is an interesting piece of pushback on some of the behavioral finance stuff we've seen over the past little while.

Did I get that right?

How it is possible that CAPM applies a constant discount rate across all stocks? How these q-factors can be beneficial?

How it is possible that firm behavior responds to asset prices? How these q-factors can be beneficial?

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