Liquidity preference in a portfolio framework and the monetary theory of Kahn

Transcription

1 Cambridge Journal of Economics Advance Access published November 29, 2010 Cambridge Journal of Economics 2010, 1 of 19 doi: /cje/beq041 Liquidity preference in a portfolio framework and the monetary theory of Kahn Theodore T. Koutsobinas* This paper examines the relation between variations in the propensity towards liquidity preference, price-adjustment and shifts in portfolio allocation by expanding Kahn s idea of marginal equilibrium under strong uncertainty in financial markets and contributes to recent post-keynesian attempts to develop a liquidity preference theory of asset prices by providing an analysis of the price-adjustment mechanism. The notion of the own-rate of money interest is utilised to develop a multi-asset liquidity preference framework, which is consistent with uneven variations of liquidity-premia across assets in response to changes in the degree of strong uncertainty that is specific to different investors with variable allocation of assets in their portfolios. More specifically, in the context of this portfolio framework it is established that an increase in the state of strong uncertainty (state of bearishness) makes less liquid assets further less inconvenient than more liquid assets. In periods characterised by greater strong uncertainty, equilibrium is restored through a greater demand for more liquid assets including money relative to the demand for less liquid assets and, therefore, through a higher own-rate of money interest for less liquid assets than warranted, which shows the ineffectiveness of standard monetary policy. Key words: Liquidity preference, Monetary theory, Portfolio, Strong uncertainty, Kahn JEL classifications: B22, E41, E43, E52, E58, E64 1. Introduction In this article, a theoretical framework is developed to examine the relation between variations in the propensity towards liquidity, price-adjustment and shifts in portfolio allocation. This theoretical framework is based on Kahn s substantive contribution to post- Keynesian monetary theory, which was presented in his paper Some Notes on Liquidity Preference (Kahn, 1954[1972]). Most post-keynesian economists accept the seminal character of this paper in the development of the theory of liquidity preference [see, e.g., Kregel (1998), Bibow (2005)]. Kahn s contribution to monetary theory was quite extensive as his analysis covers diverse areas such as the real arbitrage process in portfolio Manuscript received 7 November 2009; final version received 11 July Address for correspondence: Serron 18, Athens 16674, Greece; koutsobinas@aueb.gr *Athens University of Economics and Business, Greece. Ó The Author Published by Oxford University Press on behalf of the Cambridge Political Economy Society. All rights reserved.

2 2 of 19 T. T. Koutsobinas allocation, the relation between the transactions motive and the speculative motive and the idea of marginal equilibrium in financial markets. However, despite a few exceptions, this work has not been used analytically in recent attempts to develop a liquidity preference theory of asset prices. Kregel (1998) argued in favour of the Keynes Kahn approach that emphasises the impact of interest rates on asset prices and utilised the principle of squarerule, which is consistent with rational behaviour to analyse this process. In the present article, an alternative aspect of Kahn s work is developed, namely, the idea of priceadjustment across different categories of financial assets with variations in the state of confidence and liquidity preference under strong uncertainty in a multi-asset (portfolio) framework rather than in the standard two-asset context. The emphasis in the present paper is on the impact of the state of confidence of agents under strong uncertainty and reflects the limitations that the state of expectations pose for monetary policy because of the impact of different degrees of liquidity preference across different categories of financial assets and agents (i.e., banks, investment houses, funds and individual investors) on relative interest rates (Chick and Dow, 2002; Arestis and Sawyer, 2006) in situations that are consistent with marginal equilibrium in financial markets. This equilibrium process is attained through a behavioural adjustment process that operates in a definite mode from behavioural changes in conviction to changes in liquidity preference, changes in the term structure of interest rates and relative asset prices, changes in asset allocation and eventually income adjustment. On the other hand, the influence of monetary policy on long-term interest rates in standard contemporary macroeconomic models, which employ an interest rate rule such as the Taylor rule is acknowledged to be very weak (Romer, 2000), while the transmission mechanism and the impact of various interest rates and financial assets in orthodox contemporary models such as the new consensus model is conceded to be absent (Meyer, 2001). Thus, the contribution of Kahn is very relevant today especially if one considers the current financial crisis that began with the collapse of the subprime mortgage market in the USA in 2007 and is characterised by sharp shifts in financial portfolios and a flight to quality. In the present paper, the idea of the own-rate of money interest that was proposed by Keynes (1936) is utilised as an analytical tool. Next, Kahn s contribution to monetary theory with respect to the liquidity preference theory of term structure of interest rates is discussed as well as the subsequent interpretation and utilisation of his seminal work. This analysis is conducted in a multi-asset liquidity preference framework, which allows for the presence of varying liquidity premia across categories of financial assets. Finally, a portfolio framework is developed that manifests a fundamental proposition of Kahn regarding the impact of illiquidity. This framework explains how in turbulent financial periods, there is an asymmetric shift away from less liquid assets that is consistent with equilibrium conditions and constrains the effectiveness of monetary policy. 