The capital asset pricing model in economic perspective

Abstract

The capital asset pricing model (CAPM) is theoretically incomplete in its demand-side focus, risk-averse investors and internally inconsistent homogeneous beliefs; is not conclusively supported empirically; and yet it legitimizes a notion that investors can earn higher returns by bearing undiversifiable risk. Our article does not merely extend the CAPM with more realistic assumptions, it completes its original framework by including (1) risk-taking investors in the investor population, (2) investors who can have heterogeneous expectations or beliefs – an overlooked but required condition for the CAPM to be an internally consistent and meaningful model of competitive financial asset pricing under uncertainty and (3) a positive-sloped short-run supply curve based on a reasonable interpretation of the nature of financial asset trade. Upon a complete economic interpretation, it is shown that the equilibrium (systematic) risk-rate of return relationship depends on whose aggregate trading activity dominates, risk-averse or risk-taking investors’. There is no universal, or even general, positive relationship between systematic risk and rate of return. This has far-reaching implications for investors and investment advisors who serve them.

Keywords:

• CAPM
• risk-return paradigm
• heterogeneous beliefs
• speculation
• risk-taking

JEL Classification:

• D01
• D46
• D53
• D81
• D84
• G02
• G11
• G12
• G31
• J26
• M21

Notes

¹ The word ‘require’ in the often-used phrase ‘required rate of return’ connotes a belief that one has the power or ability to determine his rate of return.

² ‘[T]his is not a correct interpretation, because two securities may have identical risk structures in terms of their covariances with other securities in the market, and yet have different excess returns. In fact, if the parameters of the CAPM are generated in a natural way, then securities with the same risk structure almost surely will have different expected returns [p.91]. … one clearly cannot say that the CAPM investor is paid for bearing risk … [p.94]. The points I make do not change the major conclusions of the CAPM. Given the assumptions of the CAPM, the market is an efficient portfolio, and there is a linear relation between the expected return of each security and its regression against the market. But we must not interpret this [relation] as [reflecting compensation for] the bearing of risk’ (Markowitz, 2008, p. 94). See Markowitz (2010) for a summary of Markowitz (2008).

³ An unlimited ability to borrow does not imply CAPM investors choose to use that ability to take an infinite position in any asset. Their borrowing to purchase assets is limited by their wealth and preferences in the context of a fixed short-run supply curve. Increased demand for an asset raises market price, which in turn limits investors’ preference for the asset. An equilibrium is reached when all are happy with their asset holdings, at which time they stop purchasing assets and, thus, do not need further borrowing. Although CAPM investors may have access to unlimited borrowing, the pricing mechanism limits their desire to borrow. (The same conclusion applies to an unlimited short sales assumption).

⁴ ‘In equilibrium, capital asset prices have adjusted so that the investor, if he follows rational procedures (primarily diversification), is able to attain any desired point along a capital market line. He may obtain a higher expected rate of return on his holdings only by incurring additional risk’ (Sharpe, 1964, p. 425; italics original).

⁵ Markowitz (2005) also shows that, with an alternative CAPM that assumes unlimited short sales, a switch to limited or no short sales leads to the same conclusion.

⁶ The CAPM ‘investor makes portfolio decisions in accordance with the two-parameter model.… [but] It does not make sense for the investor to behave in this way unless his assessments of portfolio opportunities are accurate. If he is consistently inaccurate, he will come to feel that the decision-making framework is of little value. In short, if one assumes that investors make portfolio decisions according to the two-parameter model, then one must assume that they can obtain reasonably accurate assessments of the parameters that the model requires as inputs to a portfolio decision. This in turn implies that there is considerable consensus among investors in their assessments of the joint distribution of future values of securities and thus considerable consensus in how they view the efficient set of portfolios…. [, where] we assume the degree of agreement among investors is complete rather than just considerable’ (Fama, 1976, p. 272).

⁷ The CAPM ‘still remains a fundamental asset-pricing model taught to students’ (Economic Sciences Prize Committee 2013, pp. 35–36).

⁸ ‘The risk-return rationality of the CAPM and Fama and French three-factor models has stimulated a very substantial volume of asset price literature’ (Dempsey, 2013, p. 18). ‘The CAPM has had enormous repercussions on subsequent academic work in finance’, and ‘More empirical effort may have been put into testing the CAPM equation than any other result in finance’ (Rubinstein, 2006, pp. 175, 172). ‘Hundreds of papers have been written on the CAPM and its variants/extensions, but little concern has been expressed about the tendency of finance academics to squander a big portion of their intellectual capital on this endeavor’ (Moosa, 2013, p. 62). Dempsey (2013) ‘makes the point that maintaining the CAPM at the core of mainstream finance has served a Kuhnian (1962) purpose for the academic finance industry – namely, “facts always serve to justify more activity without seriously being allowed to threaten the paradigm core” (Dempsey, 2013). This perspective of the unchallengeable core as the basis of a self-perpetuating academic finance industry (activity without progress) was explored in depth by Keasey and Hudson (2007). …. The sacrosanct nature of the core principles makes for an endless stream of puzzles and this keeps the industry of mainstream academic finance busy’ (Cai et al., 2013, p. 52). An important question is ‘how do we create a more robust, open and ultimately useful (rather than self-serving) study of finance?’ (Cai et al., 2013, p. 53). Without ‘rigorous questioning and robust inquiry[,] … a subject can become a moribund exercise in finding the auxiliary conditions which help to protect the core. In finance, this can be equated to the search for the additional factors needed to maintain the risk/return core of the CAPM’ (Cai et al., 2013, p. 57).

