REVIEW OF ECONOMIC STUDIES be shifted by open market operations themselves, since they will change the volume of outstanding bonds or consols. For example, to establish the rate at or below min res the central bank would have to buy all outstanding bonds or consols. The size of the community s investment balances would then be independent of the rate of interest it would be represented by a vertical line through, or to the right of, B, rather than the curve ABC. Thus the new relation between cash and interest would be a curve lying above LMB, of the same general contour as LMN2w 2.6 Keynesian theory and its critics. I believe the theory of liquidity preference I have just presented is essentially the original Keynesian explanation. The general Theory suggests a number of possible theoretical explanations, supported and enriched by the experience and insight of the author. But the explanation to which Keynes gave the greatest cmphasis is the notion of a"normal "long-term rate, to which investors expect the rate of interest. to return. When he refers to uncertainty in the market, he appears to mean disagreement among investors concerning the future of the rate rather than subjective doubt in the mind of an individual investor. Thus Kaldors correction of Keynes is more verbal than substantive when he says, "It is . not so much the uncertaint concerning future interest rates as the inelasticity of interest expectations which is responsible for Mr. Keynes''liquidity preference function, Keynes'use of this explanation of liquidity preference as a part of his theory of under employment equilibrium was the target of important criticism by Leontief and Fellner Leontief argued that liquidity preference must necessarily be zero in equilibrium, regardless of the rate of interest. Divergence between the current and expected interest rate is bound to vanish as investors learn from experience; no matter how low an interest rate may be it can be accepted as"normal" if it persists long enough. This criticism was a part of Leontief,'s general methodological criticism of Keynes, that unemployment was not a feature of equilibrium, subject to analysis by tools of static theory, but a phenomenon of disequilibrium requiring analysis by dynamic theory. 3 Fellner makes a similar criticism of the logical appropriateness of Keynes explanation of liquidity preference for the purposes of his theory of underemployment equilibrium. Why, he asks, are interest rates the only variables to which inelastic expectations attach? Why don,'t wealth owners and others egard pre-depression price levels as" normal"levels to which prices will return If they did consumption and investment demand would respond to reductions in money wages and prices, no matter how strong and how elastic the liquidity preference of These criticisms raise the question whether it is possible to dispense with the assumption of stickiness in interest rate expectations without losing the implication that Keynesian The General Theory of Emp d Money(New York: Harcourt pp.168-172and201-20 of Economic Studies, vol. 7( editor The Ne W. Fellner, Monetary Policies and Full Employment(Berkeley: University of California Press, 1946)
70 REVIEW OF ECONOMIC STUDIES be shifted by open market operations themselves, since they will change the volume of outstanding bonds or consols. For example, to establish the rate at or below min rc, the central bank would have to buy all outstanding bonds or consols. The size of the community's investment balances would then be independent of the rate of interest ; it would be represented by a vertical line through, or to the right of, B, rather than the curve ABC. Thus the new relation between cash and interest would be a curve lying above LMB, of the same general contour as LMNE W. 2.6 Keynesian theory and its critics. I believe the theory of liquidity preference I have just presented is essentially the original Keynesian explanation. The General Theory suggests a number of possible theoretical explanations, supported and enriched by the experience and insight of the author. But the explanation to which Keynes gave the greatest emphasis is the notion of a " normal" long-term rate, to which investors expect the rate of interest, to return. When he refers to uncertainty in the. market, he appears to mean disagreement among investors concerning the future of the rate rather than subjective doubt in the mind of an individual investor.' Thus Kaldor's correction of Keynes is more verbal than substantive when he says, " It is . .. not so much the uncertainty concerning future interest rates as the inelasticity of interest expectations which is responsible for Mr. Keynes' ' liquidity preference function,' 912 Keynes' use of this explanation of liquidity preference as a part of his theory of underemployment equilibrium was the target of important criticism by Leontief and Fellner. Leontief argued that liquidity preference must necessarily be zero in equilibrium, regardless of the rate of interest. Divergence between the current and expected interest rate is bound to vanish as investors learn from experience ; no matter how low an interest rate may be, it can be accepted as " normal" if it persists long enough. This criticism was a part of Leontief's general methodological criticism of Keynes, that unemployment was not a feature of equilibrium, subject to analysis by tools of static theory, but a phenomenon of disequilibrium requiring analysis by dynamic theory.3 Fellner makes a similar criticism of the logical appropriateness of Keynes' explanation of liquidity preference for the purposes of his theory of underemployment equilibrium. Why, he asks, are interest rates the only variables to which inelastic expectations attach ? Why don't