2. An analytical framework for Kahn s monetary theory: the own-rate of money interest, the state of confidence and the illiquidity discount Kahn s idea of price adjustment refers in essence to the market evaluation of the monetary measures of the value of various classes of assets, particularly with respect to changes of the liquidity premium. The latter is the measure through which we can represent variations in liquidity preference across assets. In the post-keynesian literature, the most well known monetary measure of the implicit and explicit yields and costs of an asset is the own-rate of

3 Liquidity preference in a portfolio framework 3 of 19 money interest of assets. Thus, following Keynes, the own-rate of money interest of an asset consists of three elements (see Keynes, 1936, pp ). The first component is a yield or output in terms of itself net of the carrying cost, again in terms of the asset itself, which occurs through the wastage or depreciation arising from the mere passage of time. The second factor is a potential convenience or security given by the power of disposal over the asset (measured in terms of itself) that investors are willing to pay, which is called liquidity premium. Following Kaldor (1939, pp. 60 1), and for convenience of exposition, in the present article the liquidity premium is equivalently expressed by its inverse, the illiquidity discount, which measures the lack of convenience. Finally, the last component of the own-rate of money interest is the rate of appreciation of the asset relative to money. Keynes explicitly related the illiquidity discount with what in the Treatise on Probability he called weight of an argument (see Keynes, 1979, pp ). In addition, Keynes established the existence of an inverse relation between the illiquidity discount and the state of confidence (see Keynes, 1936, p. 240). In addition, the state of confidence is considered to be determined to a great extent by evidential weight. Actually, Minsky (1975, p. 65) and Kregel (1987, pp ) treat the state of confidence and evidential weight as being interchangeable terms although for Gerrard (1995, p. 190), O Donnell (1991, pp. 83 4) and Runde (1990, p. 287) the evidential weight and the state of confidence are similar but not identical terms. Thus, in the context of Keynes s discussion of liquidity preference theory, illiquidity discounts vary with respect to the state of confidence that is specifically associated with the assets held in a portfolio and, therefore, with their specific attributes such as: (i) the term to maturity or duration; (ii) the nature of assets and their marketability. First, holding assets that have a greater term to maturity involve a greater degree of uncertainty because the predictability of future events decreases as the term to maturity increases (see Lutz, 1940, p. 62). As the term to maturity for financial assets increases, say from 2 years to 10 or to 30 years, the relevant knowledge regarding a longer time horizon in the future diminishes as well as the evidential weight. Thus, the state of confidence is lower for financial assets with longer terms to maturity and there is indeed an inverse relation between term to maturity and the state of confidence. Second, if the extent of the illiquidity discount differential between different classes of assets depends on the security derived from the disposal of those assets, then it is affected to a large extent by their marketability, that is, by their ability to be liquidated easily. For example, the degree of difficulty in trading different categories of liquid assets (i.e. different categories of financial assets) is not the same. Thus, different categories of assets differentiate with respect to the thinness of the markets that they are traded. Likewise, there is a much greater difficulty in trading real capital assets than paper assets. One factor that contributes to the marketability of an asset is the availability of a second hand, orderly spot market where the asset can be resold (or bought) without much change from the previous publicly announced price due to the existence of a market maker. As Davidson (1994, p. 50) argues, real capital assets are in essence illiquid assets, that is, durables, whose spot (resale) market is poorly organized, disorderly, thin or even notional because there is no market maker to organize the markets. In addition, differences in liquidity across assets may arise from other sources because of the heterogeneity of information across markets. However, the existence of an illiquidity discount that is attributed to the marketability of assets has a noteworthy implication. In some instances, longer-term assets become more liquid than shorter-term assets because of factors associated with the specificity of each market.