⁹ Brown and Walter (2013) agree: ‘At various times beta, at the heart of the CAPM, has been declared dead; yet researchers and practitioners continue to use the CAPM, mostly, we believe, because of the strength of the intuition behind it’ (p. 49).

¹⁰ The ‘position that “there is no alternative” to the CAPM for risk-adjustment calculations was never completely true and is certainly not true now’ (Markowitz, 2005, p. 104).

¹¹ ‘SLB’ is the Sharpe (1964)–Lintner (1965)–Black (1972) version of the CAPM.

¹² ‘There is a mounting dissatisfaction with the way economies and societies are being led, there is a feeling that the perceived gains of the past decades have not been equally shared, with the wealthiest grabbing the gains, taking from society but not contributing back through fair contribution via the tax system[;] … increasing inequality in wealth across western societies further highlights this problem’ (Cai et al., 2013, p. 60).

¹³ Economists readily acknowledge that ‘… other things seldom are equal in fact over periods of time…. There are always occurring disturbing causes whose effects are commingled with, and cannot easily be separated from, the effects of that particular cause which we desire to isolate. This difficulty is aggravated by the fact that in economics the full effects of a cause seldom come at once, but spread themselves out after it has ceased to exist’ (Marshall, 1920, p. 92). Nevertheless, economists generally recognize that, although the (partial equilibrium) ‘all else equal’ assumption rarely holds true for more than short periods in practice, it is a useful strategic tool for isolating the critical elements of the specific question at hand to make that question analytically manageable and understandable: ‘The element of time is a chief cause of … difficulties in economic investigations which make it necessary for man with his limited powers to go step by step; breaking up a complex question, studying one bit at a time, and at last combining his partial solutions into a more or less complete solution of the whole riddle. In breaking it up, he segregates those disturbing causes, whose wanderings happen to be inconvenient, for the time in a pound called Caeteris Paribus. The study of some [specific] group of tendencies is isolated by the assumption other things being equal: the existence of other tendencies is not denied, but their disturbing effect is neglected for a time’ (Marshall, 1920, p. 304; italics original).

¹⁴ ‘There is … a good deal of general reasoning with regard to the relation of demand and supply which is required as a basis for the practical problems of value, and which acts as an underlying backbone, giving unity and consistency to the main body of economic reasoning. Its very breadth and generality mark it off’ from other market models (Marshall, 1920, p. 70). Economics’ market model is ‘the theoretical backbone of our knowledge of the causes which govern value’ (Marshall, 1920, pp. 269–270).

¹⁵ ‘Anyone familiar with the major mainstream finance journals cannot fail to be depressed by their increasingly formulaic articles (both in style and research approach)’ (Cai et al., 2013, p. 57). ‘[T]he majority of published research in finance has been predominantly descriptive or empirical (data driven)’ (Johnstone, 2013, p. 2). ‘A good deal of finance in now an econometric exercise in mining data’, ‘The Economist magazine (20–26 November 2010) observes that a reason for the high level of “data mining” is the opportunity that the CRSP data base offers financial economists (it estimates that more than one-third of published papers in finance represent econometric studies of the data base)’ and, in the same article of The Economist, Robert Shiller ‘is quoted as saying that with the creation of the CRSP data base, economists have been led to believe that finance has become scientific’ (Dempsey, 2013, pp. 20–21). Unfortunately, published research in finance is also ‘becoming more and more like “rocket science”, virtually unconsumable by the masses’ (Benson and Faff, 2013, p. 29). Academic economics is not immune to the same criticism. Among economists willing to be openly critical of academic economics, Wolff (2013), for example, readily admits that economics is ‘an academic discipline now extremely disconnected from most people’ and ‘for the last 40 years, economics professors turned away from the big questions and aimed instead to dazzle onlookers with their abstract mathematical methods focused on ever smaller questions …. because method had come to matter far more than substance in economics’ (pp. 150–151).

¹⁶ Sharpe (1991) seems at odds with this generally accepted characterization: ‘[T]he CAPM makes no assumptions about the “return generating process”. Hence, its results are completely consistent with any such process’ (p. 497; italics original).

¹⁷ We prefer the term ‘risk-taking’ because it characterizes an investor’s behaviour in specific trades and allows him to be both risk-taking in some trades and risk-averse in other trades. The term ‘risk-loving’ is too broad a characterization as it connotes a meaning that an investor is risk-taking in all his trades. The risk-taking characterization allows for the possibility that any given investor may exhibit both risk-taking by purchasing risky shares in a company, for example, and risk-aversion by purchasing risk-free assets, such as certificates of deposit or government securities.

¹⁸ ‘Are ex ante expected returns on risky assets always higher than the certain return on a risk-free asset? The results of Boudoukh et al. (1993), Ostdiek (1998), and this research show that this is not necessarily the case’ (McCown, 1999, p. 111).

