Forthcoming in The Journal of Banking and Finance

Transcription

1 Forthcoming in The Journal of Banking an Finance June, 000 Strategic Choices of Quality, Differentiation an Pricing in Financial Services *, ** Saneep Mahajan The Worl Bank (O) Fax an Richar J. Sweeney The McDonough School of Business Georgetown University (O) Fax , ABSTRACT: Two financial services firms (FSFs) prouce information on future returns from risky assets, incorporate this information in a report an sell the reports to investors. The FSFs make strategic choices of the quality, ifferentiation an prices of their reports. Their optimal strategic choices of quality an ifferentiation ivie the market for the report into three segments. Each FSF has a monopoly in its own segment, an the two compete hea-to-hea in a uopoly segment. The sizes of the monopoly segments increase with increases in quality an ifferentiation. An increase in ifferentiation reuces the size of the uopoly market, while an increase in quality has an ambiguous effect on the uopoly market: for high enough equilibrium ifferentiation, the size of the uopoly market ecreases with an increase in quality. The non-cooperative FSFs pursue niche strategies, each focusing on a ifferent relate set of risks, in orer to coorinate the contents of their reports to achieve the equilibrium egree of prouct ifferentiation. Recent years have seen a worlwie wave of financial-firm mergers an acquisitions. This paper s moel suggests that in equilibrium FSFs ifferentiate their proucts an evelop profitable niches; in principle, however, sufficiently strong economies of scope coul lea a small number of FSFs with little ifferentiation that ominate all financial services markets. JEL classifications: G0, D83, D43 Keywors: Financial Services Firms; Quality an Differentiation; Strategic Decisions; Niche Strategies: Segmente Markets *For helpful comments, thanks are ue to an anonymous referee. This paper buils on parts of Mahajan s issertation, Liberalization an Recent Developments in Financial Services Sectors in Emerging Market Economies, Georgetown University, 996. For comments on earlier versions, thanks are ue to Gwen Euey an Matt Canzoneri. The McDonough Business School provie summer support for Sweeney. Georgetown University s Capital Markets Research Center provie summer research assistance. Part of the work on this paper was one at the Gothenburg School of Economics, Sween. ** The results an interpretations of this paper are authors alone, an shoul not be attribute to the Worl Bank, its Boar of Governors, its management, or any of its members.

2 Strategic Choices of Quality, Differentiation an Pricing in Financial Services ABSTRACT: Two financial services firms (FSFs) prouce information on future returns from risky assets, incorporate this information in a report an sell the reports to investors. The FSFs make strategic choices of the quality, ifferentiation an prices of their reports. Their optimal strategic choices of quality an ifferentiation ivie the market for the report into three segments. Each FSF has a monopoly in its own segment, an the two compete hea-to-hea in a uopoly segment. The sizes of the monopoly segments increase with increases in quality an ifferentiation. An increase in ifferentiation reuces the size of the uopoly market, while an increase in quality has an ambiguous effect on the uopoly market: for high enough equilibrium ifferentiation, the size of the uopoly market ecreases with an increase in quality. The non-cooperative FSFs pursue niche strategies, each focusing on a ifferent relate set of risks, in orer to coorinate the contents of their reports to achieve the equilibrium egree of prouct ifferentiation. Recent years have seen a worlwie wave of financial-firm mergers an acquisitions. This paper s moel suggests that in equilibrium FSFs ifferentiate their proucts an evelop profitable niches; in principle, however, sufficiently strong economies of scope coul lea a small number of FSFs with little ifferentiation that ominate all financial services markets.

3 Strategic Choices of Quality, Differentiation an Pricing in Financial Services. Introuction In firms strategic interactions, key choices are prouct quality an prouct ifferentiation. Quality an ifferentiation choices affect competition in the inustry, an thus each firm s pricing-output strategy. Stanar moels of strategic competition frequently analyze firms' pricing-output ecisions, but not their choices of quality an ifferentiation. Unerstaning the financial services inustry requires analysis of strategic interactions over quality an ifferentiation. Past literature oes not consier strategic choices of prouct quality an ifferentiation by financial services firms (FSFs). This paper helps fill this gap with a uopoly moel that enogenizes FSFs choices of quality, ifferentiation an pricing-output strategies. The paper focuses on FSFs that prouce an sell information to investors on future returns from risky assets. Past literature on firms that sell financial information assumes these firms are enowe with a certain quantity of information. In this paper s uopoly moel, both firms face increasing costs in proucing financial information an ifferentiating their proucts. The paper assumes that risky assets in the economy are subject to a large number of risks. The FSFs inform customers in avance on the values of the realizations of a relatively small number of these risks. Each firm packages its information in a report that it sells, possibly with some price iscrimination, to investors who cannot resell the report. The effect of the reports information on market prices is assume small relative to the noise in the market; thus, the informativeness of prices can be ignore in formulating investor emans for the reports. For given prices of the reports, the investors maximize expecte utility: the quantities of the reports they eman epen on the reports quality an ifferentiation. The results are striking. The FSFs enogenously ecie to prouce ifferentiate proucts. Each FSF has a monopoly niche market where it oes not compete irectly with the other. In its niche, it sells information to investors who buy information from both firms. The firms may compete hea-on in a thir market segment where investors buy information services from one firm but not both. The monopoly markets are high-profit; the uopoly market is low-profit. The market segments exist because of heterogeneity of investors attitues towar risk. At the given price of a particular FSF s the report, the report s benefits have a greater ollar value the more funs the investor expects