4 4 of 19 T. T. Koutsobinas Following Dequech (1999, pp ; 2000A, pp ), on principle, we must distinguish between the case in which we consider the qualities of an asset (i.e., term to maturity) that contribute to the degree of its illiquidity (and, consequently, of its illiquidity discount) while assuming a given state of uncertainty and a given state of confidence in general and the situation in which we discuss the variable influence of uncertainty perception and the state of confidence on the illiquidity discount across different classes of assets with different qualities. The illiquidity discount represents a specific degree of uncertainty associated with a given asset beyond a general degree of uncertainty that is common to all assets (see Dequech, 2000A, pp ). This specific degree of uncertainty is one of the determinants of the illiquidity discount attributed to liquid assets as opposed to the general degree of uncertainty that is common to all assets, that is, liquid and non-liquid assets. However, Keynesian strong uncertainty does not influence only the security of an asset. In different degrees of strong uncertainty, there is different investment sentiment about the future course of the price of securities, which influences what Keynes called the rate of appreciation of assets relative to money. Therefore, the rate of appreciation of assets relative to money is also a function of the degree of uncertainty (Keynes, 1936, p. 231). In essence, it is difficult to draw a clear distinction between the effect of uncertainty on the illiquidity discount and on the rate of appreciation of assets relative to money. In the present article, Keynes s analysis will be followed, in which the rate of appreciation of an asset and the illiquidity discount of an asset are treated as different terms. 1 By specification, the greater is the degree of uncertainty, the lower is the evidential weight and the state of confidence and the greater are the illiquidity discounts of less liquid assets. Thus, following Dequech (2000A), the illiquidity discount of an asset can be represented at an ultimate level of abstraction in a general form as follows: lj 5 lðq; V; Lj; Q V Lj lj Fj > 0 with Fj 5 FðHj; TjÞ while at the immediate level of abstraction, the illiquidity discount of an asset can be represented as: lj 5 lðlj; CÞ lj >0; > 0 with C 5 CðQ; V; Cj ð1bþ where l j is the illiquidity discount of assets; Q is the general degree of perceived uncertainty that is common to all assets; V is optimistic disposition or animal spirits that influence uncertainty aversion; Fj is the specific degree of perceived uncertainty associated with asset j and its attributes; H j is the difficulty of liquidating any asset other than money due to its nature and to its lack of marketability; and T j is the time involved till the maturity of assets or the duration of the asset. In addition, L j is considered the illiquidity of an asset that exists given a state of uncertainty. Moreover, C is a measure of the degree of the state of 1 Another consideration is associated with the possibility of the dependency on the illiquidity discount on the relative appreciation of other assets (Dequech, 2000A, p. 165). However, the claim that investors hold liquid assets to take advantage of the relative depreciation of other assets and that the attractiveness of liquid assets is that their major return is their liquidity premium (Dequech, 2000A, p. 169) stands in contrast with Keynes s claim that a liquidity-premium, on the other hand, is not even expected to be rewarded and it is a payment, not for the expectation of increased tangible income at the end of period, but for an increased sense of comfort and confidence during the period (Keynes, 1979, pp ). In this article and, given the above mentioned difficulties, it will not be adopted.

5 Liquidity preference in a portfolio framework 5 of 19 confidence, which depends on the general degree of perceived uncertainty, the specific degree of perceived uncertainty associated with asset j and, therefore, with its attributes and uncertainty aversion that depends on optimistic disposition or animal spirits. At the immediate level of abstraction, the illiquidity discount is influenced by an indicator of the asset s degree of illiquidity assuming a given state of uncertainty and an indicator of the state of confidence as shown in equation (1B). In addition, the manner in which investors form their expectations about the future plays an important role. Following Keynes, animal spirits influence the expectations of investors. In addition, Dequech (1999, pp ) proposes a framework of liquidity preference under strong uncertainty in which he replaces Keynes s emphasis on the dichotomy between probable and non-probable expectations with the distinction between the state of confidence and expectations themselves that are viewed as different from the state of confidence. These are the immediate determinants of what he calls the state of expectations. 2 The ultimate determinants of the state of expectations are, on the one hand, the current knowledge of investors and the optimistic disposition (or animal spirits) and, on the other hand, their creativity. 3 Optimistic disposition is viewed as influencing the state of confidence, and, therefore, the illiquidity discount, as well as expectations. If there is a strong optimistic disposition the estimates about the future will be spontaneously optimistic and, therefore, the rates of appreciation of assets will be higher (see Dequech, 1999, p. 420). Thus, optimistic disposition or animal spirits influences through alternative routes the illiquidity discount and the rate of appreciation of assets. Thus, the estimates about the rate of appreciation of assets can be given by aj 5 aðvþ V >0; ð2þ where a j is the rate of appreciation of assets relative to money and V is a measure of investment sentiment, which is influenced by the degree of uncertainty regarding the shortterm outlook of the rate of return of an asset. In reality, variables such as the state of confidence and optimistic disposition are approximated today by various sentiment survey measures of market participants (i.e., fund managers, traders, individual investors etc.). Often, these measures are correlated with expected changes in weights of flows across different categories of financial assets. Global financial institutions extensively utilise a broad range of sentiment surveys such as, for example, on international institutional investor flows and on attitudes of fund managers. Moreover, analysing sentiment surveys constitutes a widespread routine among 2 Keynes argued that the state of long-term expectations does not solely depend, therefore, on the most probable forecast we can make. It also depends on the confidence with which we make this forecast (Keynes, 1936, p. 148). Thus, Keynes claimed that the state of expectations is based on probable forecasts or probable expectations and the state of confidence. Although this claim of Keynes is acknowledged, in the approach followed by Dequech the immediate determinants of the state of expectations are the state of confidence and expectations themselves that are not defined as probable (Dequech, 1999, pp ). In the place of probable forecasts or probable expectations, the idea of expectations is introduced that may be influenced by available knowledge (some of which may be used for the formation of probable forecasts) but additionally by spontaneous optimism and by creativity. 3 There are some post-keynesian economists, who emphasise the influence of creativity in the formation of expectations themselves such as Carvalho (1988), Dosi (1988) and Dequech (1999). On the other hand, institutions play an important role in reducing uncertainty according to Kregel (1980), Hodgson (1988), Davidson (1991), Carvalho (1992), Dow (1995), Minsky (1996) and Dequech (2000B). Although the role of creativity and institutions are acknowledged, these issues cannot be discussed in detail here since the objective of the present paper is different.