¹⁹ The results of empirical studies of the CAPM ‘are quite mixed’ (Rubinstein, 2006, p. 172). A literature review of these studies is not provided here, however. For a summary of the empirical literature, see Cochrane (1999), for example, ‘Now we recognize that the average returns of many investment opportunities cannot be explained by the CAPM’ (Abstract), or later summaries.

²⁰ The ‘empirical record of the model is poor – poor enough to invalidate the way it is used in applications [p.25]. In the end, we argue that whether the model’s problems reflect weaknesses in the theory or in its empirical implementation, the failure of the CAPM in empirical tests implies that most applications of the model are invalid [p. 26]. For example, finance textbooks often recommend using the Sharpe-Lintner CAPM risk–return relation to estimate the cost of equity capital. … But empirical work, old and new, tells us that the relation between beta and average return is flatter than predicted by the Sharpe-Lintner version of the CAPM’ (Fama and French, 2004, p. 43; italics added). (Fama and French (2004) characterize the CAPM as the Sharpe–Lintner–Black version of the CAPM: ‘the finance profession reserves the acronym CAPM for the specific model of Sharpe (1964), Lintner (1965) and Black (1972)’ (p. 25, n.1).)

²¹ Regarding a bias or skew in asset price variability in response to heterogeneous beliefs (i.e. do heterogeneous beliefs lead to higher or lower prices?), the ‘impact of divergence of beliefs regarding the future prospects of a capital asset on that asset’s equilibrium value remains an unresolved issue in finance in spite of the several decades of attention this topic has received in the theoretical literature’ (Schnabel, 2009, p. 148). Doukas et al. (2006, pp. 574–575) and Beber et al. (2010, p. 416) agree. We abstract from this debate by retaining the CAPM’s normal probability distribution assumption. Nevertheless, even without normal distributions and regardless of a price bias, differences of opinion are sufficient to cause financial asset prices to deviate from their fundamental prices.

²² Miller (1977) appears to describe uncertainty about returns as the cause of differences in opinion: ‘uncertainty produces both risk and divergence of opinion’ (p. 1159). Beber et al. (2010) also hold this view: ‘Uncertainty is a precondition for differences in beliefs to matter in theoretical models’ (p. 416). We assume differences in opinions or beliefs can also cause uncertainty. That is, heterogeneous beliefs about current and future asset prices can be the source of short-run speculative trading on price, a positive variance in prices and returns, and thus uncertainty about prices and returns.

²³ Mayers (1976) asks ‘what would happen to the level of prices of presently marketable assets if perfect capital markets were suddenly created for all presently nonmarketable assets?’ (p. 2). In the ‘case of constant absolute risk aversion, … there is no effect of nonmarketable assets or market segmentation on the level of asset prices’ (p. 11), the implication being the market price of nonmarketable assets that have suddenly become marketable do not experience a change in market price.

²⁴ Risks are manifested in transaction costs.

²⁵ ‘Imperfectly rational investors are not uniformly averse to risk. In some circumstances, they act as if they are risk seeking. Moreover, imperfectly rational investors do not rely on optimal statistical procedures. Instead, they rely on crude heuristics that predispose their beliefs to bias. Proponents of traditional asset pricing theory tend to use a representative investor whose beliefs and preferences set prices. This representative investor holds correct beliefs and is a traditional expected utility maximizer …. [and,] although a representative investor may set prices, a behavioral representative investor typically holds erroneous beliefs’ (Shefrin, 2005, p. 3).

²⁶ Others in finance agree, for example, Moosa (2013): ‘he is not alone in (correctly) thinking that way’ (p. 62).

²⁷ The implication being the ‘paradigm of the CAPM and efficient markets may need to be replaced with a paradigm of markets as vulnerable to capricious behaviour’ (Dempsey, 2013, p. 9). ‘Such a view of markets would imply that a research agenda aimed at understanding market fallibility and their potential for self-destruction, rather than aimed at enriching an account of “markets in equilibrium”, provides a more useful contribution to policy making’ (Dempsey, 2013, p. 9).

²⁸ Dempsey (2013) contemplates the possibility that, should finance abandon the CAPM, ‘In a non-CAPM world …. [t]he implications of not having a “scientific” model of share prices are considerable’ (Dempsey, 2013, p. 21). Although Dempsey (2013) states ‘If the CAPM must be rejected, we are obliged to return to a view of markets as predating the introduction of the CAPM’ (p. 8), he does not advocate the rejection of 50 years of academic progress in finance in total (and perhaps not even the CAPM in its entirety). Without the CAPM finance would retain considerable progress and, therefore, ‘embodies more than sufficient theoretical substance to warrant its own subfield in philosophy’ (Johnstone, 2013, p. 5). Brown and Walter (2013) cite ‘Jensen and Smith (1984) [who summarized] the fundamental building blocks for the modern theory of financial economics[, which] are, in rough chronological order, efficient market theory (EMT), portfolio theory, capital asset pricing theory, option pricing theory, and agency theory’ (p. 45). According to Smith and Walsh (2013), ‘the core ideas of finance’ also include the time value of money, diversification, and arbitrage (pp. 73–74).

