Managerial Incentives and Financial Contagion

Transcription

1 WP/04/199 ngeril Incentives nd Finncil Contgion Sujit Chkrvorti nd Subir Lll

2 004 Interntionl onetry Fund WP/04/199 IF Working Pper Policy Development nd Review Deprtment ngeril Incentives nd Finncil Contgion Prepred by Sujit Chkrvorti nd Subir Lll 1 uthorized for distribution by rinne Schulze-Ghtts October 004 bstrct This Working Pper should not be reported s representing the views of the IF. The views expressed in this Working Pper re those of the uthor(s) nd do not necessrily represent those of the IF or IF policy. Working Ppers describe reserch in progress by the uthor(s) nd re published to elicit comments nd to further debte. This pper proposes frmework for comovements of sset prices with seemingly unrelted fundmentls, s n outcome of optiml portfolio strtegies by fund mngers. In emerging mrkets, dedicted mngers outperforming benchmrk index nd globl mngers mximizing bsolute returns led to systemtic interctions between sset prices, without symmetric informtion. The model determines optiml portfolio weights, the incidence of reltive vlue strtegies, nd the systemtic devition of prices from fundmentls with limits to rbitrging this differentil. ngeril compenstion contrcts, optiml t the firm level, my led to inefficiencies t the mcroeconomic level. Conditions re identified when shocks in one emerging mrket ffect others. JEL Clssifiction Numbers: F36, G11, G15 Keywords: Finncil Crises, Index Investors, Globl Linkges uthor(s) E-il ddress: slll@imf.org, sujit.chkrvorti@chi.frb.org 1 Sujit Chkrvorti is with the Federl Reserve nk of Chicgo. The uthors thnk nn Ilyin, Rich Rosen nd seminr prticipnts t the Federl Reserve nk of Chicgo nd the Interntionl ond nd Debt rket Integrtion conference held t Trinity College for their comments on erlier drfts. The views expressed in the pper do not necessrily reflect those of the institutions with which the uthors re ffilited.

3 - - Contents Pge I. Introduction...3 II. Review of the Literture...5 III. The odel...6. The Investment Horizon...7. The enchmrk Index...8 C. Locl Investors s the Source of Uncertinty...9 D. Dedicted Fund nger s Compenstion Structure...9 E. Globl Opportunistic ngers...15 IV. The Equilibrium Dedicted (Positive Csh Holdings) nd Opportunistic ngers Dedicted nger (ero Csh Holdings) nd Opportunistic nger...1 V. Conclusion...3 References...5 ppendix: Proofs of Propositions...6 Figures 1. The Timeline...8. Dedicted Investor Demnd Spce...1

4 - 3 - I. INTRODUCTION The phenomenon of finncil contgion hs chieved considerble ttention in both cdemic nd policy circles in recent yers. The tequil crisis of , the sin crisis of 1997, the Russin defult nd the collpse of Long Term Cpitl ngement in 1998, the boom nd bust relted to the Internet bubble in the lte 1990s, the response of interntionl mrkets in the immedite ftermth of September 11, nd the run-up to the rgentine debt defult in lte 001, ll were ccompnied by the trnsmission of finncil mrket voltility cross borders. In the cse of emerging mrkets, the prices of ssets of countries which were not relted through direct mcroeconomic links (e.g. trde chnnels, linked exchnge rtes, or vulnerbility to similr commodity prices) showed comovements in excess of wht could be explined through trditionl mcroeconomic linkges. The literture on contgion cn brodly be clssified into its empiricl nd theoreticl strnds. The empiricl strnd hs focused on definitions of contgion to ccount, for instnce, for simultneous increses in voltility which show up s incresed correltions, or the impct of common externl fctors. The theoreticl strnd hs tried to identify the possible chnnels of contgion, including the herding behvior of investors, the trnsmission of pnic, nd utomted risk mngement procedures. This pper will focus on contgion s trnsmission of negtive or positive shock to nother country where finncil mrkets re not linked by economic fundmentls but ffected by the behvior of different types of fund mngers to prmeters such s index weights, voltility of the returns of the ssets, the level of risk version, nd trding strtegies. Policy pproches to contgion hve relied minly on the rgument tht informtionl symmetry drive excess comovements of prices s investors wtch ech others ctions nd often tend to reinforce ech others ctions. This hs prompted clls for greter disclosure both of mrket positioning nd key finncil nd economic dt from countries vulnerble to contgion. In relted vein, policymkers nd reserchers hve lso focused on the role of prticulr investor groups in driving mrket prices. Prticulrly fter the sin crisis, hedge funds nd other highly leverged institutions were the subject of much debte on the cuses of contgion nd policies were trgeted t reducing the sources of contgion from such sources. key ssumption in much of the literture is tht the min finncil mrkets re efficient nd tht contgion is devition from the norm. This could be driven by informtion symmetry, mrket mnipultion through size, or the destbilizing effects of leverge. This pper ims to nlyze the phenomenon of contgion by showing tht the institutionl structure of mrkets cn ply significnt role in creting mrket rchitectures tht my led to contgion. In prticulr, the incentives fund mngers fce cn led to contgion even in mrket with no symmetric informtion dominted by certin clsses of institutionl investors key feture both of emerging debt mrkets s well s mjor equity mrkets. The different compenstion mechnisms of different clsses of fund mngers, themselves n outcome of optiml principl-gent reltionships between fund mngers nd their clients, re root