6 6 of 19 T. T. Koutsobinas investors in developing their actual investment strategies in contemporary global financial markets. 3. Kahn s contribution to monetary theory: a Liquidity preference theory of price adjustment and term structure of interest rates The contribution of Kahn to monetary theory is associated with his attempt to respond to the views of proponents of Hicks s school with respect to the determination of the rate of interest. Hicks, Kaldor and Robertson (Hicks, 1939, pp ; Kaldor, 1960, pp. 37 9; Robertson, 1951, pp ) claimed that when uncertainty enters into analysis then the long-term interest rate cannot be determined and this leaves the interest rate hanging by its own bootstraps. In this vein, they rejected the implications of Keynes s liquidity preference theory regarding the determination of the long-term interest rate. However, according to Moore (1988), Kaldor (1970) embraced in his later writings monetary endogeneity and accepted that the long-term interest rate was equal to the average of expected future short-term interest rates. Similarly, Hicks, who initially embraced the early views of Kaldor with respect to the determination of the rate of interest (Hicks, 1939, p. 164) came to accept the significance of Kahn s views regarding questions associated with liquidity risk and the issue of financial intermediation (Hicks, 1983, p. 63). Kahn examined a central assumption of Hicks s school associated with the bootstraps puzzle, that is, the early views of Hicks and Kaldor, according to which investors hold only one type of asset (Kahn, 1972, p. 74). In contrast, Kahn claimed that, in practice, investors hold many types of assets and change the proportion of assets that are included in their portfolio. In this vein, Kahn rejected the views of the Hicks s school that the expected long-term interest rate depends, in general, on the average of expected short-term rates. Instead, he argued that the dependence of the expected long-term interest rate on the time pattern of short-term interest rates holds only after price-adjustment takes place and after investors become marginal between financial assets (Kahn, 1972, p. 74). When expectations change and portfolio asset balances are altered, the expected long-term interest rate depends on expectations, which are different from those that were present originally. According to Kahn, in marginal equilibrium there is no movement between different types of assets (i.e., from stocks to bonds) and the evaluation of the monetary measures of the value of assets is such that the latter become equal. Kahn also stressed the role of uncertainty and considered the lack of conviction among investors as a significant factor, which affects asset allocation decisions (Kahn, 1972, pp. 76 8). Moreover, Kahn claimed explicitly that the degree of belief of investors is an important factor in a monetary theory of interest. Kahn claimed also that a determinate monetary theory depends on the following three elements: (i) changes in the degree of belief of investors; (ii) changes in the size of the dominant or representative group of investors; (iii) the elasticity of the expected interest rate with respect to its present level (Kahn, 1972, p. 89). 4 Kahn put a great emphasis on the possibility of uneven changes across returns of assets and, therefore, across money-rates of interest of different categories of assets. He associated the possibility of a monetary explanation of the interest rate with a disproportionate change in the expected interest rate relative to a change in the actual interest rate (Kahn, 1972, p. 91). This uneven relation between those two rates was linked to the 4 Following Modigliani (1944), with respect to the latter, denoting the expected level of interest, E(i), and the present interest rate, i, the elasticity of expectations is given by: E 5 [de(i)/e(i)] / [di/i] 5 1

7 Liquidity preference in a portfolio framework 7 of 19 presence of the speculative motive, which is influenced by changes in the degree of conviction (Kahn, 1972, p. 72). In addition, he linked uneven changes of the actual returns across assets with the presence of heterogeneous expectations with different degrees of conviction and, therefore, with different degrees of the state of confidence (Kahn, 1972,p. 78). He stressed the influence of the degree of sacrifice or convenience involved in holding a given class of assets rather than another one (Kahn, 1972, pp. 90 1). He argued that eventually the own-rates of money interest of different financial assets can move towards a different direction as a result of the influence of changes in the state of confidence and that there is an interdependence in the demand and the supply of different categories of assets (Kahn, 1972, p. 80). In the context of a multi-asset framework that includes different categories of securities, the core of Kahn s analysis therefore relies on the idea of the interaction of groups with different degrees of conviction about the acceptability of various financial assets, which is equivalent to the idea that variations of the state of confidence of those groups influence the prices of financial assets (Kahn, 1972, p. 88). In this vein, when expectations are influenced by the state of confidence, investors who are indifferent across classes of assets believe, by assumption, that at some point a different set of expectations (and different liquidity preference) from their own will prevail. This implies that the long-term rate of interest is influenced eventually by expectations of banking policy (Kahn, 1972, p. 77). Kahn discussed also the influence of the speculative motive in terms of the expectation of the rate of change of the return of assets (Kahn, 1972, pp. 85 6). The state of expectations is influenced by changes in the degree of confidence (and illiquidity discounts) as was proposed earlier by Keynes (1936, p. 240). 4. The interpretation of Kahn s monetary theory In one rare contemporary assessment of Kahn s contribution to monetary theory, Dardi presented two alternative off-margin cases and one on-margin case on the basis of Kahn s marginal equilibrium analysis (Dardi, 1994, p. 100). In the off-margin approach either estimates are impossible (as is the case with extremely high uncertainty) or investors hold only one asset and not a portfolio of assets (which, however, seems inconsistent with Kahn s emphasis on conducting the analysis in a multi-asset framework). In the onmargin case, the conventional view of the dominant group of investors plays an important role but cannot be described by a price-adjustment process or by asset allocation shifts since, in this conventional context, the rates of appreciation of assets are assumed by Dardi to be consistent with unaltered interest rates. 5 Thus, starting from a state of equality of own-rates of money interest of assets, equilibrium is always preserved and there is no price- or quantity-adjustment. In contrast, in the alternative analysis that will be presented below price-adjustment and asset allocation shifts across assets do take place in response to variable changes in illiquidity discounts across assets brought about by changes in the state of confidence and 5 Dardi attempted to examine Kahn s analysis with respect to his views on liquidity preference and monetary policy. According to Dardi s interpretation of Kahn, there are two categories of prices, which seem to refer to what is common in financial markets as bid-prices and ask-prices. The bid ask spread is influenced by the expected rate of return of the security, a consideration reminiscent of Keynes s notion of the rate of appreciation of assets relative to money. The rate of appreciation of assets relative to money is influenced by various factors (i.e., among others, Dardi emphasises capital risk, income risk and convenience of money). Again, the idea of the influence of the convenience of money is reminiscent of Keynes utilisation of the liquidity premium.