²⁹ According to Dempsey (2013), ‘we cannot interpret more recent [factor] models as refinements of a fundamentally robust risk-return relation. Rather, they represent a radical departure from the essential risk-return premise of the CAPM’ (p. 20). Furthermore, factor models are considered empiricism in search of a theory: ‘the addition of other explanatory variables to the underlying model, without any explicit theory or even intuition, [is] … an attempt to salvage the model typically through data mining’ (Moosa, 2013, p. 62). ‘As is often remarked, the [factor] model derives from a fitting of data rather than from theoretical principles’ (Dempsey, 2013, p. 11). Notwithstanding these criticisms, ‘The trend of adding factors to better explain observed price behaviours has continued to dominate asset pricing theory’ unfettered (Dempsey, 2013, p. 11).

³⁰ In -space, the slope of the capital or security market line is , that is, (Fama, 1976, p. 261).

³¹ ‘Once he chooses an efficient portfolio, there is a relationship between expected security returns and their risks in that portfolio which is a direct consequence of the fact that the portfolio is efficient’ (Fama, 1976, p. 271; italics added).

³² Assuming that (which is consistent with the CAPM), and, upon rearranging, .

³³ This refers to economist Alfred Marshall’s (1842–1924) market model of supply and demand, a partial equilibrium analysis with a ceteris paribus assumption. See Marshall (1920).

³⁴ Bierwag and Grove (1965) point out the CAPM, or more specifically Sharpe’s (1964) version of the CAPM, would need to specify the original (noninverse) supply and demand functions in order to specify the necessary market equilibrium condition, which is the aggregate of the individual excess demands for asset i sum to zero. ‘Sharpe’s (1964) approach … begins with a disequilibrium …. [, where] He then postulates a dynamic model which he asserts will lead to a market equilibrium. He fails, however, to state the necessary conditions for such an equilibrium to exist. If he had focused his analysis on the quantities of assets themselves rather than upon the attributes that these assets possess, the necessity of the closure property … would have been more obvious’ (p. 92). Bierwag and Grove (1965), Mossin (1966) and Stone (1970) each include the equilibrium condition (or ‘closure property’) explicitly in their formulations of the CAPM.

³⁵ Equation 6 in specific functional form would allow us to explicitly calculate the market price. However, the nature of our specific (comparative static) analysis does not require an explicit calculation of the market price.

³⁶ Our focus is how differences in beta risk affect an asset’s rate of return. Therefore, we can remove other exogenous variables, leaving the variable of interest, . The equilibrium condition in Equation 6 reduces to . Calculate the total differential and place it in matrix equation form: . This is one equation and one unknown endogenous variable, P_i. Rearrange this matrix equation to obtain the partial equilibrium solution: , which is negative because (a) (i.e. beginning at , an increase (decrease) in increases (decreases) and decreases (increases) , which increases (decreases) ) and (b) by the assumption of risk-averse investors. Substitute , and (as calculated in footnote 37) into the equation to obtain the CAPM result, , within our market model. When switching to the assumption of risk-taking investors, , , , and therefore .

³⁷ .

³⁸ ‘The Sharpe-Lintner-Mossin theory of capital asset pricing assumes fixed supplies of securities’ (Black, 1976, p. 769). Similarly, Hirshleifer (1966) characterizes the CAPM as a theory of asset pricing that assumes a fixed supply of financial assets: Sharpe’s (1964) model ‘may be regarded as a theory of prices for mean and variability in the “very short run,” with fixed supplies of productive and financial assets’ (p. 252n).

³⁹ McDonald (2003) also incorporates the ‘assumption of variable asset supply’ by specifying a positive relationship between the quantity supplied and price after is reached, based on the empirical observation of ‘the phenomenon of equity market timing’ (p. 17), which, according to McDonald (2003), reflects the ‘consistent and strong empirical results showing that equity is issued when share prices are high’ (p. 5).

⁴⁰ Implicit in Black (1976) is the assumption that the outstanding supply of asset i, , is binding on demand in the short run. Otherwise, the market would be operating along the lower, positive-sloped portion of the supply curve, which would make the slope of the upper portion unimportant to the short-run analysis.

⁴¹ The ‘static Sharpe-Lintner-Mossin model of capital asset prices is unnecessarily restrictive in its neglect of the supply side …’ (Black, 1976, p. 776).

⁴² Strictly speaking, Lee et al. (2009) do not refer to a change in quantity supplied, which would reflect the trade of existing shares already in the market in response to price changes (along a given supply curve). More accurately, they refer to a shift in the supply curve, which occurs when new supply is provided to the market or existing supply is removed from the market (both of which would change the total shares outstanding). In the Marshallian market model, factors that change the total supply of a good, service or asset are represented by shifts in the supply curve (rather than movements along a given supply curve in response to changes in market price).