wealth owners and others regard pre-depression price l.evels as "normal" levels to which prices will return ? If they did, consumption and investment demand would respond to reductions in money wages and prices, no matter how strong and how- elastic the liquidity preference of investorS_4 These criticisms raise the question whether it is possible to dispense with the assumption of stickiness in interest rate expectations without losing the implication that Keynesian 1*J. M. Keynes, The General -Theory of Employment, Interest, and Money (New York: Harcourt Brace, 1936), Chapters 13 and 15, especially pp. 168-172 and 201-203. One quotation from p. 172 will illustrate the point : " It is interesting that the stability-of the system and its sensitiveness to changes in the quantity of money should be so dependent on the existence of a variety of opinion about what is uncertain. Best of all that we should know the future. But if not, then, if we are to control the activity of the economic system by changing the quantity of money, it is important that opinions should differ." 2 N. Kaldor, "Speculation and Economic Stability," Review of Economic Studies, vol. 7 (1939), p. 15. 3 W. Leontief, " Postulates: Keynes' General Theory and the Classicists ", Chapter XIX in S. Harris, editor, The New Economics (New York-: Knopf, 1947), pp. 232-242. Section 6, pp. 238-239, contains the specific criticism of Keynes' liquidity preference theory. 4 W. Fellner, Monetdry Policies and Full Employment (Berkeley: University of California Press, 1946), p. 149
LIQUIDITY PREFERENCE AS BEHAVIOR TOWARDS RISK theory drew from it. Can the inverse relationship of demand for cash to the rate of interest be based on a different set of assumptions about the behaviour of individual investors This question is the subject of the next part of the paper 3. Uncertainty, risk aversion, and liquidity preference 1 The locus of opportunity for risk and expected return. Suppose that an investor is not certain of the future rate of interest on consols: investment in consols then involves risk of capital gain or loss. The higher the proportion of his investment balance that he holds in consols, the more risk the investor assumes. At the same time, increasing the proportion in consols also increases his expected return. In the upper half of Figure 3.1 the vertical axis represents expected return and the horizontal axis risk. a line such as OCi pictures the fact that the investor can expect more return if he assumes more risk. In the lower half of Figure 3. 1, the left-hand vertical axis measures the proportion invested in consols. A line like OB shows risk as proportional to the share of the total balance held in consols The concepts of expected return and risk must be given more precisio The individual investor of the previous section was assumed to have, for any current rate of interest, a definite expectation of the capital gain or loss g( defined in expression (2. 1 )above) he would obtain by investing one dollar in consols. Now he will be assumed instead to be uncertain about g but to base his actions on his estimate of its probability distribution. This probability distribution, it will be assumed, has an expected value of zero and is independent of the level of r, the current rate on consols. Thus the investor considers a doubling of the rate just as likely when rate is 5% as when it is 2%, and a te just as likely when it is 1% as when a portfolio consists of a proportion A, of cash and Ag of consols, where A, and A2 initial investment balance in dollars. Negative values of A, and Ag are excluded by definition; only the government and the banking system can issue cash and government consols. The return on a portfolio R is (3.1) R=A2(+g) Since g is a random variable with expected value zero, the expected return on the portfolio E(R)
LIQUIDITY PREFERENCE AS BEHAVIOR TOWARDS RISK 71 theory drew from it. Can the inverse relationship of demand for cash to the rate of interest be based on a different set of assumptions about the behaviour of individual investors ? This question is the subject of the next part of the paper. 3. Uncertainty, risk aversion, and liquidity preference. 3.1 The locus of opportuinity for risk and expected return. Suppose that an investor is not certain of the future rate of interest on consols ; investment in consols then involves a risk of capital gain or loss. The higher the proportion of his investment balance that he holds in consols, the more risk the investor assumes. At the same time, increasing the proportion in consols also increases his expected return. In the upper half of Figure 3.1, the vertical axis represents expected return and the horizontal axis risk. A line such as OC1 pictures the fact that the investor can expect more return if he assumes more risk. In the lower half of Figure 3.1, the left-hand vertical axis measures the proportion invested in consols. A line like OB shows risk as proportional to the share of the total balance held in consols. The concepts of expected return and risk must be given more precisioThe individual investor of the previous section was assumed to have, for any current rate of interest, a definite expectation of the capital gain or loss g (defined in expression (2.1) above) he would obtain by investing one dollar in consols. Now he will be assumed instead to be uncertain about g but to base his actions on his estimate of its probability distribution. This probability distribution, it will be assumed, has an expected value of zero and is independent of the level of r, the current rate on consols. Thus the investor considers a doubling of the rate just as likely when rate is 5 % as when it is 2%, and a halving of the rate just as likely when it is 1 % as when it is 6%. A portfolio consists of a proportion A1 of cash and A2 of consols, where A1 and A2 add up to 1. We shall assume that A1 and A2 do not depend on the absolute size of the initial investment balance in dollars. Negative values of A1 and A2 are excluded by definition; only the government and the banking system can issue cash and government consols. The return on a portfolio R is: (3.1) R 4=A2(r+g) 0 < A2 < 1 Since g is a random variable with expected value zero, the expected return on the portfolio is: (3.2) E(R) = =R A2 r