5 - 4 - cuse of devitions of sset prices from wht my be the efficient mrket outcome. This lso suggests tht sset prices my continue to significntly devite from underlying fundmentls nd the behvior of fund mngers is optimlly guided not just by the fundmentls, but by their expected compenstions for tking on risky positions. The pper finds tht given the domintion of mrkets by distinct types of portfolio mngers, who re distinguished by their mndtes nd compenstion mechnisms, the optiml responses of these investor clsses to the sme informtion set nd mrket conditions vry considerbly. While groups of investors behve in well-defined wys in response to shocks, the pper finds tht the impct on equilibrium mrket prices nd fund mngers reblncing of their portfolio weights is bsed on the type of shock nd the reltive sizes of the two fund mnger clsses, nd the initil conditions in the mrket. While this model ws motivted by emerging mrkets, this frmework cn lso be used to nlyze comovements in prices in different ssets within the borders of the sme country, for exmple between stocks nd the bond mrket. key conclusion tht emerges from this pper is tht mngeril compenstion systems re key source of distortions in finncil mrkets, nd my be the source for long-term devitions of prices from the so-clled fundmentls. This lso leds to the conclusion tht the opportunity to rbitrge wy such devitions my be limited for long periods of time, nd mrkets my be over- or undervlued nd be perceived s such for extended periods. The pper considers two types of fund mngers dedicted nd opportunistic in the model. Dedicted mngers re compensted bsed on devitions from n emerging mrket index nd re not llowed to borrow csh or short ny sset. Opportunistic mngers re compensted bsed on the bsolute return on their portfolio nd re llowed to short ny sset nd borrow csh. First, the optiml weights for ech sset for ech type of investor re derived. The pper finds tht dedicted investors tend to reblnce their portfolios towrds the index when sset voltility or their risk version increses. It lso finds tht opportunistic mngers decrese the mount of leverge in response to incresed sset voltility or increse in risk version. Second, the pper derives equilibrium expected sset returns nd prices. The pper finds tht demnd shock in one sset ffects the expected price of the other sset. Specificlly, the reltive contribution of one type of trder to contgion depends on underlying mrket conditions. The pper is structured s follows. The next section provides brief overview of the literture. Section III presents the bsic frmework of the pper nd discuss fetures of the demnd functions of three types of fund mngers. In Section IV, equilibrium prices re clculted nd the impcts of chnges in prmeter vlues re investigted. Section V offers some concluding thoughts.

6 - 5 - II. REVIEW OF THE LITERTURE This pper best fits in the theoreticl literture bout contgion where the relloction of ssets by investors is not necessrily bsed on mrket fundmentls. Clvo nd Reinhrt (1996) distinguish between fundmentls-bsed contgion nd true contgion where chnnels of potentil interconnection re not present (lso see Kminsky nd Reinhrt, 000). Contgion is defined s the propgtion of shock to nother country s sset when there re no fundmentl linkges between the country hit by the shock nd the other countries, nd the comovement of sset prices cross borders is bsed on the behvior of globl investors. Clvo nd endoz (000) suggest tht informtion regrding investments in portfolio my be expensive nd investors my choose to optimlly mimic mrket portfolios. They find tht finncil globliztion in n environment of imperfect informtion my increse contgion where investors fce high costs to gther informtion on mrket fundmentls nd rely on the ctions of other investors. Kyle nd Xiong (001) construct continuous-time model with two risky ssets nd three types of trders noise trders, long-term investors, nd convergence trders. When convergence trders suffer lrge cpitl losses in one mrket, they liquidte positions in both mrkets. The liquidtion of the portfolio mplifies nd trnsmits the shock from one sset to nother. Contgion in their model is generted through the welth-effect of convergence trders. Kodres nd Pritsker (00) construct multiple sset model to study contgion through cross-mrket reblncing when one country fces n idiosyncrtic shock. Countries my be wekly linked in terms of mcroeconomic risks. They lso find tht symmetric informtion increses country s vulnerbility to contgion. Schinsi nd Smith (1999) suggest n lterntive view to contgion from those bsed on mrket imperfections such s symmetry of informtion. They construct prtil equilibrium frmework to study different portfolio mngement rules nd reblncing events nd their effects on contgion. They find tht shock to n sset in one country my hve effects on risky ssets in other countries becuse of the underlying portfolio mngement rules nd the prmeteriztion of the joint distribution of sset returns. Furthermore, they find tht reblncing my be ffected by whether or not the investor is leverged. Leverged investors will reduce their exposure to risky ssets if the return on the leverged portfolio is less thn the cost of funding. This pper extends the literture by considering the cse where investors optimlly reblnce their portfolios bsed on n idiosyncrtic shock to one mrket in terms of incresed voltility nd demnd shock to n emerging mrket sset potentilly resulting in contgion. Unlike the previous literture, the focus is on the mngeril incentives of fund mngers nd their role in dmpening or excerbting contgion. Fund mngers re often restricted in the mount tht they cn invest in emerging mrkets. In ddition, they my lso be compensted on the reltive return on the portfolio to the emerging mrket index. The pper considers two Some of these models discuss herd behvior s possible explntion. For generl discussion bout herd behvior, see nerjee (199) nd Schrfstein nd Stein (1990).