4 to have at risk. Investors fall into three categories base on their risk aversion. Those with high enough risk aversion expect to invest a small ollar amount in risky assets an o not buy a report from either FSF: the ollar price of the report is too high relative to the ollar value of the benefits that the report is expecte to provie. At the other extreme, investors with low risk aversion expect to put a large ollar amount at risk: because the two FSFs reports are ifferentiate, with information on somewhat ifferent risks, these investors buy both reports. Other investors with intermeiate risk aversion may buy a report from one but not both FSFs: these investors expect to have a large enough ollar amount at risk to justify buying one report, but view the secon report s extra information as not cost-effective. FSF ι s report contains q ι iscrete pieces of information. Ex ante, each piece of information in a given report has the same value as any other in terms of revealing information about coming rates of return an risk. Further, the same information from one FSF is as goo as from the other. The quality of the report from FSF ι is then naturally measure by q ι. Because investors will pay a higher price for a report with greater quality, an each firm prouces more information at increasing cost, FSF ι enogenously chooses the quality of its report. In equilibrium, the firms always choose to ifferentiate their proucts: this prouct ifferentiation is necessary to give each FSF its high-profit monopoly niche. Differentiation arises enogenously even if firms face the same eman an cost conitions an have no competitive avantage in proucing an marketing particular types of information: uner ientical eman an cost conitions, firms woul ientify the same number of risks in their reports, but the set of risks each firm ientifies woul have an incomplete overlap. In orer to coorinate the amount of overlap in their reports an thus achieve optimal ifferentiation, each non-cooperative firm announces an explicit niche, a relate set of risks on which it focuses. These niches are signals to investors that promise ifferentiation will be achieve, an are signals to the other FSF on which set of risks to avoi. Each FSF respects the other s niche, so that both can achieve the ifferentiation they promise buyers. Any competitive avantage the firms have in proucing ifferent pieces of information reinforces the ecision to ifferentiate by reucing ifferentiation s marginal cost. Competitive avantages also guie the irections in which the firms ifferentiate, thus reinforcing each firm s eclare niche an allowing the FSFs to coorinate to achieve optimal ifferentiation. Section ties this paper both to the literature on sales of information by FSFs, an also to the general literature on prouct ifferentiation. Section 3 escribes the economy where investors an FSFs interact. Sections 4

5 an 5 erive the paper s results. The FSFs optimally choose prouct quality, ifferentiation an pricing-output strategies. Equilibrium choices of prouct quality an ifferentiation are shown as explicit functions of moel parameters. The FSFs choices respon (mostly) unambiguously to parameter changes, such as the number of assets in the economy, investor heterogeneity, the marginal cost of improving the quality of financial proucts, an the marginal cost of increasing prouct ifferentiation. Section 5 also inclue a iscussion of how the non-cooperative FSFs can aopt niches to coorinate their behavior an achieve the ifferentiation they promise the customers. Section 6 summarizes results an offers some conclusions. Niche strategies are to be expecte an may well be successful. The main threat to a niche strategy is economies of scope: niche players might be overwhelme if large FSFs enjoy economies of scope that give them lower costs for most proucts in most circumstances. The evience on such economies is mixe.. Relationship to the Literature A small literature iscusses ecision-making by firms that sell financial information to investors: the seller is often a monopolist an oes not prouce the information, an usually faces no strategic issue of prouct ifferentiation. A much larger an oler literature consiers non-financial firms strategic ecisions on prouct ifferentiation. Amati an Pfleierer (986) an (990) stuy a monopolist selling financial information to investors. Their monopolist firm is enowe with a given quantity of information. Amati an Pfleierer (986) enogenize the equilibrium quality an quantity of information the firm sells from its enowment. They show that the firm might sell a noisy version of its enowe information, to reuce the ilution of the information s value from its incorporation in informative asset prices. Amati an Pfleierer (990) compare the monopolist s choice of selling the enowe information irectly to investors as oppose to selling it inirectly through the creation of a fun that makes portfolio choices as a function of the enowe information. They show that inirect sale allows the firm greater control over investors reactions to the information, but may not allow the firm to extract as much surplus. The firm s optimal choice epens on the informativeness of equilibrium asset prices. Allen (990) stuies the creibility problem of a monopolist who sells information an fins that the problem nee not rule out the existence of markets for financial information. He has the firm announce a pricing rule an a portfolio rule that escribe the price of information an the firm s portfolio allocation across assets 3

6 corresponing to each possible set of information with which the firm may be enowe. He shows that in these circumstances there exis ts a set of portfolios an information prices that ensure that the firm correctly reveals its information to buyers. Fishman an Hagerty (995) consier price competition between two firms selling financial information from enowment. A firm has an incentive to sell information rather than only trae on it. They show that selling information allows the firm creibly to commit to trae more aggressively, inucing other informe traers to trae less aggressively, an thus allowing the information seller to capture a larger share of traing profits. This paper s analysis of competition has similarities to the literatures on spatial or horizontal ifferentiation, beginning with Hoteling (99), an vertical ifferentiation or ifferentiation by quality, beginning with Shake an Sutton (98). In these literatures, firms soften competition by ifferentiating themselves horizontally or vertically, an then price their proucts. The moel evelope here iffers in important ways from these earlier moels of ifferentiation. First, though the location ecision in earlier ifferentiation moels is typically one-imensional, this paper s moel has two-imensional optimization--choices of quality an ifferentiation. Secon, the eman functions for the firms proucts, typically exogenous in spatial ifferentiation moels, are erive enogenously here. Thir, in the current analysis, at a given price, the exact same output prouce by ifferent firms woul give the same utility to consumers. In earlier moels of prouct ifferentiation, at a given price, otherwise ientical proucts of ifferent firms give ifferent levels of utilities to consumers. Fourth, earlier moels of ifferentiation restrict consumers to buying from one or none of the firms. Here, investors may buy from one, both or neither firm. In earlier moels, sellers benefit from prouct ifferentiation because it reuces price competition among them. Here, firms benefit because ifferentiation expans the two high-profit monopoly markets, largely at the expense of shrinking the low-profit uopoly market where they compete irectly. 3. The Economy This section presents the risky consumption/investment environment where consumers maximize expecte utility an FSFs make strategic ecisions on quality, ifferentiation an pricing-output. Sections 4 an 5 erive the paper s results. Assume an economy with a continuum of population, where agents are heterogeneous in their risk aversion. Each consumer s inex is a point in the continuity between 0 an K. Each agent's coefficient of absolute risk 4

