Nội dung

Chapter 45 THE MOMENTUM TRADING STRATEGY K.C. JOHN WEI, Hong Kong University of Science and Technology, Hong Kong Abstract A strategy that buys past winners and simultaneously sells past losers based on stock performance in the past 3 to 12 months is profitable in the U.S. and the European markets. This survey paper reviews the literature on the momentum strategy and the possible explanations on the momentum profitability. Keywords: past winners; past losers; momentum strategy; individual momentum; industrial momentum; international momentum; underreaction; overreaction; overconfidence; self-attribution; valuation uncertainty; conservatism; representative heuristic; gradual information diffusion 45.1. Introduction ‘‘Trend is your friend’’ is a very popular saying in Wall Street since the inception of stock markets. However, whether this momentum trading strategy that is based on buying past winners and selling past losers is really profitable was controversial until recently. Jegadeesh and Titman (1993) were the first to comprehensively test the profitability of the momentum trading strategy based on the past 3-to 12-month performance. They document that momentum strategies implemented in the U.S. market from 1965 to 1989 generated a positive profit of about one percent per month over 3-to 12-month holding periods. In their recent followup study, Jegadeesh and Titman (2001) find that momentum strategies continued to be profitable after 1990 with past winners outperforming past losers by about the same magnitude as in the earlier period. Rouwenhorst (1998) studied individual stock momentum with a sample of stocks listed on 12 European exchanges during the period from 1978 to 1995. The results demonstrate that momentum profits of about one percent per month are not limited to a particular market, but instead they are present in all 12 markets in the sample. Rouwenhorst (1999) also finds that momentum strategies are profitable although not to the same degree in 20 emerging markets. Chui et al. (2002) examine the profitability of momentum strategies in eight different Asian countries: Hong Kong, Indonesia, Japan, Korea, Malaysia, Singapore, Taiwan, and Thailand. Their evidence indicates that the momentum effect is present in all of the Asian countries except Korea and Indonesia but it is generally weak and is statistically significant only for Hong Kong, Malaysia, Singapore, and Thailand for the pre-crisis period. Interestingly, they find that the Common Law=Civil Law distinction provides an indicator of whether or not a market exhibited a momentum effect prior to the financial crisis. Asness et al. (1996), Chan et al. (2000), and Richards (1997) document that momentum strategies are profitable when implemented on stock market indices. Recently Moskowitz and Grinblatt (1999) find that industry momentum strategies, which advocate buying stocks from past winning industries and selling stocks from past losing industries, THE MOMENTUM TRADING STRATEGY appear to be highly profitable. This industry momentum accounts for much of the profitability of individual stock momentum strategies in the United States. Once returns are adjusted for industry effects, momentum profits from individual equities are significantly weaker, and for the most part are statistically insignificant. However, Grundy and Martin (2001) have a different view on the contribution of industries to individual momentum profits. They argue that a one-month interval between the ranking period and the holding period has a pivotal role in the conclusion that industry momentum strategies are profitable. Industry momentum strategies are significantly profitable only when the ranking period is contiguous to the holding period as documented by Moskowitz and Grinblatt (1999). However, given a onemonth interval between the two periods, industry momentum strategies cannot earn significant profits. Grundy and Martin (2001) conclude that industry effects are not the primary cause of the individual momentum profitability. Liu and Wei (2004) document that industries in 12 European markets, like their counterparts in the U.S. market, also explain the profitability of individual momentum strategies. Specifically, past winner industries outperform past loser industries by more than one percent per month. However, unlike their counterparts in the U.S. market, industries cannot solely explain the profitability of individual momentum strategies in 12 European markets. In addition, industry momentum strategies can still earn significant profits even with a one-month interval between the formation and holding periods. 