⁴³ Even existing supplies of the average product may not be exhausted and binding on demand in the short run. According to Marshall (1920), on any given trading day the quantity supplied in a competitive market comes from stocks of a good ‘already in existence’ (p. 281) and, as a general matter, not all potential sellers of existing supplies (e.g. of corn in a local corn market) necessarily have offered for sale their goods in the market at the current market price. In such short periods when ‘“supply” means in effect merely the stock available at the time for sale in the market’ (p. 275), Marshall (1920) explains, ‘The amount which each farmer or other seller offers for sale at any price is governed by his own need for money in hand’ (p. 277) (as well as other supply curve shift factors), but his quantity supplied generally increases as the supply price increases, such that ‘There are some [low] prices which no seller would accept, some [high prices] which no one would refuse [, and] There are other intermediate prices which would be accepted for larger or smaller amounts by many or all of the sellers’ (p. 277). In another example, Marshall (1920) explains the ‘normal price for any given daily supply of fish … is the price which will quickly call into the fishing trade capital and labour enough to obtain that supply in a day’s fishing of average good fortune’ (p. 307; italics original), reflecting the ‘almost universal law’ of supply: in the ‘short period of time[,] an increase in the amount demanded raises the normal supply price. This law is almost universal’ (p. 308; italics original). Marshall (1920) clarifies by noting that economic laws are ‘statements with regard to the tendencies of man’s [aggregate] action under certain conditions’ (p. 32), and are the result of studying ‘“the course of action that may be expected under certain conditions from the members of an industrial group,” … and in these broad results the variety and fickleness of individual action are merged in the comparatively regular aggregate of the action of many’ (p. 83).

⁴⁴ Contrary to Black (1976) and Lee et al. (2009), it is not necessary that a firm be assumed to issue new and redeem existing outstanding shares in the short run.

⁴⁵ Only in the special case where market demand is so large relative to outstanding supply could the outstanding supply bind demand (as was illustrated in Fig. 2), a case that, given the nature of financial assets, is not generally representative of the typical financial asset’s market. In addition, by definition, a competitive market is characterized by a high degree of supply elasticity – i.e. the short-run supply curve must have a positive, and relatively gradual, slope.

⁴⁶ In the literature, ‘there is evidence that decision-makers are not globally risk averse, but rather they exhibit local risk seeking behaviour’ (Post and Levy, 2002, p. 2). For example, the average investor may be risk-averse with his longer-term investments (which reflect, perhaps, the core portion of his asset portfolio that is expected to meet future retirement needs and to provide a safe cushion of liquid assets to meet liquidity needs for reasonably possible life events). He may have savings in excess of expected retirement/possible liquidity needs that he invests in more-risky (short-term or long-term) assets. He can trade assets from both portions of his well-diversified asset portfolio, exhibiting both risk-taking and risk-aversion depending on the portion of his portfolio to/from which he trades. A general distinction between risk-taking and risk-averse investors might be the former tends to have a shorter-term investment focus (i.e. taking on the risk of short-run, volatile price changes) while the latter tends to be longer-term oriented (i.e. investing with the long-term trend in asset prices). Speculation typically is defined as trading activity aimed at maximizing capital gains based on short-term deviations in price from fundamental price, but all investors are speculative since, regardless of their investment horizon, their motivation for investing is to earn a capital gain by buying at a low price and selling at a high price at some future date (as well as possibly earning dividends in the interim). The key distinction between short-term versus long-term investors is the length of their respective holding periods. For a given risky asset, short-term investors have shorter holding periods (of, let’s say, up to a year), while longer-term investors (both medium-term and long-term) have longer holding periods (of, let’s say, a year or more). For a given investor and the portion of his asset portfolio to/from which he trades and his risk-tolerance with respect to that portion, he determines his asset preference and, thus, the general risk class of assets (as well as the assets within that risk class) he chooses to invest. Risk-averse investors generally invest a larger portion of their savings in low-risk and risk-free assets (i.e. their portfolios tend to have a larger core), while risk-taking investors generally invest a larger portion of their portfolios in riskier assets (Damodaran, 2008, p. 28).

⁴⁷ For example, Mody (2012) casually observes (albeit in a somewhat over-generalized statement) that the typical ‘investor’s behavior in terms of risk taking or risk averseness, fluctuates on the basis of market conditions. In a bull market, everyone is a gambler. … In a bear market, everyone is a pessimist. … What this means is that investors do not always require a “premium” for volatility’.

⁴⁸ Keynes (1936) defines ‘enterprise’ investing as ‘the activity of forecasting the prospective yield of assets over their whole life’ (p. 158) by the ‘long-term investor’ (p. 157) who purchases ‘investments on the best genuine long-term expectations he can frame’ (p. 156) with the aim of earning a capital gain (in our words, the trade of long-term investors who invest based on the expected long-run trend in asset prices). ‘Speculation’ is defined as ‘the activity of forecasting the psychology of the market’ (p. 158), investing short term in a financial asset based on a forecast of ‘what the market will value it at, under the influence of mass psychology, three months or a year hence’ (p. 155), ‘forecasting changes in the conventional basis of valuation a short time ahead of the general public’ (p. 154) by ‘game-players’ (p. 156) with the aim ‘“to beat the gun”, as the Americans so well express it, to outwit the crowd, or to pass the bad, or depreciating, half-crown to the other fellow’ (p. 155) (in our words, investing short-term based on the short-run variability of asset prices, on one’s expectation of where the price will go in the near future).

⁴⁹ ‘With the separation between ownership and management which prevails to-day and with the development of organised investment markets’ (p. 150) to trade equity shares, individual investors can sell their shares quickly at low cost per trade when they expect the price to decline or continue to decline. ‘This is the inevitable result of investment markets organized with a view to so-called “liquidity”’ (Keynes, 1936, p. 155). Short-term speculation cannot be achieved without the liquidity needed to sell short term.