7 aversion correspons to a point in the continuous uniform interval (a 0... a K ); or each point in the interval 0 K has a one-to-one mapping with one point in the interval a 0... a K. Each agent is born with an initial wealth enowment W, lives for two ays (ays an ), an erives utility only from ay- consumption, C. There are N risky assets an one risk-free asset. Investors make portfolio ecisions on ay an consume on ay. The risk-free asset gives the rate of return r from ay to ay. The value of r is known to all on ay before information on risky-asset returns is prouce an sol. Without loss of generality r = 0. The rate of return on the risky asset j, unknown until ay, is represente by a ranom variable, R j *, whose realization on the morning of ay is R j. (The superscript * emphasizes that a symbol represents a ranom variable.) R j * is generate as () R j * = n i= e* i,j j =, N. The realize value of the risk-variable e* i,j on ay is enote e i,j. n is the total number of e* i,j s per asset, equal for all assets for convenience. Prior to buying information from the FSFs, investors have only their common beliefs about the istributional properties of the e* i,j s in eqn (). Each believes the e* i,j s are multinormal with (a) E(e* i,j ) = µ, i =...n, j =...N, (b) cov(e* i,j, e* g,h ) = 0, unless i = g an j = h, (c) var(e* i,j ) = σ, i =...n, j =...N. This simple structure is tractable an ais in presenting results; it coul be substantially generalize without changing qualitative results. The two financial services firms prouce an sell information on ay- rates of return from risky assets. The financial services sector exists in this moel because information prouction is costly, an because the FSFs have a comparative avantage over iniviual investors in proucing information on future returns from risky assets. FSF prouces q units of information, with a cost function specifie below, incorporates this information in a report, an sells the report to investors; an similarly for FSF. Each unit of information in the report perfectly ientifies one realization e i,j. Thus, q l measures the quality of FSF l s report the higher q l, the higher the quality. Assume that the FSFs truthfully reveal their information. Allen (990) iscusses in etail the incentive problem between a monopolist information seller an the buyers of information. In the present moel, incentive problems woul likely be resolve in a repeate game setting, where FSFs woul have incentives to buil reputations for honesty. 5

8 In the morning of ay, each agent faces the choice of buying a report from each FSF, or not. She buys a maximum of one report from each FSF, the ecision epening on parameters specifie below. In the evening of ay each investor allocates her portfolio using the information she then has; her information epens on the number of reports she bought in the morning, the quality of the reports an their ifferentiation. The results of the investor's investment are realize on ay, after which all investors consume. For tractability, the analysis assumes that asset prices are not informative enough to affect investors expectations about istributions of rates of return. This assumption is the limit of the case where the percentage of investors who buy the report is small an the effects of their portfolio ecisions on asset prices are negligible relative to noise in those prices. (See, for example, Grossman an Stiglitz (980), Hellwig (980), Diamon an Verrechia (98), Amati an Pfleierer (986) an Mahajan (996)). Amati an Pfleierer (986) stuy the case where a monopolist FSF takes account of the effect of its information sales on asset prices an thus on the eman it faces. A Two-Firm Financial Services Sector: There are two financial-services firms; results are easily generalize to a financial services sector with more FSFs. The two FSF s are pre-existing; incumbent-entrant issues are not examine. For convenience, government regulations prevent entry of other firms. Each FSF prouces one financial prouct, its report. The paper neglects issues of the FSFs economies of scope, to preserve tractability. Each FSF may have a competitive avantage in proucing an marketing particular types of information, or may have natural niches; as shown below, competitive avantage is not necessary to ensure that reports are ifferentiate in equilibrium. The FSFs ecisions can be thought of in two steps. Subject to the eman function for their proucts, erive in Section 4, the two FSFs first choose the quality an ifferentiation of their proucts. They then ecie on their pricing-output strategies in light of the competition they face from each other. It is costly for a given FSF to increase the quality of its prouct by fining information on a larger number of e* i,j s, an to ifferentiate its prouct by fining information on ifferent e* i,j s. Differentiation epens inversely on the number of common e* i,j s ientifie in both reports. The increasing marginal cost of prouct ifferentiation epens inversely on the strength of the FSF s competitive avantage, if any. In eciing how much to ifferentiate its prouct, each FSF weighs the marginal cost of increasing ifferentiation against the marginal benefits of expaning its market niche. 4. Deman for the FSFs' Proucts 6