REVIEW OF ECONOMIC STUDIES The risk attached to a portfolio is to be measured by the standard deviation of R The standard deviation is a measure of the dispersion of possible returns around the mean value uR. A high standard deviation means, speaking roughly, high probability of large deviations from uR, both positive and negative. A low standard deviation means low probability of large deviations from uR; in the extreme case a zero standard deviation would indicate certainty of receiving the return Hr. Thus a high-or portfolio offers the investor the chance of large capital gains at the price of equivalent chances of large capital losses. A low-oR portfolio protects the investor from capital loss, and likewise gives him little prospect of unusual gains. Although it is intuitively clear that the risk of a portfolio is to be identified with the dispersion of possible returns, the standard deviation is neither the sole measure of dispersion nor the obviously most relevant measure. The case for the standard deviation will be further discussed in section 3. 3 below The standard deviation of R depends on the standard deviation of g, g, and on the amount invested in consols (3.3) Thus the proportion the investor holds in consols Ag determines both his expected return FR and his risk oR. The terms on which the investor can obtain greater expected return at the expense of assuming more risk can be derived from(3. 2) and(3. 3) (34) 0≤aR≤ Such an opportunity locus is shown as line OC(for r= ri) in Figure 3. 1. The slope of the line is. For a higher interest rate ra, the opportunity locus would be oc 2, and for ra, a still higher rate, it would be OCa. The relationship(3. 3 )between risk and invest- ment in consols is shown as line OB in the lower half of the Figure. Cash holding A 1-Aa) can also be read off the diagram on the right-hand vertical axis. .2 Loci of indifference between combinations of risk and expected return. The investor is assumed to have preferences between expected return uR and lisk or that can be repre- sented by a field of indifference curves. The investor is indifferent between all pairs (uR, or) that lie on a curve such as I, in Figure 3. 1. Points on I2 are preferred to those or 11: for given risk, an investor always prefers a greater to a smaller expectation of return Conceivably, for some investors, risk-lovers, these indifference curves have negative slopes Such individuals are willing to accept lower expected return in order to have the chance of unusually high capital gains afforded by high values of oR. Risk-averters, on the other
REVIEW OF ECONOMIC STUDIES The risk attached to a portfolio is to be measured by the standard deviation-of R, aR. The standard deviation is a measure of the dispersion of possible returns around the mean value VLR. A high standard deviation means, speaking roughly, high probability of large deviations from (lR, both positive and negative. A low standard deviation means low probability of large deviations from VtR; in the extreme case, a zero standard deviation would indicate certainty of receiving the return gR. Thus a high-aR portfolio offers the investor the chance of large capital gains at the price of equivalent chances of large capital losses. A low-gR portfolio protects the investor from capital loss, and likewise gives him little prospect of unusual gains. Although it is intuitively clear that the risk of a portfolio is to be identified with the dispersion of possible returns, the standard deviation is neither the sole measure of dispersion nor the obviously most relevant measure. The case for the standard deviation will be further discussed in section 3.3 below. The standard deviation of R depends on the standard deviation of g, ag, and on the amount invested in consols: (3.3) aR = A2 0 < As2 < 1. Thus the proportion the investor holds in consols A2 determines both his expected return ILR and his risk aR. The terms on which the investor can obtain greater expected return at the expense of assuming more risk can be derived from (3.2) and (3.3): r (3.4) zR -= a R 0 < OR < a, Such an opportunity locus is shown as line OC1 (for r = rl) in Figure 3.1. The slope of the line is -s-. For a highei interest rate r2, the opportunity locus would be OC 2; and as for r3, a still higher rate, it would be OC3. The relationship (3.3) between risk and investment in consols is shown as line OB in the lower half of the Figure. Cash holding A1(= 1 - A2) can also be read off the diagram on the right-hand vertical axis. 3.2 Loci of indifference between combinations of risk and expected return. The investor is assumed to have preferences between expected return V[R and iisk aR that can be represented by a field of indifference curves. The investor is indifferent between all pairs ([LR, cR) that lie on a curve such as I1 in Figure 3.1. Points on I2 are preferred to those on I ; for given risk, an irnvestor always prefers a greater to a smaller expectation of return. Conceivably, for some investors, risk-lovers, these indifference curves have negative slopes. Such individuals are willing to accept lower expected return in order to have the chance of unusually high capital gains afforded by high values of aR. Risk-averters, on the other 72