701 securities in the bottom 10 percent (or 20 percent or 30 percent) are assigned to the loser (denoted as ‘‘L’’) portfolio, while those in the top 10 percent (or 20 percent or 30 percent) are assigned to the winner (denoted as ‘‘W’’) portfolio. These portfolios are value-weighted using the market capitalization of the security at the end of the ranking month as the weight. Each of these portfolios is held for six months. To reduce the effect of nonsynchronous trading and the bid–ask bounce, Jegadeesh and Titman (1993) suggest that we measure returns on these portfolios one month after the ranking takes place. If a security has any missing returns during the holding period, we replace them with the corresponding value-weighted market returns. If the returns on the security are no longer available, we rebalance the portfolio in the month the security is deleted from our database. Excess returns on a security are calculated as the returns on that security minus the risk-free rate, which we assume is equal to the one-month government short-term rate, such as the U.S. Treasury bill rate. To increase the power of our tests, we construct overlapping portfolios. The winner (loser) portfolio is an overlapping portfolio that consists of the ‘‘W’’ (‘‘L’’) portfolios in the previous six months. The returns on the winner (loser) portfolios are the simple average of the returns on the six ‘‘W’’ (‘‘L’’) portfolios. For instance, the January return on the winner portfolio is the simple average of the January returns on the ‘‘W’’ portfolios that are constructed from June to November in the previous year. The momentum portfolio we examine is the zero-cost, winner-minus-loser portfolio. 45.2. The Implementation of Momentum Strategies To show how to implement a momentum strategy, we use a momentum strategy that is based on the past six-month performance with a six-month holding period an illustration. Specifically, to form momentum portfolios, at the end of each month all securities in each of the samples are ranked in ascending order based on the past sixmonth cumulative returns with dividends. The 45.3. Explanations of Momentum Profits Jegadeesh and Titman (2001) discuss three potential explanations for the profitability of momentum strategies and examine the performance of momentum portfolios over longer horizons in order to differentiate between these hypotheses. The three explanations include: (1) stock prices underreact to information, (2) there is a delayed 702 ENCYCLOPEDIA OF FINANCE overreaction to information, and (3) the profits are generated from cross-sectional differences in expected returns. The first two explanations are consistent with some recent behavioral models. For example, the underreaction explanation is consistent with the Barberis, Shleifer, and Vishny (1998) model where a ‘‘conservatism bias’’ can lead investors to underreact or underweight new information. In the case with a pure conservatism bias, once the information is fully incorporated in prices, there is no predictability in stock returns. In this case, the expected post-holding period returns are zero. There are a number of behavioral models that are consistent with a delayed overreaction. Barberis et al. (1998) also discuss this possibility and describe what they call the ‘‘representative heuristic,’’ which suggests that investors may overly extrapolate a firm’s past extraordinary earning growths into the future, and hence overreact to positive (or negative) information that is preceded by positive (or negative) information. In addition, Daniel et al. (1998) argue that delayed overreaction can arise because of ‘‘self-attribution (or cognitive) bias.’’ That is, investors tend to become more overconfident when their stock picks become winners and take more aggressive positions that push up the prices of winners above their fundamental values. Finally, Hong and Stein (1999) propose a model with two groups of investors: informed investors and technical traders, who do not fully take into account the actions of each other. As a result, information is incorporated slowly into stock prices, providing a potential profit opportunity for technical traders. These traders, however, tend to push prices of past winners above their fundamental values. In each of these behavioral models, prices tend to eventually overreact to information and then reverse when prices eventually revert to their fundamentals. All these behavioral models predict the expected post-holding period returns to be negative. The third explanation is consistent with an efficient market where stocks have different expected rates of return because of different risk exposures. In particular, Conrad and Kaul (1998) emphasize that there would be some evidence of momentum even if there were no time-series variation in expected returns since stocks with high-(low) expected returns would be expected to have the highest (lowest) returns in adjacent periods. This explanation suggests that the profits from a momentum strategy should be the same in any postranking period. To test these competing hypotheses, we normally examine the post-holding period returns of momentum portfolios beyond the first year after formation, typically up to five years. The empirical evidence from the U.S. (Jegadeesh and Titman, 2001) and Asian markets (Chui et al., 2002) appears to support the delayed overreaction explanation. That is, the returns on the momentum portfolio eventually reverse to negative 2–5 years after formation. In addition, Fama and French (1996) find that the Fama–French (1993) three factors cannot explain the momentum profits in the United States. 