9 This section iscusses the investor s choice problem, shows how the problem is solve recursively, an erives some results for the competitive structure of the financial services inustry. The following section then iscusses the strategic choice problem facing each firm, an characterizes equilibrium in the inustry, incluing how niche strategies coorinate the risks ientifie to minimize costs an give optimal prouct ifferentiation. Because of the structure of risk in (a) - (c) above, the value of the reports to the consumer can be summarize by the amount of information in each report, q an q, an by the ifferentiation across the reports, or how much q overlaps with q. This overlap is measure below by the variable h, the heterogeneity of the reports. This simple structure allows analysis of the consumer s choice problem, at a given set of prices for the reports, in terms of the variables q, q, h. Investors' Optimization an the Market Deman for the Reports: The kth investor, k (0, K), has the utility function V k (W k ), where W k is investor k's ay- wealth. The V k function is strictly increasing, strictly concave, an everywhere twice ifferentiable V k ' > 0 an V k '' < 0. For analytical tractability assume that V k is the negative exponential utility function () V k (W k ) = - exp (- a k W k ); W k = C k, k (0, K), where a k is investor k's absolute risk aversion an C k her ay- consumption. Because V k is strictly increasing, the investor consumes all of her ay- wealth, W k = C k. Each investor maximizes the expecte value of her utility function, eqn (), in perio. Consier the investor s maximization problem (the subscript k is suppresse). The investor is enowe with X j units of risky asset j, j =,, N, an B units of the riskless asset. P j is the current price of asset j; use the riskless asset as the numeraire an set its price to unity. The investor s initial wealth, W, equals N j= P j X j + B. The investor faces the choice of buying a report from one, both or none of the FSFs at price P Rι per report for ι =,. The investor's buget constraint is (3) N j= P j X j + B + P R Q + P R Q = N j= P jx j + B = W ; Q ι = [0,], ι =, where Q ι is the number of reports, one or none, bought from FSF ι at P Rι per unit, in the morning of ay, with ι =,. X j is the number of units of the jth risky asset the investor hols in the evening of ay. Given the portfolio (X,, X N, B) the investor hols at the en of ay, her ay- wealth will be (4) W = N j= ( + R j *)P j X j + B, 7

10 where R j * is the ranom ay- rate of return from risky asset j. Combining eqns (3) an (4) gives (5) W = W + N j= R j * P j X j - P R Q - P R Q. Subject to eqn (5), the investor maximizes the expecte value of eqn () with respect to the Q ι in the morning of ay an with respect to the X j in the evening. The investor s choice of Q ι in the morning affects her optimal choice of X j in the evening. The problem is solve recursively, first for the X j conitional on the information the investor has in the evening, an then for Q ι using the compute functional values of the X j. Making use of eqn (5), from eqn () the investor's objective function in the evening is (6) Max EEv {- exp [- a ( N j= R j * P j X j + W - P R Q - P R Q )]}, Q ι = [0, ], ι =, Xj by choice of X j, where E Ev is the exp ectations operator conitione on the information set I EV available in the evening. I EV, therefore, epens on the choice of Q ι in the morning of ay. For a normally istribute ranom variable ε it is known that E e ε = exp [E ε - var(ε)/]. Using this rule for the ranom variables R* i,j s in eqn (6), or the e* i,j s that might be substitute in, rewrite eqn (6) as maximizing eqn (7), with respect to X j. N a N Max (7) * (- exp[-a(w - P * RQ- PR Q + Xj( + E( Θj IEv) - P j) ) + X Var( )]), Q = [0, ],,. X j Θj ι ι = j j= j= From eqn (7), the investor's optimal choice of X j is (8) X j = E(R* j I Ev )/[ap j Var(R j * I Ev )], j =,, N, the familiar result for moels with negative exponential utility functions (for example, Grossman an Stiglitz 980). The investor's eman for the risky asset j epens irectly on the asset s expecte rate of return, inversely on both the asset s price an the conitional variance of its returns, an is inepenent of the investor s enowe wealth. To choose which report(s) to buy in the morning of ay, the investor inserts the functional values of X j, given in eqn (8), in eqn (7). Taking expectations base on information available in the morning of ay, the investor s problem is (9) Max EM {-exp[-a( W - P R Q P R Q + N j= (E(R* j I Ev )) / (a Var(R* j I Ev ))]}, Q ι = [0, ], ι =,, Q ι where the subscript M on the expectations operator stans for morning. 8

11 The investor buys a report from one, both or neither of the FSFs, epening on which of the three choices gives her the highest expecte utility. If the reports prices (P R, P R ) are small enough, an the range of absolute risk aversion coefficients, a k, has a large enough maximum (a K ) an small enough minimum (a 0 ), then three classes of investors exist. () Investors with high enough risk aversion buy neither report; () Investors with low enough risk aversion buy both reports; (3) Investors with intermeiate risk aversion may buy one but not both reports. This is formalize in Theorems an in the Appenix. The following assumes the range a K to a 0 is sufficiently large. To sharpen the analysis, assume the two FSFs are ientical in the following two ways. First, it costs each the same amount to ientify a given number of e* i,j s, i.e., both face ientical increasing cost functions for increasing the quality of the report. The cost function is c = c(q ), c > 0, where the cheapest risks to ientify are chosen first. Secon, both face ientical increasing costs for increasing the ifferentiation of the report, in the sense of holing constant the number of e* i,j s ientifie, but ientifying a set of them that has less overlap with the other firm s set. The cost function for ifferentiation is G ι = G(h e, e ), where e ι is the set of the e* i,j s chosen by firm ι. Now, let q ι an h ι be the equilibrium quality an heterogeneity of the report offere by firm ι {ι =, } in equilibrium, where the superscript is for the uopoly equilibrium. Then, by symmetry of their optimization problem for prouct quality an ifferentiation, q = q = q, h = h = h. Because the two FSFs offer reports with the same quality an ifferentiation, the prices of reports in the uopoly market are equal, P uo R = P uo R = P uo R, an the prices of reports in the monopoly market are equal, P m R = P m R = P m R. But prices may iffer between the monopoly an uopoly markets because of price iscrimination; that is, P m R an P uo R may iffer. In equilibrium, the FSFs choose the same values of prouct quality, q, that is, ientify the same number of e* i,j s in their reports, but o not necessarily ientify the same e* i,j s in their reports, which allows for ifferentiation. Let h measure the number of e* i,j s that are common to the two FSFs reports. Scale h such that for h = no e* i,j is ientifie in the reports of both FSFs; for h = 0.5, e* i,j s ientifie in the report of one FSF are ientifie in the report of the other. With these assume eman an cost conitions, each FSF has a monopoly segment but also competes hea-to-hea in a uopoly segment. Theorems an in the Appenix show that, when the ratio q / Nn is small enough, as require for prices to be uninformative, there exist absolute risk aversion coefficients a buy an a buy, Teious but straightforwar complications arise when q q an the report prices iffer to reflect this quality ifference. Theorems an in the Appenix provie examples of the complications. 9