8 8 of 19 T. T. Koutsobinas optimistic disposition. This process takes place under circumstances that are completely absent in Dardi s approach, namely in situations in which it is assumed that portfolios include many assets and that gradable strong uncertainty is present. Kahn s analysis explains the determination of the term structure of interest rates in the context of a multi-asset mode. In a multi-asset framework, there are as many interest rates as assets, and the long-term interest rate, which is influenced by liquidity preference, becomes the important rate in the term structure of interest rates. Thus, in a multi-asset context the term liquidity preference is not identical to the demand for money because it affects the demand for other non-money liquid assets. Davidson argued that the liquidity preference decision is associated with an allocation process among various time machine liquid assets that involve the speculative demand for money (Davidson, 1994, p. 114). As a consequence, it is more appropriate to conduct the analysis in terms of the liquiditypreference theory of the term structure of interest rates, which is applicable in a multi-asset framework, rather than in terms of the liquidity preference theory of the interest rate, which is applicable in a two-asset model. 6 Kahn examined the interplay between the speculative and the transactions motive (Kahn, 1972, pp. 81 3; for a recent analysis of the configurations between those motives, see Tymoigne, 2008). However, with respect to strong uncertainty, Kahn warned that it is to the speculative motive alone that we must look at for the interest-responsiveness of the liquidity preference and not at all to the precautionary motive and that the latter is actually inelastic to the rate of interest (Kahn, 1972, p. 85). Kregel (1988) argued that Keynes s monetary theory of interest and production, according to which the rate of interest is a monetary factor, implies that the multiplier and liquidity preference are two aspects of the same phenomenon. In such a context, Kahn seems to support Keynes s monetary theory of interest, which he eventually develops further. In essence, the importance of Kahn s contribution to post-keynesian monetary economics lies in the fact that he provides a more elaborated paradigm of a liquidity preference process influenced by variable states of confidence in a multi-asset framework. In this context, price adjustments are not attributed solely to variations of the interest rate but take place as part of a broader adjustment in the term structure of interest rates because there is interdependence in the determination of interest rates. If, according to Kregel, Keynes s position might be described as a theory of shifts in the demand for money, then by the same token Kahn s difference from neo-classical theory might be described best as a theory of shifts in the demand for all financial assets, that is, a theory of shifts in portfolio allocation that depends on liquidity preference under strong uncertainty. 5. The application of the principle of square-rule and portfolio variation under strong uncertainty Kregel (1998, pp ) argues that Kahn s emphasis on changes of relative asset prices is consistent with the conduct of modern portfolio management. He also claims that the Keynes Kahn approach, which emphasises the impact of interest rates on capital assets, is also more appropriate for modern capital markets conditions. In Kregel s treatment, a crucial process is the expectation of the long-term interest rate relative to the short-term borrowing rate. The real arbitrage process, which was developed by Kahn in his work, is 6 The difference between the liquidity preference in a multi-asset model and the two-asset model (i.e., speculative demand for money) was noted explicitly by Leijonhufvud (1968), who echoes the discussion of the speculative demand for money by Kahn (1954[1972]) and Kalecki (1939).