⁵⁰ Keynes (1936) would tend to agree: ‘As the organisation of investment markets improves, the risk of the predominance of speculation does, however, increase’ (p. 158).

⁵¹ ‘Investment based on genuine long-term expectation is so difficult to-day as to be scarcely practicable’ (p. 157). ‘The outstanding fact is the extreme precariousness of the basis of knowledge on which our estimate of prospective yield have to be made[, where] …. Our knowledge of the factors which will govern the yield of an investment some years hence is usually very slight and often negligible’ (p. 149). ‘It needs more intelligence to defeat the forces of time and our ignorance of the future than to beat the gun. Moreover, life is not long enough; – human nature desires quick results, there is a peculiar zest in making money quickly, and remoter gains are discounted by the average man at a very high rate’ (p. 157; italics original). The short-term liquidity available in financial markets promotes short-term speculative tendencies, ‘tendencies [that] are a scarcely avoidable outcome of our having successfully organised “liquid” investment markets’ (p. 159).

⁵² Keynes (1936) also recognized the role of differences of opinion, reflecting less-than-perfect knowledge or information across investors, in creating short-run variability or volatility of financial asset prices. A price that is ‘established as the outcome of the mass psychology of a large number of ignorant individuals is liable to change violently as the result of a sudden fluctuation of opinion due to factors which do not really make much difference to the prospective [long-term] yield; since there will be no strong [fundamental] roots of conviction to hold it steady’ (p. 154).

⁵³ According to the Economic Sciences Prize Committee (2013), ‘We now know that asset prices are very hard to predict over short time horizons’ (p. 45). Short-run asset pricing generally follows a random walk: ‘the asset price may go up or down tomorrow, but any such movement is unpredictable: the price follows a martingale, which is a generalized form of a random walk’ (p. 5). And, although some find a statistically significant empirical influence of fundamental variables on short-run asset pricing, ‘Shiller and Perron (1985) and Summers (1986) argued … formally that the power of short-run predictability tests is likely to be very low’ (Economic Sciences Prize Committee, 2013, p. 31). ‘To the extent that short-term return predictability can be found, it is too small to profit from because of transaction costs’ (Economic Sciences Prize Committee, 2013, p. 42).

⁵⁴ ‘Why do prices fluctuate so much compared to economic fundamentals? This question has been strongly debated in financial economics’ (Boswijk et al., 2007, p. 1938). If this is an unsettled empirical issue, that it is unsettled would be sufficient to justify an assumption that short-term speculative trade can dominate financial asset pricing in the short run. As Summers (1986) points out, ‘the evidence found in many studies that the hypothesis of efficiency cannot be rejected should not lead us to conclude that market prices represent rational assessments of fundamentals valuations. Rather, we must face the fact that most of our tests have relatively little power … [and remember that] the hypothesis that market valuations include large persistent errors is as consistent with the available empirical evidence as is the hypothesis of market efficiency’ (p. 598).

⁵⁵ ‘It is hardly plausible that speculative prices make effective use of all information about probabilities of future dividends. It is far more plausible that the aggregate stock market price changes reflect inconstant perceptions. changes which Keynes referred to with the term “animal spirits,” changes that infect the thinking even of the most of the so-called “smart money” in the market’ (Shiller, 2014, p. 16). In general, ‘Most stock market investors do not pay much attention to fundamental indicators of value. We might argue that their inattention is in some sense rational, since there is a cost to collecting information’ (Shiller, 2014, p. 25). Even well-informed investors are human and, thus, can be boundedly rational.

⁵⁶ This does not necessarily mean there is a predictable empirical relationship between short-term speculative trading and short-run asset price movements. Even though investors in general have access to the same set of information, they possess diverse and unpredictable thought processes and associated diverse and unpredictable beliefs/expectations and, therefore, they form unpredictable heterogeneous beliefs/expectations about prices. As such, it is reasonable to expect speculative trading on short-run price movements to transmit a significant, if not substantial, random influence on intra-day and daily movements in share prices about their long-run trends in fundamental levels. This would suggest an effort to establish whether there exists a predictable empirical relationship between short-run speculative trades and short-run stock price variability/volatility would be futile. Paradoxically, the explanatory power of short-run speculate financial asset trade lies in the randomness it imparts to short-run price movements. Thus, the lack of a statistically verifiable relationship between short-term speculative trade and short-run asset price movements would not necessarily indicate that short-term speculative trade could not dominate short-run financial asset price movements. This view parallels short-run exchange rate determination: ‘Exchange rate volatility is very high’, but ‘it is extremely difficult to predict the short-run direction of exchange rates. Economists often view changes in exchange rates as following a random walk, which means that a future increase is as likely as a decrease. Short-run fluctuations are difficult to explain even after the fact. Some short-run movements no doubt reflect attempts by market participants to ascertain the future direction of macroeconomic fundamentals. But many short-run movements are hard to explain and may be due to ineffable determinants such as some vague “market sentiment” or “speculative bubbles.” (Speculative bubbles are movements of the exchange rate that are not related to macroeconomic fundamentals, but instead result from self-fulfilling changes in expectations.) …. Given the high volatility of exchange rates, even those with strong and well-founded theories about the likely direction of future movements must acknowledge the high level of uncertainty. Indeed, differences in opinion are what give rise to much of the very high volume of trade in foreign exchange. In other words, in every transaction there is a buyer and a seller, and usually they have opposite views regarding likely future movements in the exchange rate’ (Frankel, 2007).