12 (i) a buy = (N/P R) ln[(nn)/(nn - q )]; (ii) a buy = (N/P m R) ln[(nn - q )/(Nn - h q )]. Proposition : All investors with risk aversion less than or equal to a buy prefer to buy over 0 reports. All investors with risk aversion less than or equal to a buy prefer to buy reports overreport. Investors with risk aversion less than or equal to a buy buy both reports, investors with risk aversion higher than a buy but less than or equal to a buy, buy an only report, an investors with risk aversion higher than a buy buy 0 reports. This proposition follows from Theorems an in the Appenix. The eman conitions FSFs face in their monopoly markets an the uopoly market are: Proposition : In two segments, each firm has monopoly power over sales to investors whose risk aversion is less than or equal to a buy. The eman function face by each firm in its monopoly segment is D = K(a buy - a 0 )/(a K - a 0 ). In the thir segment the firms are irect competitors; the eman function is D = K(a buy - a buy )/(a K - a 0 ). Firms' equilibrium choices of quality an ifferentiation etermine the sizes of the three markets. An increase in equilibrium ifferentiation increases the sizes of the two monopoly markets equally, an simultaneously ecreases the size of the uopoly market. The ecrease in the size of the uopoly market equals the aggregate increase in the sizes of the monopoly markets. An increase in equilibrium quality increases the size of each firm s monopoly market equally, an ecreases (increases) the uopoly market s size for high (low) enough ifferentiation. This proposition follows from efinitions of a buy an a buy in (i) an (ii), an the market-segment eman functions. 5. Equilibrium in the Financial Services Sector For the emaner s ecisions, analysis in terms of q an h is sufficient. From the moel s simple structure, it oes not matter which risks the firm inclues in its set of q risks. The FSFs, however, choose the q risks to minimize costs. Further, they must act to ensure that their non-cooperative choices of risks in their q s achieve the esire egree of heterogeneity. This section first analyzes the FSFs choice of q an h. It then analyzes how the FSFs aopt niche strategies to guie their choices of q an q, both to control costs an to achieve their optimal heterogeneity, in other wors, how choices of q ι map into the e* i,j s the firms ientify. 5.A. Optimal Choices of Quality an Differentiation In strategically choosing quality an ifferentiation, the FSFs face two steps: 0

13 Step : FSFs simultaneously choose the optimal quality an ifferentiation of their reports, q an h. As Section 4 shows, these choices give three market segments. In two market segments, each FSF has monopoly power. In a thir segment they irectly compete as uopolists. Step : The FSFs simultaneously choose the optimal price, P R, of their reports in the uopoly market, an also choose P m R, the optimal price each sets in its monopoly market. Duopoly-market interaction is assume to be Bertran. From the eman functions foun in Section 4, choice of prices implies quantities sol. The step- optimization problem is solve first to fin the FSFs' optimal pricing-output choices in the monopoly an uopoly markets as functions of prouct quality an ifferentiation (the step- choice variables) an moel parameters. These optimal functional values are use to formulate the reuce-form optimization problem in step, which is then solve to give the FSFs' optimal prouct quality an ifferentiation as functions of moel parameters. These optimal values of quality an ifferentiation are then use in the step- optimal functional solutions to give optimal monopoly an uopoly prices/quantities as functions of moel parameters. Pricing Decisions: Conitional on Quality an Differentiation The Monopoly Market: Assume the two FSFs successfully price iscriminate between the uopoly an monopoly markets. Let the FSFs face the same constant marginal cost, C, of proucing, istributing, an in general supporting the report. As Section 4 shows, in its monopoly market, firm faces the eman function D R = K (a buy - a 0 )/(a K - a 0 ). Its monopoly-market profit function, using this eman function an the expression for a buy in (ii), is Nn - q N Ln( Nn - h q ( PR - C)K[ Π PR = Max PR ( ak - a0 ) ) - a (). Optimizing eqn () with respect to P R gives firm s optimal price, P m R, an quantity, Q m, (a) P m R = {(CN/a 0 ) ln[(nn - q )/(Nn - h q )]} /, (b) D m R = [{(K Na 0 /C) ln[(nn - q )/(Nn - h q )]} / - a 0 K]/(a K - a 0 ), where the superscript m is for equilibrium choice in the monopoly market. Because the two FSFs face ientical cost an eman functions, in equilibrium P m R = P m R = P m R > 0, an D m R = D m R = D m R > 0. The total number of reports sol in the two monopoly markets is D m R. From eqn (b), D m R / q > 0, D m R / h > 0: 0 ]