45.4. Momentum Profits and Firm Characteristics Firm characteristics such as book-to-market ratios, market capitalization, and turnover have shown to have the ability to predict the cross section of expected stock returns in the United States. Behavioral models also predict that momentum profits are related to firm characteristics. The overconfidence model by Daniel, Hirshleifer, and Subrahmanyam (1998) suggests that momentum profits arise because investors are overconfidence. Daniel and Titman (1999) argue that overconfidence is likely to influence the perception of investors relatively more, when they analyze fairly vague and subjective information, and use book-tomarket ratios as a proxy for information vagueness. Consistent with their hypothesis, they find that momentum profits are negatively related to the firm’s book-to-market ratio in the U.S. market. Chui et al. (2002) also find similar results for Asian markets. Trading volume or turnover could also proxy for information vagueness. As suggested by asym- THE MOMENTUM TRADING STRATEGY metric information models (see for example, Blume et al., 1994), trading volume reflects investors’ disagreement on a stock’s intrinsic value. The more vague the information used to value the firm, the more disagreement among the investors, and hence, the greater the trading volume. Therefore, the momentum effect should be stronger for firms with high trading volume or turnover. Lee and Swaminathan (2000) find that momentum profits are indeed higher for firms with high turnover ratios in the U.S. market. Chui et al. (2002) also find similar results for Asian markets. In contrast, Hong and Stein (1999) predict that stocks with slow information diffusion should exhibit stronger momentum. Hong et al. (2000) provide tests that support this prediction. In particular, except for the very smallest decile stocks, the profitability of momentum investment strategies declines sharply with firm size. Hong et al. (2000) also look at momentum profits and analyst coverage and find that holding size fixedmomentum strategies work better for stock with low analyst coverage. In addition, they find that the effect of analyst coverage is greater for stocks that are past losers than for stocks that are past winners. They conclude that their findings are consistent with the gradual information diffusion model of Hong and Stein (1999). Acknowledgment The author would like to acknowledge financial support from the Research Grants Council of the Hong Kong Special Administration Region, China (HKUST6233=97H). REFERENCES Asness, C.S., Liew, J.M., and Stevens, R.L. (1996). ‘‘Parallels between the cross-sectional predictability of stock returns and country returns.’’ Working Paper, Goldman Sachs Asset Management. Barberis, N., Shleifer, A., and Vishny, R. (1998). ‘‘A model of investor sentiment.’’ Journal of Financial Economics, 49: 307–343. 703 Blume, L., Easley, D., and O’Hara, M. (1994). ‘‘Market statistics and technical analysis: The role of volume.’’ Journal of Finance, 49: 153–181. Chan, K., Hameed, A., and Tong, W. (2000). ‘‘Profitability of momentum strategies in the international equity markets.’’ Journal of Financial and Quantitative Analysis, 35: 153–172. Chui, A.C.W., Titman, S., and Wei, K.C.J. (2002). ‘‘Momentum, legal system, and ownership structure: an analysis of Asian stock markets.’’ Working Paper, University of Texas at Austin. Conrad, J. and Kaul, G. (1998). ‘‘An anatomy of trading strategies.’’ Review of Financial Studies, 11: 489–519. Daniel, K.D. and Titman, S. (1999). ‘‘Market efficiency in an irrational world.’’ Financial Analysts Journal, 55: 28–40. Daniel, K., Hirshleifer, D., and Subrahmanyam, A. (1998) ‘‘Investor psychology and security market under-and overreactions.’’ Journal of Finance, 53: 1839–1886. Fama, E.F. and French, K.R. (1993). ‘‘Common risk factors in the returns on stocks and bonds.’’ Journal of Financial Economics, 33: 3–56. Fama, E. and French, K. (1996). ‘‘Multifactor explanations of asset pricing anomalies,’’ Journal of Finance, 51: 55–84. Grundy, B.D., and Martin J.S. (2001). ‘‘Understanding the nature of the risks and the source of the rewards to mementum investing,’’ Review of Financial Studies, 14: 29–78. Hong, H. and Stein, J.C. (1999). ‘‘A unified theory of underreaction, momentum trading and overreaction in asset markets.’’ Journal of Finance, 54: 2143– 2184. Hong, H., Lim, T. and Stein, J.C. (2000). ‘‘Bad news travels slowly: size, analyst coverage, and the profitability of momentum strategies.’’ Journal of Finance, 55: 265–295. Jegadeesh, N. and Titman, S. (1993). ‘‘Returns to buying winners and selling losers: Implications for stock market efficiency.’’ Journal of Finance, 48: 65–91. Jegadeesh, N. and Titman, S. (2001). ‘‘Profitability of momentum strategies: an evaluation of alternative explanations.’’ Journal of Finance, 56: 699–720. Lee, C.M.C. and Swaminathan, B. (2000). ‘‘Price momentum and trading volume.’’ Journal of Finance, 55: 2017–2069. Liu, S. and Wei, K.C.J. (2004). ‘‘Do industries explain the profitability of momentum strategies in European markets?’’ Working Paper, Hong Kong University of Science and Technology. 704 ENCYCLOPEDIA OF FINANCE Lu, C. and Shen, Y. (2005). ‘‘Do REITs pay enough dividends?’’ Unpublished working paper, Department of Finance, Yuan Ze University. Moskowitz, T.J. and Grinblatt, M. (1999). ‘‘Do industries explain momentum?’’ Journal of Finance, 54: 1249–1290. Richards, A.J. (1997). ‘‘Winner-loser reversals in national stock market indices: Can they be explained?’’ Journal of Finance, 52: 2129–2144. Rouwenhorst, K.G. (1998). ‘‘International momentum strategies.’’ Journal of Finance, 53: 267–284. Rouwenhorst, K.G. (1999). ‘‘Local return factors and turnover in emerging stock markets,’’ Journal of Finance, 55: 1439–1464. Chapter 46 EQUILIBRIUM CREDIT RATIONING AND MONETARY NONNEUTRALITY IN A SMALL OPEN ECONOMY YING WU, Salisbury University, USA Abstract 46.1. Introduction This paper modifies the well-known Mundell–Fleming model by adding equilibrium credit rationing as well as imperfect asset substitutability between bonds and loans. When the representative bank’s backward-bending loan supply curve peaks at its profit-maximizing loan rate, credit rationing can be an equilibrium phenomenon, which makes creditdependent capital investment solely dependent upon the availability of customer market credit. With credit rationing, an expansion in money and credit shifts the IS curve as well as the LM curve even in a small open economy under a regime of fixed exchange rates, and the magnitude of offset coefficient between domestic and foreign asset components of high-powered money is less than one. In contrast, if there is no credit rationing, imperfect asset substitutability between bonds and loans per se cannot generate the real effect of money in the same model. Is money non-neutral in a small open economy with international capital mobility and a fixed exchange rate regime? Can monetary policy affect real output in these circumstances? The answer to these questions is widely construed to be negative because the money supply has lost its role of a nominal anchor in this case.1 In the orthodox money view, it is the interest rate that serves as the channel through which monetary policy affects the real sector of an economy; however, because the interest rate channel of monetary policy is highly correlated with exchange rates, and because the monetary authority commits to the maintenance of the fixed exchange rate, the consequent foreign exchange intervention by the monetary authority using official reserves necessarily washes out any real effect of the monetary policy that it has previously initiated. The same approach is used in most of the existing literature on small open economies, such as the traditional IS=LM analysis, which holds a lopsided view of bank liabilities and bank loans. Other than influencing interest rates via manipulating deposits (a money asset and bank liability), banks have no active leverage to play with; the role of bank loans escapes unnoticed since bank loans are grouped together with other nonmonetary assets such as bonds. JEL classification: E51 F41 Keywords: credit rationing; monetary policy; capital flow; Mundell–Fleming model; monetary neutrality; open market operation; IS-LM curves; offset coefficient; monetary base; small open economy 706 ENCYCLOPEDIA OF FINANCE In contrast to the money view, the credit view of monetary transmission mechanism rejects the notion that all nonmonetary assets are perfect substitutes. According to the credit view, due to information asymmetries between borrowers and lenders in financial markets, banks can play a particular role in reducing information costs. It is financial intermediation that can help a firm with risk-sharing, liquidity, and information services; as a result, a large number of firms have in fact become bank dependent. Furthermore, although a rise in the loan rate increases, ceteris paribus, the bank’s expected return by increasing interest payment when the borrower does not default, it lowers the bank’s expected return by exacerbating adverse selection