9 Liquidity preference in a portfolio framework 9 of 19 acknowledged by Kregel as providing a monetary determination of the long-term interest rate. Kregel (1998, p. 132) argues that the arbitrage between bonds and bills and the variation of the spread between the long-term and the short-term interest rate is an application of Keynes s square-rule. This process takes place because the expected capital gains from buying long determine borrowing short-term funds. According to the principle of the square-rule, a fall in the price of bonds will not cause capital losses relative to the coupon interest except in the case in which the change of the current yield to maturity changes at a rate that is equal to the square of its value (Kregel, 1998, p. 127). Yet, it is unclear whether the square-rule applies in a rational decisionmaking environment alone or extends to situations of strong uncertainty. This happens because, following a comment by Keynes, Kregel discusses explicitly the behaviour of a rational investor regarding his decision to hold money or a financial asset (Kregel, 1998, pp ). It must be acknowledged at this point that Keynes discusses the square-rule principle explicitly in terms of notions such as risk of illiquidity and balance of probabilities (Keynes, 1936, p. 202), terms that are consistent with rational decisionmaking. However, in Keynes s analysis (1936, p. 202) of the so-called square-rule principle, there are also certain assumptions, which are associated with the presence of strong uncertainty. First, in his framework the general view of what is considered a safe level of interest rate remains unchanged. This assumption implies that the safe level of interest rate does not necessarily adjust rationally to the level associated with the monetary policy rule. In addition, the square-rule implies the existence of a running yield, which can offset a very small measure of fear (i.e., illiquidity discount) as long as the expected future experience will not be very different from past experience (Keynes, 1936, p. 202). Thus, it is also implicitly assumed that the measure of fear is substantive on certain occasions. Finally, in the discussion of the own-rates of money interest of assets, it is also assumed that changes in monetary policy cannot be effective as long as the propensity towards liquidity is unchanged (Keynes, 1936, p. 234). The above-mentioned three lines of argument that were used by Keynes suggest that there are circumstances in which investors do not adjust their state of expectations so that the latter become consistent with monetary policy. To the extent that the latter reflects the true state of the economy, investors expectations are not rational since they are not adjusted to the true state. It seems, therefore, that the claim of investors rationality applies because a certain coupon is compared with the expected yield when the degree of bearishness is considered as given or exogenous. However, if expectations influenced by strong uncertainty become endogenous as was manifested in the case of the equality of own-rates of money interest of financial assets (Panico, 1989), which is influenced by variable illiquidity discounts, the calculation of capital gains or losses cannot be rational. To explain the significance of strong uncertainty and variable liquidity preference in portfolio allocation, let us assume two financial assets bills and bonds. Monetary policy sets the federal funds rate at a level consistent with the true model. If the public investing in bills is reassured by monetary policy, the rate on bills will be consistent with the federal funds rate and, therefore, the illiquidity discount on bills is zero. Still, the equality of ownrates of money interest implies that the long-term interest rate will be influenced by expectations of the short-rate of interest rate and the own illiquidity discount of bonds that is influenced by strong uncertainty expectations. Therefore, in turbulent financial periods characterised by strong uncertainty, calculations of capital gains or losses according to the square-rule take place in fact on the basis of the effect of strong uncertainty expectations

10 10 of 19 T. T. Koutsobinas on the illiquidity discount of long-term bonds. Thus, the adjustment, which is associated with the square-rule is, in essence, an alternative process (and, in turbulent financial periods, a less influential one) to the real arbitrage that arises because of the adjustment of variable liquidity preference across financial assets due to the influence of strong uncertainty. In practice, both liquidity preference and non-liquidity preference dependent processes may take place simultaneously in such a way that their interplay produces trading noise. In this case, what is important in periods of financial turbulence is not only how low the short-term rate of interest is but also how the adjustment of variable liquidity preference across assets in portfolio holdings eventually determines the value of less liquid assets such as, for example, the long-term interest rates relative to short-term interest rates. It must be noted that a characteristic element of the analysis associated with the square-rule principle is that in essence it is conducted in a two-asset framework in which the yield to maturity is influenced by uncertain expectations and is compared to the certain coupon interest. In this two-asset framework, in the case in which the capital loss more than offsets the interest rate received, the user cost of money is negative and money will dominate consols in portfolios absolutely. In fact, the presumption that one investor is fully invested in bonds is equivalent to the idea that the illiquidity discount of this asset is nil. Thus, the adoption of a two-asset framework is eventually restrictive in the sense that investors hold effectively only one type of asset. In this connection, there is scope for extending the analysis of liquidity preference in a multi-asset framework with bonds of different maturities influenced by variable states of