7 - 6 - types of interntionl fund mngers, dedicted nd opportunistic fund mngers, which re discussed in detil below. III. THE ODEL This pper considers simple discrete time model with two risky emerging mrket ssets ( nd ) mture mrket sset (), nd csh (). The emerging mrket nd mture mrket ssets cn be viewed s long-term bonds. There re three types of trders: dedicted emerging mrket fund mngers (investing in only emerging mrket ssets nd csh), globl opportunistic fund mngers (investing in emerging mrkets nd mture mrkets), nd noise trders (locl investors). Risk verse mngers will ttempt to mximize their risk-djusted compenstion. Locl Investors trde in sset or sset, nd do so bsed on conditions in other sset mrkets in tht country. They do not invest outside of their respective country, nd hence only choose between sset (or ). For purposes of this model, noise trders dd rndom element to the demnd of ssets nd. Dedicted fund mngers llocte their cpitl between two risky ssets nd nd riskfree sset (csh), nd cn only invest in these ssets (their mndte does not llow investing in the mture mrket sset ). The compenstion of dedicted fund mngers is tied to the performnce of the funds under their mngement reltive to the benchmrk index for emerging mrket ssets. 3 Opportunistic fund mngers re llowed to invest in ll three ssets, nd. While their min investment universe is defined s mture mrket ssets, they hve the opportunity to invest in the emerging mrket sset clss to enhnce their overll returns. Thus, their decision is whether to invest smll mount of their portfolio in emerging mrket ssets or mture mrket ssets. Opportunistic mngers my either increse or reduce their exposure to ssets, nd depending on the reltive returns/voltilities of mture nd emerging mrket ssets. 4 sset cn be interpreted s risk-free sset such s U.S. Tresuries with fluctutions in secondry mrket prices. Unlike dedicted mngers, opportunistic mngers my sell ssets short to finnce long positions in other ssets. 5 Since comprehensive dt on the composition of the investor bse is difficult to compile, one hs to rely on the evidence presented by interntionl bnks who re the min mrket mkers 3 Typicl benchmrks re the JP orgn s Emerging rket ond Index Plus (EI+) nd EI Globl indices. 4 Such investors re often linked to broder indices such s the Lehmn Universl or Lehmn ggregte or Slomon s rod Investment Grde (IG) index. 5 The model llows for short selling to exmine the behvior of hedge funds s one type of globl investor.