⁵⁷ With homogeneous beliefs there would be no asset transactions. By contrast, with heterogeneous beliefs, ‘Over time all investors, if appropriate, revise their probability assessments, thereby generating transactions’ (Williams, 1977, p. 220). According to Davis et al. (2007), ‘participants may trade with each other simply because they disagree with each other’ (p. 88). Lehmann (2005), in discussing the legacy of Fischer Black (in the context of heterogeneous beliefs formed by asymmetric information), agrees: ‘complete market models of financial market equilibrium in the absence of information asymmetries predict little or no trade, an observation grossly at variance with the volume of trade in the real world’ (p. 28).

⁵⁸ That well-informed investors trade with, in the aggregate, less-than-well-informed investors does not mean each well-informed investor must physically locate a less-than-well-informed investor to trade with. Different investors trade in different quantities and at different times, where the bulk of financial asset trade is conducted anonymously through intermediaries facilitated by the existence of market makers. It is not necessary to identify who is trading with who.

⁵⁹ For example, Treynor (1962, 1999) assumes ‘Investors have perfect knowledge of the market, … every investor knows a) present prices b) what every other investor knows that might have some bearing on future investment values. If we further grant equal intelligence and equal effort to all investors, … [this] is tantamount to assuming that investors agree in their forecast of future values’ (p. 2).

⁶⁰ Presumably Guth (1994) equates ‘common knowledge’ here with ‘agreed common knowledge priors’ (also referred to as ‘agreed common knowledge beliefs’) (p. 117).

⁶¹ ‘Without common knowledge assumptions, investors … face intrinsic uncertainty over which firms the rest of the market regarded as undervalued or overvalued … [and/or] face uncertainty over how the market’s beliefs will change with the arrival of new information …. [, both of which] can affect future prices’ (Guth, 1994, p. 129).

⁶² ‘[I]nvestors in the CAPM paradigm do not face intrinsic uncertainty [p.138]. The CAPM implicitly makes beliefs common knowledge by endowing investors with perfect foresight about asset returns [p.131; italics added]. … [S]ince the CAPM assumes investors know the returns, these expected (future) values are known constants, rather than some expected value over a genuine probability distribution …. [, and therefore] the CAPM effectively eliminates any source of speculating over the beliefs of others [p.141]. Common knowledge beliefs assumptions … eliminate speculative changes in market prices’ (Guth, 1994, p. 139).

⁶³ Asset i’s rate of return, , must deviate from and fluctuate around its expected rate of return, , for its variance, , to be nonzero. Deviations from are necessary for , and thus for . And, for to be a random or uncertain variable, . With no uncertainty, , , and, therefore, .

⁶⁴ ‘Our central result is that … if the initial allocation is ex ante Pareto-optimal (as occurs, for example, when it is the outcome of a prior round of trading on complete, competitive markets), then the receipt of private information cannot create any incentives to trade [p.17]. [A]ny attempt to speculate on the basis of new information must result in that information becoming impounded in prices, so that profitable speculation is impossible [p.26]. This no-trade result depends crucially on the rational expectations assumption that … is common knowledge’ (Milgrom and Stokey, 1982, p. 18; italics original).

⁶⁵ According to Miller (1977), ‘it is implausible to assume that although the future is very uncertain, and forecasts are very difficult to make, that somehow everyone makes identical estimates of the return and risk from every security. In practice, the very concept of uncertainty implies that reasonable men may differ in their forecasts [p.1151; italics added]. … [T]he outcomes of most investments are subject to true uncertainty, and such uncertainty normally implies divergence of opinion [p.1155]. In practice, uncertainty, divergence of opinion about a security’s return, and risk go together’ (p. 1154). Beber et al. (2010) agree: ‘Uncertainty is a precondition for differences in beliefs to matter in theoretical models’ (p. 416). Miller (1977) further hypothesizes the most volatile stocks are, in general, the stocks about which investors have the greatest divergence of opinion about expected returns and probability distributions of return.

⁶⁶ French (2003, p. 68).

⁶⁷ ‘[I]nvestors would only make portfolio decisions according to the two-parameter model if their assessments were descriptively valid’ (Fama, 1976, p. 272), that is, if they were correct, which can occur only with homogeneous expectations.

⁶⁸ Others, for example Partington (2013), also acknowledge the CAPM is incomplete with respect to its limited two-factor determination of asset pricing: ‘When it comes to the determinants of asset prices it is doubtful that the CAPM provides a complete description of reality’ (p. 72).

⁶⁹ ‘The noise that noise traders put into stock prices will be cumulative …. Offsetting this, though, will be the research and actions taken by the information traders. The farther the price of a stock gets from its [(perceived) fundamental] value, the more aggressive the information traders will become. More of them will come in, and they will take larger positions. …. Thus the price of a stock will tend to move back toward its value over time. …. the farther the price of a stock moves away from value, the faster it will tend to move back. This limits the degree to which it is likely to move away from value’ (Black, 1986, pp. 532–533).

