(This blog post is the first of a 4-part sequence based on my working paper fresh from the oven: "
q-factors and investment CAPM, which is a solicited, analytical essay on the big-picture of the investment CAPM. Due to its length, I am splitting it into 4 parts on my blog. The link above gives the complete pdf, which also provides detailed references.)QuestionsA voluminous literature in empirical asset pricing and capital markets research in accounting documents a wide range of relations between firm characteristics and average stock returns. These relations are often called “anomalies” because they cannot be explained by the standard consumption-based Capital Asset Pricing Model (the consumption CAPM), in which the classic Sharpe-Lintner CAPM (Sharpe, 1964; Lintner, 1965) is a special case. Prominent anomalies include post-earnings-announcement drift (Ball and Brown 1968; Bernard and Thomas 1989, 1990), long-term reversal (De Bondt and Thaler 1985), momentum (Jegadeesh and Titman 1993), long-term underperformance following initial and seasoned equity offerings (Ritter 1991; Loughran and Ritter 1995), the value anomaly (Lakonishok, Shleifer, and Vishny 1994), and the accrual anomaly (Sloan 1996). Behavioral economists interpret these anomalies as predictable pricing errors, which reject Fama’s (1970) efficient markets hypothesis (EMH) as well as Muth’s (1961) and Lucas’s (1972) rational expectations hypothesis. However, as emphasized by Fama (1991), anomalies do not necessarily reject EMH because the expected-return models used to isolate “pricing errors” in empirical tests can be incomplete (the joint-hypothesis problem). In particular, a coherent theory of inefficient markets with predictable pricing errors has yet to appear (Fama, 1998). Fama and French (1993, 1996) defend EMH by adding a size factor, SMB, and a value factor, HML, into the CAPM to form their 3-factor model. They interpret SMB and HML as sources of risk in the intertemporal CAPM (Merton, 1973) or Arbitrage Pricing Theory (APT) (Ross, 1976). However, this interpretation has not been persuasive. Both the intertemporal CAPM and APT are silent about the identities of state variables. As a result, SMB and HML are motivated from their empirical performance, rather than a priori theoretical arguments. Within this historical context, many fundamental questions arise. What explains all the CAPM anomalies? Why does the consumption CAPM fail so badly in explaining these anomalies? Given its abysmal performance, what confidence should one put in equilibrium theories that embed the consumption CAPM and permeate virtually all Ph.D. level textbooks in finance and economics? A prominent example is New Keynesian DSGE models. Graham and Dodd’s (1934) Security Analysis has worked for 85 years in practice. Why has it so far not found a rightful place in finance theory? Given that firm characteristics are so important in describing returns empirically, why do characteristics barely show up in finance theory? How should we interpret characteristics-based factors exactly? If anomalies are driven by expectation errors, what exactly are the psychological biases at play? Why do these systematic mistakes persist for so long, in some cases, such as post-earnings-announcement drift, for 50 years since Ball and Brown (1968)? Why has there not been a coherent theory of behavioral finance for almost 35 years since De Bondt and Thaler (1985)? An old science joke says: “Theory is when you know everything but nothing works. Practice is when everything works but no one knows why. In our lab, theory and practice are combined: Nothing works and no one knows why.” Finance is better. 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. MechanismsThe basic philosophy of the investment CAPM is to price risky assets from the perspective of their suppliers (firms), as opposed to their buyers (investors) (Zhang, 2017), building on an early precursor of Cochrane (1991). 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 ≥ 0, 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. To keep things simple, consider first one-period projects. The last project with NPV = 0 means that its investment costs = profitability / discount rate. The investment CAPM turns the NPV rule, which is a fundamental principle in Corporate Finance, on its head and transforms it into an Asset Pricing theory. Rewriting the NPV rule yields: Discount rate = profitability / investment costs. Intuitively, given profitability, high costs of capital (discount rates) imply low NPVs of new projects and low investments, and low costs of capital imply high NPVs of new projects and high investments. In addition, given investments, high profitability must imply high discount rates 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. If projects last more than one period as in a multiperiod model, the NPV rule becomes: Investment costs = (profitability + present value of cash flows from next period onward) / discount rate. With optimal investment, the present value of cash flows from next period onward equals expected investment costs next period (marginal q equals marginal costs of investment). As such, the investment CAPM says: Discount rate = (profitability + expected investment costs) / investment costs. Intuitively, if investment and expected investment costs are high next period, the present value of cash flows from next period onward must be high. Consisting primarily of this next period present value, the benefits to investment this period must also be high. As such, if investment is high next period relative to current investment (expected investment growth is high), the discount rate must be high. The discount rate must be high to offset the high benefits of investment this period to keep current investment low. As such, expected growth is another key driver in the cross section of expected stock returns.
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## Lu Zhang
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