confidence and illiquidity discounts. Bibow (2009) provides a discussion of Keynesian theories of liquidity preference. Bibow acknowledges that Kahn s 1954 Manchester School paper is a rich source of inspiration (see Bibow, 2009, p. 206), but he does not discuss Kahn s seminal paper because the emphasis is on the analysis of Tobin s proposition of liquidity preference as aversion to risk and Hicks waiting theory of liquidity preference (2009, pp ). According to Bibow, there is a financial channel of falling security prices, which may be attributed to a widespread rise in liquidity preference (Bibow, 2009, p. 82) and to quantity adjustment towards money till the desire to stay liquid disappears. This approach can be considered as providing a complementary analysis to the framework advanced in the present article, which focuses explicitly on Kahn s monetary theory, the asymmetric price-adjustment across different categories of financial assets and the behaviour of the long-term interest rate, which was a focal variable in Kahn s analysis. 6. Variations in the propensity towards liquidity, price-adjustment and shifts in asset allocation Kahn s idea of price adjustment in response to variations in the security offered by an asset was not elaborated so far in the literature. As was mentioned above, Hicks accepted that Kahn s idea, according to which there is a shift in asset allocation in capital markets in response to changes in the propensity towards liquidity constituted the modern post- Keynesian view of interest (see Hicks, 1983, p. 63). However, despite a growing literature over the years on a liquidity preference theory of asset prices, which includes the work of Townsend (1937), Boulding (1944), Minsky (1975), Davidson (1978) and, more recently, that of Kregel (1988), Wray (1992) and Dardi (1994), the idea of the price-adjustment mechanism has not received sufficient attention. In what follows, Kahn s analysis will be

11 Liquidity preference in a portfolio framework 11 of 19 utilised as the basis for the development of a framework, which provides a liquidity preference analysis of the term structure of interest rates. 7 Aggregation is dealt by summing up the different portions of assets that exist in portfolios of different individual investors with heterogeneous expectations. In this context, a bullish investor will tend to hold in his portfolio a greater portion of higher yielding but less liquid assets than a share of more liquid assets, while a bearish investor will tend to hold a greater portion of more liquid assets than a share of less liquid assets. Equilibrium is characterised by the equality of own-rates of money interest of various categories of assets, which are expected values. Thus, marginal equilibrium is described in essence by the equality of monetary expected values. This is a representation of shifting equilibrium in the context that Keynes put it, in which changing views about the future are capable of influencing the present situation (Keynes, 1936, p. 293). Given the supply of assets, the aggregation of positions held by investors who have heterogeneous states of expectation determines an average level of own-rate of money interest across assets and average proportions of assets held in portfolios. According to Kahn, these average levels do not have to be marginal in the sense that the average investor may have a state of expectations about the future that is not consistent with the marginal equilibrium of the equality of own-rates of money interest because he may speculate on his views in order to profit or to reduce losses (Kahn, 1972, p. 74). If the views of an average investor prove correct in the next period, then he will not have an incentive to change his asset allocation if there is no change in economic news and he will become marginal himself. Thus, at the present moment, equilibrium is expressed by that marginal investor whose state of expectations is such that he views the own-rates of money interest of assets as equal and holds his asset allocation unchanged. However, if the views of the average investor prove incorrect (which means that the expectations of some of the bullish or the bearish investors that contribute their share to the average position are wrong), the divergence between average and marginal positions can initiate a price-adjustment process towards marginal equilibrium. For example, in the case in which very bearish expectations prove to be wrong, the elasticity of bearish expectations with respect to time will tend to diminish so that there is a convergence of the average position towards the marginal position. Of course, before this process is completed, there may be new economic developments that initiate changes in the state of expectation, changes in the position of marginal equilibrium and changes in the identity of marginal investors (Kahn, 1972, p. 77). In any case, for Kahn, when, on average, markets are in disequilibrium there is always a force for adjustment towards marginal equilibrium across assets although there are different groups of investors that are not viewed as holding the same portions of assets in their portfolios (Kahn, 1972, p. 76). It must be noted that price adjustment under Keynesian strong uncertainty is specified differently from the notion of arbitrage in neoclassical financial theory. For example, the essence of arbitrage in neoclassical financial theory as proposed by Ross (1976) relies on the existence of a constant riskless rate of return and on the existence of a constant positive linear pricing rule, which prices correctly the effect of various exogenous factors that influence the price of an asset. In addition, in neoclassical financial theory arbitrage is viewed as applying to assets that are perfect substitutes. On the contrary, under Keynesian strong uncertainty there are many pricing rules, as different states of expectation may 7 A similar argument was made with respect to the term structure of interest rates. Lutz (1940) argued that Keynes s theory is a liquidity preference theory of interest structure.