and moral hazard problems, and thus raising the probability of default. Hence, the bank’s loan supply curve can be backwardbending, and credit rationing may occur as an equilibrium phenomenon.2 Credit rationing per se makes monetary credit availability rather than interest rates in order to be the conduit for the real effect of money, therefore providing a major theoretical underpinning for the effectiveness of monetary policy under fixed exchange rates. This paper begins with a study of the loan market setting with asymmetric information as a microfoundation for consumption and investment, and further develops a macromodel of a small open economy under a fixed exchange rate regime with perfect capital mobility in the bond market and imperfect asset substitutability between bonds and loans. As far as the credit view is concerned, this paper in spirit is close to Bernanke and Blinder (1988), who address the credit channel of monetary policy in a variant of the IS=LM model. They differ in several regards, however. Unlike Bernanke and Blinder, the model in this paper incorporates the possibility of equilibrium credit rationing while maintaining the assumption of imperfect substitutability of bank loans and bonds. With imperfect substitutability between bonds and bank loans, this paper nests both credit-rationed and creditunrationed equilibrium regimes. Additionally, by placing the credit channel of monetary policy in the setting of a small open economy, this chapter allows the possibility to explore the relevance of the ‘‘monetary policy ineffectiveness’’ proposition in the existing mainstream small-open-economy literature. Partly based on Wu (1999) by drawing on its microeconomic foundation setting, this study has made important and substantial revisions to its macroeconomic analysis. With the credit availability channel, this study shows that money in the fixed exchange rate model is not completely endogenous by appealing to the asymmetry between customer market credit and auction market credit under equilibrium credit rationing.3 Incorporating bank credit into the fixed exchange rate model leads to two fundamental changes. First, it extends the scope for monetary policy to affect economy from the standard interest rate channel to the one including the bank lending channel and balance sheet channel as well; the latter two conduits can be independent of changes in interest rates. Second, and more importantly, monetary policy will no longer be deemed impotent since it can directly ‘‘shift’’ the goods market as well as money market equilibrium schedules in such a way that the targeted real effect could be achieved while the fixed exchange rate is sustained. The next section presents the analytical structure of bank behavior and credit market; the following two sections explore how credit market conditions determine macroeconomic equilibrium in an open-economy IS=LM framework, and demonstrate the real impacts of monetary shocks through its credit channel, respectively. The final section concludes the study. 46.2. Bank Behavior and Credit Market It is well known that due to the credit risk associated with adverse selection and moral hazard problems a banking firm has an inverse U-shaped loan supply curve with a backward-bending portion. This section essentially modifies the pedagogical model in Christopher and Lewarne (1994) by extending the spectrum of bank investment into the portfolio selection between bonds and loans. EQUILIBRIUM CREDIT RATIONING AND MONETARY NONNEUTRALITY IN A SMALL OPEN ECONOMY The representative banking firm is assumed to hold exactly the required amount of reserves, and allocate all of its excess reserves between the two bank assets: bonds and loans. Thus, it chooses loans, l, subject to its balance sheet identity, to maximize its profits from lending g P ¼ u(r)lr þ bb r
dr
l 2 2 s:t: bb þ l ¼ (1
k)d, (46:1) where r is the loan rate, u(r) the probability of loan repayment, g the cost parameter of servicing loans, bb denotes bonds held by the banking firm, r is the interest rate on bond, d represents total deposits, and k is the required reserve ratio for deposits. Here, the low-risk or risk-free interest rate on bond holding is assumed to be the same as the interest cost of taking in deposits. Thus, deposits and bonds are perfectly substitutable assets to depositors so that they pay the same expected return per dollar. The key characteristic of the bank profit is that the repayment probability depends on the loan rate. Following the existing literature on equilibrium credit rationing, an increase in the loan rate makes it more likely for borrowers to default, hence the repayment probability is a decreasing function of the loan rate.4 In addition, the representative bank takes the flow of deposits as given when making its portfolio decisions. Substituting the balance sheet identity into the bank’s objective function and maximizing it with respect to l yields the banking firm’s loan supply curve lS ¼ u(r)r