8 - 7 - for emerging mrket debt, in guging the reltive size of investor clsses. The totl sovereign emerging bond mrket universe investible by interntionl investors is estimted t some $5 billion. While the size of outstnding bond mrket cpitliztion is somewht lrger, the bove estimtes exclude smller nd illiquid sovereign bond issunces, nd emerging mrket corporte issunces of bout $100 billion, nd others not meeting the criteri for inclusion in the mjor mrket indices. Of this pool of vilble ssets, between percent is thought to be held by dedicted investors including both emerging mrket mutul funds s well s emerging mrket funds mnged independently but belonging to lrger fmily of funds. Hedge funds typiclly comprise between 10 nd 0 percent of the investor bse. The reminder is dominted by globl investors who either invest in the whole emerging mrkets index or who selectively nd opportunisticlly cross over into emerging mrkets. Direct retil investors do not form significnt proportion of overll emerging mrket investor bses.. The Investment Horizon For the purposes of modeling portfolio mngers behvior, this pper considers time horizon consisting of three periods s below (see figure 1): 0 t = T T + 1. Period 0 is the initil period, where fund mngers begin with certin portfolio lloction, nd certin knowledge of prices nd returns, which is n outcome of the previous period s portfolio decisions nd shocks. They then updte their informtion set I 0 in this period bsed on which they form their expecttions of the future demnd of locl investors for ech sset, nd the vrince (distribution) of ll ssets. sed on tht, in rtionl expecttions frmework, they mke decision on their new optiml portfolio, bsed on expecttions of the vribles. Period T is when portfolio mngers, bsed on I 0 nd their initil conditions, put in plce their new portfolios, nd when the reliztion of the rndom vrible tkes plce. The ctul outcome of equilibrium prices nd returns in period T will be the result of the reliztion of the rndom vrible on the new portfolio positions. These equilibrium prices hve to be compred ginst the prices under lterntive scenrios to nlyze the dynmics of contgion. Since expected returns re the inverse of prices, s will be shown, the lloction of proportion of portfolio to n sset will help determine its price, nd hence expected return. 6 6 The derived demnd curves cn be seen s nlogous to n uction mechnism wherein investors put in their bids for ssets long price schedule, nd depending on the equilibrium price will be llocted prticulr mount of the sset.

9 - 8 - Period T+1 is terminl condition on prices. The terminl condition is significntly beyond the time period focused on in the model. The terminl price is bsed on sset nd economywide fundmentls is fixed nd known. These ssets my be viewed s long-term bonds where the terminl pyout is known but the price in secondry mrkets fluctutes. Figure 1: The Timeline reliztion of shock determintion of ctul prices terminl prices I 0 0 T T+1 portfolio decisions tken The model will be bsed on the rtes of return of vrious ssets, which is the inverse of their prices. The model will determine the totl demnd for ech sset, nd set tht ginst fixed supply of ech sset to determine equilibrium prices. Note tht the rtes of return will be computed s the difference between the equilibrium prices determined in the model nd the terminl prices. Let. The enchmrk Index I r denote the return on the benchmrk portfolio in period (T +1) s: where: r P P 1 + (1 ) 1, I T+ 1 T+ 1 α α PT PT α (0,1).

10 - 9 - s is usully the cse, fund mngers tke α s given exogenously, s the weights of the components of the index re determined by the proprietor of the benchmrk index, nd re only modified periodiclly. 7 C. Locl Investors s the Source of Uncertinty Locl investors dd uncertinty to the demnd (nd hence equilibrium prices) of ssets nd. Their demnds re given by: 8 D D N(0, ) L, N(0, ) L, (5.1) The mrket clering conditions then re s follows: D + D + D = S D, O, L, D + D + D = S D, O, L, Note tht the only source of uncertinty is the demnd for ssets by the locl investor, with fixed supply of n sset, the uncertinty on the equilibrium price will be equl to the uncertinty ssocited with the demnd by the locl investor. This will be true for ny shpe of the ggregte demnd curve. 9 D. Dedicted Fund nger s Compenstion Structure D Let r denote the net return on the portfolio held by the index investors from period T to period (T + 1), where λ is the proportion of their welth invested in sset nd τ is the proportion of their welth invested in sset, with (1 λ τ ) being the proportion invested in csh. Then, the net return on the dedicted mnger s portfolio is: where: ( ) ( ) ( ) r D = λ r + τ r + 1 λ τ ( r ), 7 n extension of the model could study the effects of chnges in benchmrk weights in longer-time horizon model. 8 For simplicity it is ssumed tht the both ssets shre the sme distribution properties though not necessrily the sme prmeters. 9 This is esy to see digrmmticlly.

11 P T+ 1 PT P T+ 1 PT P T+ 1 + P T + P T + P T T P r r r,,. D I Let r r denote the totl excess return of the dedicted fund mnger s portfolio t time (t +1). The excess return is defined s the return of the mnged portfolio over portfolio which simply trcks the mrket index. The fund mnger s compenstion is fixed proportion k of the excess return she erns for the portfolio, nd her utility is incresing in his expected income nd decresing in the vribility of his income (with () denoting the coefficient of constnt bsolute risk version). ssuming tht ech fund mnger s initil portfolio vlue is normlized to one, the dedicted fund mnger s optimiztion problem is s follows: where: λτ, D I { ke U r r } mx [ ( )], D I D I ( ( r r )) Ur ( r) = e nd D I 1 D I ( [ E[ r r ] Vr[ r r ]) D I EU [ ( r r )] = e. The excess return of the portfolio is given by: r D r I = ( λ α) r + ( τ 1 + α) r + (1 λ τ) r. Then, nd E( r r ) = ( λ α) E( r ) + ( τ 1 + α) E( r ) + (1 λ τ) r D I ( ) D I Vr( r r ) = ( λ α) + ( τ 1 + α).

