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The q-factor model for equity returns

Investment-based capital asset pricing looks at equity returns from the angle of issuers, rather than investors. It is based on the cost of capital and the net present value rule of corporate finance. The q-factor model is an implementation of investment capital asset pricing that explains many empirical features of relative equity returns. In particular, the model proposes that the following factors support outperformance of stocks: low investment, high profitability, high expected growth, low valuation ratios, low long-term prior returns, and positive momentum. According to its proponents, the investment CAPM and q-factor model complement the classical consumption-based CAPM and explain why many so-called ‘anomalies’ are actually consistent with efficient markets.

Zhang, Lu (2019), “q-factors and Investment CAPM”, Fisher College of Business WP 2019-03-030

The below are excerpts from the paper. Headings and emphasis have been added and some formulaic terms have been replaced by conventional grammar.

What is the q-factor model?

“The q-factor model is an empirical implementation of the investment capital asset pricing model (investment CAPM)… The model says that the expected return of an asset in excess of the risk-free rate is described by its sensitivities to the market factor, a size factor, an investment factor, and a return on equity factor…The basic philosophy is to price risky assets from the perspective of their suppliers (firms), as opposed to their buyers (investors).”

“The q-factor model explains the impact of a firm’s investment behavior and profitability on expected average stock returns – factors not explained by the Fama and French (1993) three-factor model. The q-factor model derives the investment and profitability factors and their relation to expected returns from Tobin’s q theory, which states that the firm’s investment decisions depend on the ratio of the market value of capital to the replacement cost of capital – termed the marginal q. Firms tend to invest more when the marginal q is high and less when it is low. Similarly, all else equal, a high cost of capital means low investment and a low cost of capital means high investment.” [Asad and Cheema, 2017]

What is investment-based capital asset pricing?

“Mathematically, the investment CAPM is a restatement of the Net Present Value (NPV) rule in Corporate Finance. The NPV of a project is its present value – discounted value of its future cash flows – minus its investment costs today. The NPV rule says that a manager should invest in a given project if and only if its NPV is greater than or equal to zero. When initially facing many projects with NPV larger or equal to zero, the manager will start with the project with the highest NPV and work her way down the supply curve of projects. For the last project that the manager takes, its NPV should equal zero.”

“The investment CAPM turns the NPV rule…on its head and transforms it into an asset pricing theory. Rewriting the NPV rule yields the discount rate as the ratio of profitability and investment costs. Intuitively, given profitability, high costs of capital [high theoretical return to equity investors] imply low NPVs of new projects and low investments, and low costs of capital imply high NPVs of new projects and high investments.”

“The investment CAPM has broad-ranging implications for academic finance and asset management practice…The [classic] consumption CAPM…is conceptually incomplete…It blindly focuses on the demand of risky assets, while abstracting from the supply. Alas, anomalies are primarily relations between firm characteristics and expected returns. By focusing on the supply, the investment CAPM is the missing piece of equilibrium asset pricing.”

“The consumption CAPM theory is well developed, but it doesn’t work. Anomaly strategies work, but no one knows why. In the investment CAPM, theory and practice are combined: Everything works and I know why.”

What can practitioners learn from the q-factor model?

“Intuitively, high investment relative to low expected profitability must imply low costs of capital [low theoretical return to equity investors], and low investment relative to high expected profitability must imply high costs of capital [high theoretical return to equity investors].”

“Given investments, high profitability must imply high discount rates [high costs of capital and theoretical expected returns] to give rise to low NPVs of new projects to keep investments constant. Low profitability relative to investments must imply low discount rates to offset low profitability to keep the NPVs of new projects and investments constant. In all, investment and profitability are two key drivers in cross section of expected returns.”

“Less financially distressed firms have higher profitability and, all else equal, should earn higher expected returns than more financially distressed firms. As such, the distress anomaly is just another manifestation of the profitability factor.”

“If investment is high next period, the present value of cash flows from next period onward must be high. Consisting mostly of this next period present value, the benefits to investment this period must also be high. As such, high investment next period relative to current investment (high expected investment growth) must imply high costs of capital (to keep current investment low)… As such, expected growth is another key driver in the cross section of expected stock returns.”

“In the investment CAPM, investment increases with marginal q, which in turn equals average q with constant returns to scale. Average q and market-to-book equity are close cousins and are identical twins without debt. As such, value stocks with low valuation ratios should invest less and, all else equal, should earn higher expected returns than growth stocks with high valuation ratios.”

“High valuation ratios come from a stream of positive shocks on fundamentals, and low valuation ratios a stream of negative shocks on fundamentals. Growth stocks typically have high long-term prior returns, and value stocks low long-term prior returns. As such, long-term reversal also reflects the investment factor. Firms with high long-term prior returns should invest more and have lower costs of capital than firms with low long-term prior returns.”

“Sorting on earnings surprises, short-term prior returns, and financial distress is closer to sorting on profitability than on investment. As such, these diverse sorts reflect their common implied sort on profitability. Intuitively, shocks to earnings are positively correlated with shocks to returns, contemporaneously. Firms with positive earnings shocks experience immediate stock price increases, and firms with negative earnings shocks experience immediate stock price drops. As such, momentum winners should have higher expected profitability and earn higher expected returns than momentum losers.”

How does the q-factor model relate to classical equity factors?

“The consumption CAPM anomalies are the investment CAPM regularities, all of which conform to the NPV rule in Corporate Finance…Most anomalies are just different manifestations of investment and profitability… [For example] post-earnings-announcement drift [has persisted] for 50 years…because it is part of expected returns, as predicted by the investment CAPM.”

“The q-factor model has effectively ended the quarter-century reign of the Fama-French 3-factor model as the leading model in empirical asset pricing.”

“The investment CAPM retains [the assumption of] efficient markets, with cross-sectionally varying expected returns, depending on firms’ investment, profitability, and expected growth. As such, capital markets follow standard economic principles, in sharp contrast to the teachings of behavioral finance.”

“The efficient market hypothesis is down in the dumps only because the consumption CAPM is a rundown dumpster truck. I have yet to meet an asset manager who even mentions the consumption CAPM, not even once, yet the consumption CAPM is virtually all we are allowed to talk about in academia (unless you are a behavioral economist).”


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