14 an increase in either quality or ifferentiation causes an increase in the monopoly-market quantity emane. Using the eman function each firm faces, the equilibrium functional value of the monopoly-market price is Nn - q NKLn( ) Nn- h q m [(ak - a0 )D + a K] 0 (3) =. P m R The Duopoly Market: Assume uopoly-market interaction is Bertran the FSFs simultaneously choose uopolymarket prices. Total uopoly-market eman is D uo R = K(a buy - a buy )/(a K - a 0 ). Let each firm face half the uopolymarket eman (this assumption is not crucial). Using efinitions (i) an (ii) an the uopoly-market eman function, firm- s objective function is Π Max P ( P R Nn(Nn - q - C)NKLn[ h (Nn - q ) 4( ak - a0 )PR (4) =, R ) ] where C is the constant marginal cost of physically proucing, istributing, an in general supporting its reports. Because the two FSFs simultaneously choose their report prices, a Bertran-Nash equilibrium results. The only equilibrium report price for both FSFs is P uo R = P uo R = P uo R = C: price equals the common, constant marginal cost (Bertran 883), P m R > P uo R = C. This conition implies each firm makes zero uopoly-market profit in equilibrium. In equilibrium each FSF sells D uo R units of its report in the uopoly market. From the uopolymarket eman function an efinitions (i) an (ii), Nn(Nn- q NKLn[ h (Nn - q ) 4( ak - a0 )C ) ] (5) =. D Total uopoly-market sales are D R. The FSFs' optimization in the monopoly an uopoly markets therefore gives: Proposition 3: () Equilibrium sales in each monopoly market increase in quality or ifferentiation. () An increase in ifferentiation ecreases equilibrium sales in the uopoly market, an the aggregate ecrease in uopoly-market sales equals the aggregate increase in monopoly-market sales by both firms. (3) An increase in quality ecreases (increases) the uopoly-market equilibrium sales when equilibrium ifferentiation is high (low) enough.

15 These results are clear from eqns () an (5). Choices of Optimal Quality an Differentiation In step, both FSFs simultaneously choose optimal prouct quality an ifferentiation, with the knowlege of how choices of q an h affect monopoly-market price an output in step, from eqns (b) an (3). Each also knows that quality an ifferentiation o not affect equilibrium uopoly-market profits, because these are always zero. In step, then, firm optimizes the function (6) Π Max q,h Nn- q m [NKLn( ) - C]DR( q,h,q Nn - q h - qh = m [(a K - a 0 )D R ( q,h,q,h )+a0 K],h ) - c( q )- G(h ), subject to D m R?0, where G(h ) is firm 's cost of increasing ifferentiation, an c(q ) its cost of improving the quality of the report; G'(h ) > 0, c'(q ) > 0, c''(q ) > 0. The function G reflects the strength of firm s competitive avantage; the stronger its competitive avantage, the cheaper to ifferentiate its prouct. The first of the three terms in eqn (6) is firm 's monopoly-market profit function in eqn (), the prouct of P m R in eqn (3) an quantity in eqn (b). Call this first term in eqn (6) the Benefit Function. Eqn (6) is optimize simultaneously, subject to constraint D m R?0, to etermine the equilibrium values of h an q. To fin the Kuhn-Tucker (K-T) conitions for this problem, combine constraint D m R?0 with eqn (6) to form the Lagrangian function Z = π + λ D m R ( q, h, q,h ), where λ is a Lagrange multiplier. Assuming that the π function is concave an continuous, the K-T conitions are Z π D m q,h,q,h ) (7) = + λ R ( = 0, q q q Z π D m q,h,q,h ) (8) = + R λ ( = 0, h h h Z m Z (9) = DR( q,h,q,h ) 0, λ 0, λ = 0. λ λ The K-T conitions in eqns (7) - (9) are solve simultaneously to fin h an q, the equilibrium choices of firm, an λ. From eqns (7) - (9), 3

16 Proposition 4: The extreme case of zero ifferentiation between the proucts of the two FSFs is not a feasible equilibrium. Zero ifferentiation implies h = 0.5, from the efinition of h. From the monopoly-market eman function in eqn (b), h = 0.5 implies D m R < 0, which is rule out by eqn (9). Suppose further that equilibrium monopoly-market sales are positive. Then D m R >?0, an from eqn (9), λ = 0. Using this in eqns (7) an (8), in equilibrium Π q Π q Π D D q m m m R (0) = + - c ( q )= 0 Π h Π h m R () = + - G ( )=0, Π D R m R D h m h where Π m is firm- s Benefit Function, its profit function in the monopoly market (the first term in eqn (6)). From π m the envelope theorem, = 0, because firm maximizes with respect to D R (equivalently P R ) in step. DR Therefore eqns (0) an () can be rewritten as Π q m () = - c ( )= - c ( )=0, Π q q NKD (Nn - q h )[(ak m R ( q,h )h m - a0 )DR ( q,h )+a 0 K] q Π h R (3) = - c ( q )= ' )=0. Π h m m NKD ( q (Nn - q h )[(ak - a 0,h )D m R )q ( q,h - G ( h )+a0 K] By symmetry of the problem for the two FSFs, in equilibrium q = q = q an h = h = h : These equalities are impose in the first-orer conitions above. Eqns () an (3) are solve simultaneously to fin the equilibrium values q an h. Inserting the functional value of D m R from eqn (b) into the equilibrium conitions () an (3), Π q NKq K 0 (4) = - c' ( q )= 0. (Nn - q Nn - q Nao ln ( ) Nn - q h C a - a h ) - a Nn - q Nao ln ( ) Nn - q h C 0 4