12 The return on csh is known constnt r. To isolte the effects of index-linked investing on comovement of sset prices, it is ssumed tht Cov( r, r ) = 0, i.e. it is ssumed there is nothing inherent in sset prices of nd tht lredy hs contgion incorported in it. ximizing the expected utility of welth (since the fund mnger gets fixed percentge k of the excess returns on the portfolio, he will mximize his utility by mximizing the excess returns on the portfolio) is equivlent to mximizing: 1 E r r Vr r r D I D I ( ) ( ) The following function is mximized with respect to λ ndτ :. ( ) ( ) ( λ α) E( r ) + ( τ 1 + α) E( r ) + (1 λ τ) r mx λτ, [( λ α) + ( τ 1 + α) ] (5.) subject to: λ 0, τ 0, λ + τ 1. Note tht dedicted mngers re not llowed to short either sset or, or borrow csh. The dedicted fund mngers demnd spce for ssets nd is digrmmed in Figure. When csh holdings re zero, the mnger is on the digonl line. When csh holdings re positive, the mnger is below the digonl line. ecuse dedicted mngers re not llowed to short either sset or borrow csh, their lloctions re bounded from below by the λ nd τ xes. If the mnger is underweight sset but overweight sset, then she will be in the tringle lbeled I. If the mnger is overweight sset nd underweight sset, she will be in the tringle lbeled III. If she is underweight both ssets she will be in rectngle II. Even if the mnger knows n sset is likely to bring negtive returns, the compenstion nd indextion structure results in her holding some mount of the sset under certin conditions s elborted below.

13 - 1 - τ Figure : Dedicted Investor Demnd Spce 1 No Csh line 1 α I Index lloction II III Only csh α Proposition 1: The solution of the dedicted fund mnger s optimiztion problem (5.) is s follows: 10 1 λ For the region of prmeter vlues where portfolio weights * * ( λ, τ ) re: 0 nd 0, the optiml * Er ( ) Er ( ) * Er ( ) Er ( ) λ = + α nd τ = + (1 α) ( + ) ( + ) For these prmeter vlues, csh holdings re zero. The investor will be long the nocsh line in Figure bove. For the region of prmeter vlues where ** ** optiml portfolio weights ( λ, τ ) re: < 0 nd/or < 0, the 10 ll derivtions nd proofs of propositions pper in the ppendix.

14 Er ( ) r Er ( ) r + α, whenever + α > 0 ** λ = 0, whenever + α 0 nd τ ** Er ( ) r Er ( ) r + (1 α), whenever + (1 α) 0 = 0, whenever + (1 α) < 0 For these prmeter vlues, csh holdings re: r E( r ) r E( r ) ** ** +, whenever 0 < λ < 1 nd 0 < τ < 1, ** ** 1 -, whenever 0 1 nd 0, ** α < λ < τ = λ δ = Er ( ) r ** ** 1 -(1- α), whenever λ = 0 nd 0 < τ < 1, ** ** (1 ) 1, whenever λ = 0 nd τ = 0. Proposition 1 demonstrtes tht the index weights α nd 1 α re key determinnts of dedicted mngers portfolio lloction towrds n sset. Other things equl, country with greter weight in the index will utomticlly get greter lloction of funds in n optiml behviorl frmework. Note lso tht the devition of the lloction from the index weight is independent of tht weight. Proposition describes the behvior of dedicted mngers when one or both emerging mrket ssets underperform csh.

15 Proposition : Suppose tht the risk-djusted excess return of n emerging mrket sset underperforms csh: ) If E( r ) > r nd E( r ) < r or E( r ) > r nd E( r ) < r, the mnger will go overweight sset tht outperforms csh. Conversely, if E( r ) < r or E( r ) < r or both, the mnger will be underweight sset ( λ < α ) nd/or sset ( (1 λ) < (1 α) ), but will not necessrily hold zero of either sset. b) s the weight of sset in the benchmrk index α rises, mnger who is overweight the sset will increse her exposure further by mintining the overweight. mnger who is underweight sset will lso increse her exposure, but mintin the underweight. c) s the risk version coefficient () rises, the demnd for sset or flls, if the mnger is overweight the sset. If the mnger is underweight the sset, n increse in () results in her reducing her underweight position. In other words, higher degree of risk version cuses hugging of the index. d) s or sset. If the mnger is underweight the sset, s her underweight. In other words, n increse in index. rises, the demnd for sset or flls if the mnger is overweight the or or increses, the mnger reduces results in greter hugging of the e) n increse in (), or, my reduce the demnd for csh nd greter hugging of the index. Proposition sttes tht dedicted mngers my hold positive vlues of n emerging mrket sset even when it underperforms csh. Intuitively, it is esy to see tht while lower weights to n sset with lower returns thn csh would increse utility, the low weight reltive to the benchmrk increses the risk of underperforming the index nd hence lowering utility. For some rnges, the return element domintes nd hence zero lloction my be optiml, but in other rnges, the risk element domintes leding to positive lloction. This result cn be esily generlized to more thn two emerging mrket ssets. When the dedicted mnger reblnces her portfolio weights closer to the index, the demnd for ll ssets where she ws underweight will increse nd the demnd for ll the ssets where she ws overweight will decrese. Thus, the behviorl chrcteristics of the dedicted investor results in linkges between otherwise unrelted mrkets bsed on whether the portfolio weight is greter or less thn the mrket index.