⁷⁰ Although our model is generally stable, we do not assume investors necessarily correct or revise their expectations in subsequent periods (i.e. their heterogeneous expectations may remain unchanged). This is similar to Levy et al. (2006), who assume ‘investors are not necessarily fully rational. Namely, investors may or may not adjust their expectation as a result of the observed prices; hence we do not impose rational expectations. We rather employ Lintner’s (1965a) framework in which equilibrium prices are determined by all the heterogeneous beliefs, but prices do not necessarily affect the subjective expectations’ (p. 1321).

⁷¹ Formal derivations of the supply curve’s positive slope (i.e. the Law of Supply) and demand curve’s negative slope (i.e. the Law of Demand) based on rational utility or wealth maximizing investor behaviour are well documented in the economic literature.

⁷² This form of heterogeneous beliefs/expectations is supported as follows: According to Haltiwanger and Waldman (1985), ‘agents in the real world are obviously heterogeneous in terms of information-processing abilities’ (p. 328); ‘That is, some agents in our economy are able to process information in a very sophisticated manner, while others are much more limited in their capabilities’ (p. 326). Davis et al. (2007) agree that our assumption may generally characterizes actual investor experience: ‘each person forms his or her own expectations about the stock’s future expected returns and risks according to a common information set that people may all have’ (p. 84). Kurz (1994) suggests ‘it is an empirical fact that intelligent economic agents may exhibit drastic differences in beliefs even when they have the same information’ (p. 878).

⁷³ A ‘“major problem of finance theory is an overreliance on the assumption of common beliefs. …. It is difficult, however, to figure out how to proceed in relaxing this assumption”. Richard Roll, 1988’ (Guth, 1994, p. 129). (Guth (1994) doesn’t provide a reference for Richard Roll (1988), except for ‘R²’ (Journal of Finance, 1988, Vol. 43, pp. 541–566), but the quote does not appear in that paper).

⁷⁴ Even though investors can interpret commonly known full information differently, we assume they process and interpret ‘common knowledge’, including the well-known benefits of portfolio diversification, identically and correctly. It is implicit, therefore, that rational investors have established themselves as owners of well-diversified asset portfolios, such that the portion of asset 1’s increased variance in rates of return due to nonsystematic risk factors (if any) does not lead them to buy less (or sell more of their current holdings of) asset 1.

⁷⁵ One might presume there should be no change in asset 1’s expected rate of return because its normal probability distribution has become wider by equal amounts on both sides with no change in its (mathematical) expected rate of return. However, this is a snapshot in time immediately after the risk increase, but before the market has adjusted to that risk increase.

⁷⁶ As the market price increases toward P₂, existing owners (who are potential sellers of existing supplies of asset 1 in the secondary market) increase their quantity supplied to the market, which is illustrated by a movement up along the S₀ curve to the new equilibrium at the intersection between supply curve S₀ and demand curve D₂.

⁷⁷ The comparative static results: In our market model, and . The sign of depends on whose trading activity dominates. When risk-averse (risk-taking) investor trades dominate, , and therefore . The partial equilibrium, comparative static beta risk-rate of return result is when risk-averse (risk-taking) investor trades dominate the asset market.

⁷⁸ We believe the risk-averse–risk-taking dichotomy is misapplied in the literature. The correct dichotomy is less-risk-taking versus more-risk-taking investors because all trade in risky financial assets is, by definition, undertaken by investors who exhibit risk-taking behaviour in those trades (even though they may be risk-averse in general). An important distinction here is how they are taking risks. Short-term risk-takers seek to buy low and sell high based on short-run asset price variations, while longer-term risk-takers seek to buy low and sell high based on the long-term trend in asset prices.

⁷⁹ It is implicit that investors, being rational, have already positioned themselves as owners of a sufficient value and quality of marketable assets (in the core portion of their asset portfolios) as a safety net for short-term liquidity needs (for reasonably possible life events) and for retirement. Only then would it be rational for generally risk-averse investors to invest in risky assets. Regardless of the degree of risk-aversion they exhibit in the core portion of their portfolios, investors are risk-taking in their risky asset purchases (in varying degrees across investors, as reflected in the degree of risk individually borne).

⁸⁰ This is similar to Fama (1976), who, in the context of his presentation of the CAPM, has ‘in mind a multiperiod world where, period after period, the investor makes portfolio decisions in accordance with the two-parameter model’ (p. 272).

⁸¹ Financial asset supply curves generally have a positive slope and are fixed in position during any given trading day, such that investors’ decisions to supply more or less to the market (in response to demand curve shift-induced price changes) come from existing owners of outstanding supplies in the form of movements up or down along the positive-sloped supply curve (i.e. demand is not bound by outstanding supply).

⁸² Consistent with a longer-term investor’s view, the static one period need not be assumed to be a year, but rather a single long-term holding period that corresponds to that specific investor’s investment horizon.

⁸³ We use the term ‘technical analysis’ with the descriptor ‘of underlying fundamentals’, or simply ‘fundamental analysis’, to distinguish it from ‘charting’ or a ‘technical analysis’ of patterns in asset prices (not necessarily linked to fundamentals) to detect potentially profitable trading strategies. We interpret ‘technical analysis’ more broadly to include a ‘fundamental analysis’, with all technical analyses being of, or relating to, underlying fundamentals.