17 Π h NKq [ (5) = )=0, (Nn - q h Nn - q Nao ln( ) Nn - q h C )( a K - a0) - a0] Nn - q Nao ln( Nn - q h C ) - G ( h From eqn (4), for given values of h, the Marginal Benefit function of q, MB(q ), is upwar sloping. From eqn (5), for given values of q, the Marginal Benefit function of h, MB(h ), is upwar sloping. Assume that both of the upwar-sloping marginal cost functions c'(q ) an G'(h ) are steeper than their respective marginal benefit functions. Then, from the equilibrium conitions (4) an (5), Proposition 5: The equilibrium values of prouct quality an ifferentiation ecrease with: () An increase in N, the number of risky assets in the economy. () An increase in n, the number of risk variables per asset. (3) An increase in C, the marginal cost of physically proucing, istributing, an in general supporting the reports. (4) An increase in investor heterogeneity, measure by (a K - a 0 )/K. (5) An increase in c', the marginal cost of increasing prouct quality. An (6), an increase in G', the marginal cost of increasing prouct ifferentiation. From Proposition 6 an eqns () an (5), Proposition 6: The equilibrium quantity of reports sol in the monopoly market ecreases with increases in parameters ()-(6) liste in proposition 5. An increase in any of these six parameters has an ambiguous effect on the quantity of reports sol in the uopoly market. If the equilibrium level of ifferentiation is low enough, however, an increase in these six parameters ecreases the equilibrium quantity sol in the uopoly market. 5.B. Achieving Optimal Heterogeneity: The Role of Niche Strategies The moel s simple risk structure allows analysis in terms of q, q an h. The consumer s choice problem naturally focuses on these three variables. For tractability, this focus on q, q an h continues in analysis of the firms strategic choices of quality an ifferentiation. Analytical results are foun for quality an ifferentiation, but not for the actual risks that the FSFs ientify in their reports. Turn now to how the FSFs map their optimum choices of quality an ifferentiation into the actual risks e* i,j their reports ientify. 5

18 Firms can calculate the optimal q an can thus be assure of achieving their optimum quality. To be concrete, if q = 0, each firm chooses 0 e* i,j s. Achieving their optimal h is less straightforwar. If h implies an overlap of 0 to achieve optimum ifferentiation, the non-cooperative FSFs must evelop a mechanism for choosing e*,j s an e*,j s that reliably results in ientifying 0 common an 0 separate risks. This choice problem arises in starkest terms in the limiting case where firms face ientical eman an cost conitions, but arises even if firms have competitive avantages on the cost sie in ientifying particular risks or particular types of risks. Assume that each firm orers the risks from cheapest to most expensive to ientify, an that the firms face ientical, increasing-cost conitions: they have the same orerings, the same increasing cost functions, an the same optimal q, h. Each firm chooses to ientify the same 0 risks with lowest costs. Each aims at ientifying 0 more risks that o not overlap. But this optimal heterogeneity can be obtaine in many ways, an the heterogeneity of one firm s prouct epens in part on the other firm s choices. Firm may choose its secon set of 0 risk factors with an eye towars achieving optimal heterogeneity, but firm may en up choosing the same 0; both achieve no heterogeneity rather than the jointly optimal egree. A non-cooperative way to avoi fortuitous overlap is require. One possibility is to assume that firms have competitive avantages that impose unique, cost-minimizing sets of non-overlapping risks for each firm s secon set of 0, but this is a hoc an nee not hol in general. Niche strategies provie a mechanism that reliably results in the non-cooperative FSFs achieving the jointly optimal heterogeneity. In this case where neither firm has a competitive avantage, each may stakes out an explicit niche, a group of relate risks, in which it specializes. Because neither has a competitive avantage, niche selection is wholly arbitrary. But once each selects a niche, the other knows which risks to avoi in orer to generate the jointly optimal heterogeneity. When one firm eclares its niche, this information oes not alter either firm s strategic problem or solution to the strategic problem. Rather, explicit niches provie a coorination mechanism an ensures that the q, h solution can be achieve, an hence strengthens each firm s commitment to the solution. Some niches are more expensive to service than others. If many niches exist with the same low but increasing costs for heterogeneity, it oes not matter which niches the ientical firms pick. Both have incentives to respect other s niche to achieve their optimal heterogeneity; each loses by failure to respect niches. (One may imagine that one niche is so much lower cost than any other niche that the firms battle intensely over who gets this niche; there appears to be no reason to view this as the general case.) Financial services firms have a strong incentive to follow niche strategies, in the sense of having only 6