16 Proposition lso sttes tht dedicted mngers tend to hug the index more closely when voltility of returns on emerging mrket ssets nd risk version increse. If the mnger is underweight n sset nd the voltility of tht sset increses, she will increse her holdings of tht sset. Interestingly, dedicted mngers reduce their csh holdings when voltility nd risk version increse. The model next considers the cse when both emerging mrket ssets outperform csh. Proposition 3: Considering the cse when λ + τ = 1. ) The dedicted mnger is overweight the sset with the higher expected return nd is underweight the sset with the lower expected return. b) n increse in risk version coefficient () would result in hugging of the index or lloctions closer to the index. If the mnger is underweight n sset, n increse in () would result in the dedicted mnger incresing her exposure of tht sset nd decresing her exposure of the other sset. Similrly, if the dedicted mnger is overweight n sset n increse in () would result in decrese in exposure of tht sset nd n increse in exposure of the other sset. c) n increse in or reduces the size of the overweight/underweight positions s well, forcing the dedicted mnger to move closer to the benchmrk index. When dedicted mngers do not hold csh, they increse their holdings of n underweight sset when its voltility increses nd decrese their holdings of the other emerging mrket sset. In other words, n increse in the voltility of n underweight sset results in decrese in the demnd for the other emerging mrket sset when there re only two ssets. If there re more thn two ssets, the demnds for ll the underweight ssets vis-à-vis the index increse while the demnds for ll the overweight ssets decrese. In this sense, n increse in the voltility of one sset spills over into the demnd for the other sset. Propositions nd 3 stte tht chnges in the expected returns, level of risk version, nd vrince of the emerging mrket ssets my led to chnges in the demnd for the underlying ssets. It is lso found tht increses in, or would result in mngers choosing lloctions closer to the index. E. Globl Opportunistic ngers This subsection considers opportunistic fund mngers tht mximize their expected portfolio vlue from holding ssets,, nd nd do not follow ny index or benchmrk. The globl opportunistic fund mnger s optimiztion problem is:

17 mx φδ, O O jr W, O O where r is the return on the opportunistic fund mnger s portfolio, W is the initil welth of the opportunistic mnger, j is the percentge of compenstion for the opportunistic mnger,φ is the proportion llocted to sset, δ is the proportion llocted to sset, nd (1 φ δ ) is the proportion llocted to sset. The return on the opportunistic mnger s portfolio is: O r = φr + δr + (1 φ δ) r. The return on the mture mrket index, mnger. 11 nd r, is stochstic nd exogenous for the opportunistic O E( r ) = φe( r ) + δe( r ) + (1 φ δ) E( r ) Vr( r O ) = φ + δ + (1 φ δ). s before, it is ssumed tht ll covrince terms re zero. The opportunistic fund mnger mximizes the following problem with respect to φ nd δ : mx φer ( ) + δer ( ) + (1 φ δ) Er ( ) φ + δ + (1 φ δ) φδ,. (5.3) Unlike the dedicted mnger, the opportunistic mnger is llowed to short ny sset to finnce positions in other ssets. Proposition 4: The solution of the opportunistic fund mnger s optimiztion problem (5.3) is s follows. The optiml portfolio weights * * * ( φ, δ,(1 φ δ) ) re: φ Er ( ) Er ( ) Er ( ) Er ( ) U U, * = The mture mrket sset cn be interpreted s return on mture mrket bonds where the opportunistic investor is price tker.