r : g (46:2) Several implications of the loan supply curve can be derived. First, the loan supply curve is backward bending. The co-movement of the loan rate and loan volume hinges on the elasticity of the odds of repayment with respect to the loan rate. Only when the repayment probability is inelastic can a positive relationship exist between the loan rate and loan volume. To be specific, consider 707 a linear repayment probability u(r) ¼ f
cr, where f is the autonomous repayment probability determined by noninterest factors such as the liquidity of balance sheet positions, and c measures the sensitivity of the repayment probability to the loan rate (0 < c < f  1). Figure 46.1 depicts the loan repayment probability function. In the case of linear loan repayment probability function, the loan volume supplied increases with the loan rate until the loan rate achieves f=2c, after which a higher loan rate actually reduces the loan volume. In Figure 46.1, the loan rate at which the loan supply curve begins to bend backward points to the repayment probability halfway to its maximum within the possible range. Substituting u(r) ¼ f
cr into (46.2) and differentiating (46.2) with respect to r,f, c, and g produces the responses of loan supply to the parameters of servicing loans. In particular, an increase in the bond interest rate, r, ceteris paribus, makes bond holding more attractive; accordingly, banks will reduce loans and hold more bonds. Another interpretation for the decrease of bank loans is based on the equivalence between the bond interest rate and the deposit rate: the higher the interest expenses of raising loanable funds by issuing deposits, the higher the economic cost of making loans. Next, banks tend to issue more loans when the autonomous repayment probability, f, is higher, for example due to borrowers’ increased net worth,. In addition, the larger the sensitivity of the repayment probability to the loan interest rate, c, the more deteriorating the problems of adverse selection and moral hazard, thus it is more likely for credit rationing to occur. Finally, an increase in the cost of servicing loans, g, also tends to reduce loans as long as the expected return per dollar of loans exceeds the corresponding real opportunity cost. Applying the envelope theorem to the representative bank’s profit function in Equation (46.1) while incorporating Equation (46.2) and u(r) ¼ f
cr generates the following marginal bank profit with respect to the loan rate: 708 ENCYCLOPEDIA OF FINANCE q(r) f f 2 f 2Ψ Figure 46.1. f Ψ r Loan repayment probability dP(r) 1 ¼ [2c2 r3
3cfr2 dr g (46:3) 2 þ (2cr þ f )r
fr]: The bracket term on the RHS of Equation (46.3) is a cubic expression but two of the three roots are degenerated solutions at which loans are zero, respectively; thus the only feasible root for Equation (46.3) is r ¼ f=2c, at which the bank’s expected profits are maximized. Recall that the bank’s loan supply curve peaks exactly at the same loan rate as the profit-maximizing loan rate here. Therefore, the result suggests the existence of equilibrium credit rationing. Further, the result for profitmaximizing loans also imply that the loan interest rate p exceeds the bond interest rate such that ffiffiffiffiffiffiffiffi r > r=c > r, which captures the existence of risk premium of bank lending, and therefore signifies the imperfect substitutability between loans and bonds. Moving from the representative bank to the aggregate banking system, the aggregated bank balance sheet identity shows Bb þ L þ R ¼ D, where Bb represents the bonds held by banks, D denotes deposits, and L is the volume of loans. For simplicity, currency is abstracted from the model. The required reserve of the banking system, R, constitutes the monetary authority’s liabilities, or high-powered money, H, which are generated by its acquisition of bonds (Ba ) and foreign exchange (F ). The high-powered money in this framework is composed of exclusively required reserves; the money supply can be expressed by H=k. Suppose there are n banks, with the representative bank’s supply of loans specified in Equation. (46.2) aggregating, and which generates the total supply of loans. A structural view of the aggregated balance sheet of banks suggests that if banks allocate a fraction of their excess reserves into loans and the rest into bonds, the aggregate supply of loans is given by «(1
k)  (H=k), where « represents the ratio of loans to excess reserves. Accordingly, the share of loans in excess reserves must characterize the banks’ loan-making behavior and it is thus actually a function of the same set of variables that determine aggregate supply of loans.   1
k S L ¼ «(r, r, f, c, g, n) H, k (46:4) ?