19 partial overlap in the information they provie. To ensure that they achieve their optimal heterogeneity, FSFs have a strong incentive to specify their niches, signals that allow them to avoi unintentionally proucing suboptimal heterogeneity. The consumer is inifferent to the niches chosen, as long as the promise quality an ifferentiation of the financial information are achieve. The niches that the FSFs choose an avertise are not oriente towar the eman sie as a marketing tool, nor are they cost reucing evices in the case of ientical firms. Rather, the niche strategies are evices that allow non-cooperative firms to coorinate their activities. Cost-sie competitive avantages make it cheaper, but by no means straightforwar, for FSFs to achieve optimum ifferentiation: firms still have to make a conscious an coorinate effort to achieve ifferentiation. FSFs with competitive avantages are naturally biase towars selecting risks e* i,j s that are low cost for them to ientify; there is built-in heterogeneity. But this built-in heterogeneity is optimal only by chance; otherwise, the FSFs face the problem of ajusting their chosen e* i,j s to achieve optimal heterogeneity. The problem returns: how are the FSFs to ensure they achieve the heterogeneity they both esire? As above, the evice of eclaring a niche, an if necessary a list of mainstream common risks, serves to coorinate the risk selections of non-cooperative financial services firms. 6. Summary an Conclusions This paper is the first to stuy uopolists strategic choices of quality, ifferentiation an pricing-output in the financial services inustry. In previous work, Amati an Pfleierer (986, 990) an Allen (990) stuy monopoly markets for financial information. Fishman an Hagerty (995) stuy pricing strategies for financial services in a uopoly framework, but o not consier issues of prouct quality an ifferentiation. These papers also assume information-sellers are enowe with a certain quantity of information, rather than proucing it at increasing marginal costs. In contrast, the competitors in the present paper face increasing costs in the quality an ifferentiation of their proucts. This paper s uopoly financial service firms (FSFs) strategically choose the optimal quality an ifferentiation of their proucts as well as their optimal pricing-output strategies. The uopolists optimal quality an ifferentiation are solve for as explicit functions of the moel s parameters. The moel provies rich results on strategies on quality an ifferentiation. In equilibrium, both quality an ifferentiation ecrease with an increase in: () The number of risky assets in the economy. () The number of factors that contribute to the riskiness of each risky asset. (3) The marginal cost of physically proucing, istributing an in general supporting the financial 7

20 proucts. (4) The heterogeneity of investors, measure here by their absolute risk aversion. (5) The marginal cost of improving quality. An, (6) the marginal cost of increasing the ifferentiation of their financial proucts. The uopolists optimal strategic choices of quality an ifferentiation result in market segmentation. Some investors who are quite risk averse, expect to put only a small ollar value of funs at risk, an o not fin it worthwhile to buy information from either FSF. At the other extreme are the economy s least risk averse investors. Their unconitional expectation, before buying information, is that they will have a relatively large exposure to risky assets; therefore, they have a relatively high eman for the FSFs information proucts, an buy information from both FSFs. Thus, each FSF has monopoly power in selling to these investors, an each sets a monopoly price. Another market segment consists of those investors, with intermeiate risk aversion, who fin it worthwhile to buy information from one, but only one, FSF; the two FSFs compete hea-to-hea in this market. In equilibrium, the firms always choose to ifferentiate their proucts, even if they face the same eman an cost conitions an have no competitive avantage in proucing an marketing particular types of information. Any competitive avantage the firms have in proucing ifferent pieces of information reinforces the ecision to ifferentiate by reucing the marginal cost of increasing ifferentiation. In orer to coorinate the amount of overlap in their reports an thus achieve optimal ifferentiation, each non-cooperative firm announces an explicit niche, a relate set of risks that it focuses on. These niches are signals to investors that promise ifferentiation will be achieve, an are signals to the other FSF on which area to avoi. Each FSF respects the other s niche, so that both can achieve the ifferentiation they promise buyers. Any competitive avantage the firms have will help guie the irections in which the firms ifferentiate, thus reinforcing each firm s eclare niche an helping the FSFs to coorinate to ensure they achieve optimal ifferentiation. An increase in ifferentiation of the FSFs proucts increases the size of each monopoly market, an simultaneously reuces the size of the uopoly market. The ecrease in the uopoly market s size equals the aggregate increase in the sizes of the monopoly markets. An increase in the quality of the FSFs' prouct increases the size of each monopoly market. This increase in quality has an ambiguous effect on the size of the uopoly market; for high (low) enough equilibrium values of ifferentiation, an increase in quality causes a ecrease (increase) in the size of the uopoly market. An increase in any one of the six exogenous factors mentione above causes a ecrease in both quality an ifferentiation, an thus in sales in the monopoly markets. The effects of the six factors on sales in the uopoly 8

21 market are ambiguous; for low enough levels of equilibrium prouct ifferentiation, sales in the uopoly market fall with an increase in the six factors. Recent years have seen a worlwie wave of financial-service-firm mergers an acquisitions, an increase competition in financial services in emerging market economies (EMEs). Some observers fear that the increase M&A activity will result in the survival of only very large FSFs. This paper s moel suggests that equilibrium will see FSFs evelop profitable niches an offer partial prouct ifferentiation, where investors pay for incremental information they cannot get elsewhere. Contrariwise, firms that attempt to compete across the market may fail. Similarly, some EME policy makers fear that evelope-country FSFs will ecimate local FSFs. This paper s moel suggests that local FSFs may well survive by fining niches in the ientification of local risks, leaving ientification of international risks to evelope-country firms. This paper s results epen crucially on the assumption that economies of scope are not ominant. If large firms that compete across the financial-services market have lower costs in most areas because of economies of scope, then the outlook for niche firms is bleak. The evience on economies of scope is mixe. Both those FSFs aiming to compete across the market an those FSFs focussing on niche strategies may, in effect, be making large bets on simple hunches about economies of scope. This paper moels only two FSFs, but the analysis is easily generalize to any fixe number of firms. Entrant-incumbent issues are not consiere here, but woul be an interesting application of this paper s approach. This assumes the uopolists have no concerns about entry by other firms government restrictions on entry were assume. Generalizing the analysis to allow free entry woul permit consieration of strategies to eter entry, or if it is infeasible or sub-optimal to eter entry, strategies for the perio before entry occurs. 9