18 δ Er ( ) Er ( ) Er ( ) Er ( ) U U, * = + + nd * Er ( ) Er ( ) Er ( ) Er ( ) (1 φ δ) = 1 U U, where: U = + +. Some behviorl chrcteristics of opportunistic mngers to chnges in prmeter vlues re considered next. Proposition 5: The opportunistic mnger rects to chnges in the underlying prmeters in the following wys: ) The opportunistic mnger will hold incresing mounts of n emerging mrket sset if the expected return on tht sset increses. This increse in exposure will come t the expense of her exposure to both the other emerging mrket sset nd the mture mrket sset. b) The proportions of relloction wy from the other emerging mrket sset nd from the mture mrket sset will depend on the reltive voltilities of the two ssets. If the emerging mrket sset is more voltile thn the mture mrket sset, then the reduction will be greter for the mture mrket sset, nd vice vers. c) If E( r ) > E( r ) nd E( r ) > E( r ), the opportunistic mnger would short sset nd go long t lest one other sset tht hs higher positive expected returns if: Er ( ) Er ( ) Er ( ) Er ( ) + >. This is the reltive vlue strtegy (lso known s the long-short strtegy) of hedge funds. Note tht returns do not hve to be negtive to short the sset, just less thn tht of the other two. d) If E( r ) > E( r ) nd E( r ) > E( r ), the opportunistic mnger would go long sset.

19 e) If E( r ) > E( r ) nd E( r ) > E( r ), then the mnger will short sset if: ( ) ( ) ( ) ( Er Er < Er Er ). f) s () increses, the opportunistic mnger would reduce her exposure to the highest yielding sset, nd increse her exposure to the lowest yielding sset. s cn be seen, the opportunistic investor my hold negtive quntities (i.e. go short) of both emerging mrket ssets if the expected return on mture mrket sset is sufficiently high reltive to emerging mrket ssets nd the product of the voltilities of the other emerging mrket sset nd the mture mrket sset re sufficiently low. Conversely, the investor my short the mture mrket sset if emerging mrket ssets offer sufficiently high expected returns. The opportunistic mnger my lso go long one emerging mrket sset nd go short the other, strtegy commonly employed by reltive vlue hedge funds. Similrly, it is observed tht shorting the mture mrket sset implies tking leverged position in emerging mrkets, with the optiml mount of such leverge given bove. In rel life, the mture mrket sset return in such cse would be the cost of borrowing for the hedge fund. gin, the mount of leverge would be endogenous nd function of the cost of leverge. s the cost of leverge rises, overweight positions in emerging mrkets ssets re reduced ceteris pribus, which is consistent with the evidence tht rise in globl interest rtes induces selloff in emerging mrkets often bsed purely on technicl considertions of reduction of leverge in the mrket. IV. THE EQUILIRIU The previous sections derived the optiml behvior of two min clsses of fund mngers in emerging mrket bond mrkets, nmely dedicted emerging mrket mngers nd globl opportunistic mngers. Now the equilibrium returns (nd implicitly prices) tht re derived from the interction of these two clsses of mngers re computed. D, D, The supply of sset, ( S ), nd sset, ( S ), re known nd fixed. D nd D denote O, O, the dedicted mngers demnd for ssets nd, respectively. Similrly, D nd D, L, denote the opportunistic mngers demnd for ssets nd, respectively, nd D nd L, D denote the locl investors demnd for ssets nd, respectively. For dedicted mngers, their compenstion mechnism is linked to the performnce of their portfolio reltive to benchmrk portfolio. ost dedicted investors re benchmrked to either the EI+ or the EI Globl index. In equity mrkets, they re typiclly benchmrked to orgn Stnley Cpitl Interntionl Emerging rkets Free index. Hedge funds nd the proprietry desks of commercil nd investment bnks ct like the globl opportunistic mngers described bove. They essentilly re focused on the bsolute risk-djusted returns of their portfolios, nd hve ccess to both emerging nd mture mrket

20 ssets, nd cn go long or short ssets, thereby llowing significnt expnsions of their blnce sheets. Wht the model shows is tht such mngers look t the reltive risk-djusted returns for ll ssets. The min determining fctor for their positioning, including whether to go long or short ny sset, is their expected excess return over other ssets they cn invest in, for given levels of voltilities. Therefore, whether they will tret two emerging mrket ssets similrly or differently will depend on how the returns compre with tht of the mture mrket sset in three-sset cse. Defining contgion s comovement of sset prices (nd hence returns) in the sme direction, nd reverse contgion s the offsetting movements (in the opposite direction) of two sset prices, contgion cn be nlyzed by compring the returns on the two ssets when subject to shock. The shocks of prticulr interest re when investor expecttions of locl trders in prticulr country chnges nd its effect on the expected return on the other emerging mrket s sset vi the trding strtegies of cross-border mngers. The impct on emerging mrket bond prices from the interction of dedicted nd opportunistic mngers cn be seen from the computtion of equilibrium prices. For this, the totl demnd of ssets nd from two types of mngers is set equl to their respective supplies nd compute equilibrium prices. Suppose tht there re n number of dedicted investors nd q number of globl investors. When dedicted nd opportunistic mngers long with locl investors re present, the mrket clering conditions re: S nd qd D D, O, L, = + + (6.1) S nd qd D D, O, L, = + + (6.). Dedicted (Positive Csh Holdings) nd Opportunistic ngers This subsection considers the equilibrium expected returns for ssets nd when there re dedicted mngers tht hold csh in their portfolios nd opportunistic mngers. Substituting the optiml portfolio lloctions to ech sset for ech type of investor nd plugging into (6.1) nd (6.) yields: S Er ( n ) q E r E r E r E r D L, = + α ( ) ( ) ( ) ( ) U (6.3) nd S Er ( n ) q Er Er Er Er D L, = + (1 α) ( ) ( ) ( ) ( ) U (6.4)