þ

þ where the symbols underneath each of the arguments in «(.) denote the signs of the partial derivatives associated with them. For simplicity, it is assumed that bank credit is the only debt instrument for firms to finance their investment; investment demand and the demand for bank loans are taken to be equal.5 Thus, aggregate demand for EQUILIBRIUM CREDIT RATIONING AND MONETARY NONNEUTRALITY IN A SMALL OPEN ECONOMY loans is negatively related to the loan interest rate, and its standard linear form is LD ¼ a
br: (46:5) Indeed, as demonstrated by the existing literature on markets in disequilibrium, the loan market may or may not be at the market-clearing equilibrium.6 Nevertheless, unlike disequilibrium economics, the loan quantity traded in the market is not uniformly characterized by the minimum of demand and supply sides. Loan rationing can arise in an unrestricted market setting flawed only by plausible information asymmetries; the loan rate can always freely adjust to a level consistent with market forces driven by the profit-maximization incentives. Therefore, credit rationing could exist at the profit-maximizing loan rate, r ¼ f=2c, and sustain as an equilibrium phenomenon. The excess demand fails to drive the loan rate upward because the associated credit risk would reduce banks’ profits; however, if at the same loan rate there is an excess supply, the loan interest rate will adjust downward to clear the loan market, since holding excess reserves does not add to profits at all. Consider the demand for and supply of loans specified in Equations (46.4) and (46.5), respectively, then the equilibrium interest rate in the loan market is given by 8 f f > > ; < , if LD  LS at 2c 2c r¼ f > > , : min (r1 , r2 jLD ¼ LS ), if LD < LS at 2c (46:6) where r1 and r2 are the two roots of the quadratic equation given by LD ¼ LS . Recall that r ¼ f=2c is the loan rate that corresponds to the maximum quantity of loans. If an excess supply exists at r , LD must cross LS once at a loan rate below r and once at a loan rate above r . Since r is the profit-maximizing loan rate, the bank has no incentive to raise the loan rate to any level above r , and credit is then rationed at the equilibrium. On the other hand, the profit-maximizing loan rate is not attainable if there is excess supply at r , since 709 the bank cannot force the firms to borrow in excess of the amount that maximizes their profits. It follows that if a bank cannot maximize its profit at r due to deficient demand, the best attainable outcome for the bank is to allow a downward adjustment in the loan rate until the loan market clears. Therefore, the loan quantity traded is at the market-clearing equilibrium level if the market interest rate of loans is below the banks’ desired level, r ; otherwise, it would be determined by supply at the profit-maximizing loan rate. 46.3. Macroeconomic Equilibrium Assume that investment is solely dependent on the availability of bank credit, and investment demand is equivalent to the demand for loans. Based on the analytical results in the preceding section, there is an implicit positive relationship between the interest rates on loans and bonds, which can be explicitly expressed as r ¼ l(r). If credit demand is not rationed in the loan market, we have I(r)  LD [l(r)], with I 0 ¼ L0D l0 < 0, however, with credit rationing, investment demand is totally determined by the aggregate supply of loans. 46.3.1. Case for Credit Rationing With credit rationing, the quantity of loans effectively traded is given by LS as specified in Equation (46.4). In this case, the monetary authority can help loosen credit rationing through open market purchases: the nonbank public, which sells bonds to the monetary authority deposits the proceeds into banks, and the loan supply increases with the deposits. The rationing situation improves and the resulting increase in output increases money demand, and thus imposes upward pressure on the interest rate and the exchange value of the domestic currency. This in turn relieves the money market of the adjustment burden resulting from the monetary authority’s commitment to the fixed exchange rate under the circumstances of open market purchases. Therefore, following the monetary authority’s open market purchases,