12 12 of 19 T. T. Koutsobinas prevail over time that are influenced by different degrees in the state of confidence. In addition, the existence of only one constant pricing rule is inconsistent with the presence of premia, which are time variant, as Summers (1985) notes. Equivalently, in post-keynesian financial theory there is no room for a constant risk-free interest rate because the liquidity premia, or illiquidity discounts, vary over time in the sense that they are influenced by changes in uncertainty perception and in the state of confidence over time. As such, assets with different and varying illiquidity discounts are considered imperfect substitutes while arbitrage in neoclassical financial theory applies only to assets that are specified as perfect substitutes. Thus, price adjustment towards equilibrium under Keynesian strong uncertainty does not involve a transition from incorrect to correct pricing for every asset but a transition from a disequilibrium situation in which investors value unevenly the ownrates of money interest of certain assets to a situation in which they equalise the own-rates of money interest of all assets and become indifferent across them. As was mentioned above, Kahn s idea of adjustment towards marginal equilibrium is, in essence, a representation of Keynes shifting equilibrium. In a multi-asset portfolio framework, the magnitude of change in the state of confidence and in the state of expectations plays an important role and when this change is significant we can distinguish between several cases. If there is a very large change in the state of expectations and the state of confidence under Keynesian strong uncertainty, then the shift from one equilibrium point to another can be very sharp. On the other hand, if there are less large but nevertheless substantive (and sometimes consecutive) changes in the state of expectations and in the state of confidence over a long period of time, then the adjustment process will be slower. But, there is a case in which equilibrium cannot be attained because uncertainty is so high and the magnitude of a fall in the state of confidence is so great that, as Keynes stresses, the conventional evaluation breaks down and no reasonable estimates can be attempted about the future values of assets (Keynes, 1936, p. 154). Another assumption of Kahn s adjustment process towards marginal equilibrium is that it operates in a definite mode from changes in conviction and in the state of confidence to changes in the illiquidity discounts across assets, changes in the term structure of interest rates, variations in relative prices and changes in asset allocation. Thus, for example, changes in asset prices should be considered by themselves as an event that provides new evidence that alters the balance of relevant knowledge to relevant ignorance of investors and, thus, alters their uncertainty perception, evidential weight and state of confidence. This process changes the evaluation of illiquidity discounts across assets and upsets the price adjustment towards equilibrium. For example, in the case of heterogeneous states of expectations, let us consider the case in which that there are three groups of investors, one marginal, one bullish and one bearish, who already hold portfolios of various assets according to their investment views and their estimates. A change in asset prices that increases uncertainty perception leads to an overall fall of confidence and to an increase in the illiquidity discounts across assets. Then, some marginal investors will become bearish, some bullish investors will become less bullish, while some bearish investors who assume that their views were correct will not alter their portfolios and will become marginal themselves. The framework presented here is not confined to the traditional market equilibrium condition of the equality of the supply and demand for assets. For some assets (i.e., n 2 assets), the equilibrium condition is given by the asset closure mechanism of the equality of the own-rates of money interest across assets. For example, in a four-asset framework that includes money, bills, bonds and stocks, some of the equilibrium conditions regarding the

13 Liquidity preference in a portfolio framework 13 of 19 price-adjustment mechanism, which are given by the equality of the own-rates of money interest replace the market equilibrium conditions for the quantity adjustment as described by the general form of the traditional market equilibrium. The framework can be extended to form a multi-asset model with as many interest rates as assets. For example, in an n-asset context with more than four assets, there are an additional n 4 equations that can be solved either by means of the traditional market equilibrium form or by means of the priceadjustment mechanism described by the equality of the own-rates of money interest. While there is a clearing process for some assets with a price adjustment process that equalises own-rates of money interest on those assets, other markets clear with a quantity adjustment equation. Thus, both quantity adjustment and price adjustment take place. In this respect, we are able to reconcile economic analysis and quantity adjustment with financial analysis within which the arbitrage process is predominant. This reconciliation is in the spirit of the views of Summers (1985) for the integration of financial and economic analysis. Regarding the specific form of the equilibrium conditions, one equation can be omitted. For example, the equality between the supply of bills and the demand for bills can be arbitrarily omitted since, by Walras law, its specification is implicit in the other equations. The demand for money depends then on the opportunity cost of holding money, which can be determined by the own-rate of money interest rate on the more liquid asset other than money such as bills. If at an initial equilibrium position at which the own-rates of money interest of assets are equal there is a change in the specific state of confidence of investors who hold different classes of assets with variable attributes, then price adjustment across assets results again in the equality of own-rates of money interest across assets. With respect to the bonds markets, Kahn argued that when expectations change and portfolio asset balances are altered, the expected long-term interest rate depends on expectations that differ from those that existed originally (Kahn, 1972, p. 74). Kahn s position that different types of beliefs and different types of expectations are responsible for a sequence of marginal equilibria stresses clearly the influence of variations in liquidity preference. The possibility of price adjustment across assets is given through variations in illiquidity discounts due to changes in the state of confidence of investors as well as through variations in the rate of appreciation of assets. The latter are attributed to changes in the sentiment of investors (i.e., as opposed to the normal rate of appreciation, which they form if they hold rational expectations). For the purpose of simplicity in exposition, the analysis takes place solely in terms of the variation in the illiquidity discounts of assets, which is attributed to a change in the specific degree of perceived uncertainty associated with different categories of liquid assets. This factor is important for comparison across classes of liquid assets. Thus, the effect of the illiquidity discount due to the general degree of uncertainty, which is common to all assets, is not taken into account. In addition, it is assumed that there is no change in the estimated rates of appreciation of assets or in the illiquidity discounts that are influenced by uncertainty aversion or by the illiquidity of an asset. As a point of departure, there is a marginal equilibrium, which represents the sum of heterogeneous expectations at a given time. In the case of an uneven change in the illiquidity discount across categories of financial assets with respect to changes in the state of confidence and to the specific degree of uncertainty, price adjustment and quantity adjustment take place simultaneously towards marginal equilibrium. Let us assume that the money market is in equilibrium at a given period and that in the beginning of the next period there is a significant unfavourable evidence associated with an economic event (i.e., a fall in effective demand). Keynes stressed that an increase in the