21 - 0 - where: U = + +. Rerrnging equtions (6.3) nd (6.4) nd solving for E( r ) nd E( r ), yields : n q L, q + ( ) S D nα E r U + + U Er ( ) = n q n q q + U U U q L, q S D n(1 α) + E( r ) U U + n q n q q + U U U (6.5) n q L, q + (1 ) ( ) S D n α E r U + + U Er ( ) = n q n q q + U U U q L, q S D nα + E( r ) U U + n q n q q + U U U (6.6) Proposition 6: If dedicted nd opportunistic mngers long with locl investors comprise the types of investors demnding ssets nd, the effects of chnges in the expecttions of locl investor demnd will ffect the returns (nd prices) of both ssets, leding to contgion from one country to nother. In other words, if locl investors re expected to buy ssets in country (or ), portfolio reblncing will force equilibrium prices of both ssets nd to rise nd their expected returns to fll. Conversely, if locl investors re expected to sell ssets in country (or ),

22 - 1 - equilibrium prices of both nd will fll. This is simple yet powerful result tht shows tht locl investors in one mrket cn impct prices in ssets in countries unrelted through fundmentls, with the propgtion of contgion rising purely from the investors in the mrket. The model is lso ble to study the mgnitude of ech type of mnger s contribution to expected prices in the mrket with the shock nd the mrket without the shock. While the totl effect of reduction in demnd of either sset results in decrese in the price of both ssets, the mgnitude of the fll in price depends on the type of investor. If q (no opportunistic mngers) is equl to zero, equtions (6.5) nd (6.6) show tht neither sset is ffected by chnge in expected demnd of locl investors of the other sset. In other words, when t lest one emerging mrket sset underperforms csh, portfolio reblncing by dedicted mngers does not led to contgion or reverse contgion. However, from equtions (6.5) nd (6.6), it is observed tht the reblncing of dedicted mngers reblncing from n expected chnge in the locl investors demnd ffects the price of tht sset more thn the opportunistic mngers. The model lso predicts tht the equilibrium expected price for both ssets flls when there is n increse in the expected return of the mture mrket sset. Intuitively, ll else equl n increse in the return of the mture mrket sset would result in n outflow of emerging mrket ssets. It is observed in equtions (6.5) nd (6.6) tht if q = 0, then chnge in the expected return of the mture mrket sset does not ffect the expected price of either sset. While this result is not surprising given tht dedicted mngers re not llowed to invest in mture mrket ssets, it illustrtes tht restricting fund mngers set of investments cn lso hve ffects in mrkets tht would otherwise be unrelted.. Dedicted nger (ero Csh Holdings) nd Opportunistic nger This section exmines the equilibrium expected prices when dedicted mngers do not hold csh. Substituting the optiml portfolio lloctions to ech sset for ech type of investor nd plugging into (6.1) nd (6.) yields: S Er ( n ) Er ( ) q E r E r E r E r D nd L, = + α ( ) ( ) ( ) ( ) ( + ) U S Er ( n ) Er ( ) q Er Er Er Er D L, = + (1 α) ( ) ( ) ( ) ( ) ( + ) U Solving for the expected returns for ssets nd yields:

23 - - n q L, q + ( ) ( ) ( ) + S D n α + E r ( + ) U U Er ( ) = n q n q n q + ( ) ( ) ( + ) U ( + ) U ( + ) U n q L, q + S (1 ) D n α + Er ( ) ( + ) U + U n q n q n q + ( ) ( ) ( + ) U ( + ) U ( + ) U (6.7) n q L, q + ( ) (1 ) ( ) + S D n α + E r ( + ) U U Er ( ) = n q n q n q + ( ) ( ) ( + ) U ( + ) U ( + ) U n q L, q + S ( ) D n α + Er ( ) ( + ) U + U n q n q n q + ( ) ( ) ( + ) U ( + ) U ( + ) U (6.8) Proposition 7: If dedicted nd opportunistic mngers long with locl investors comprise the types of investors demnding ssets nd, chnges in the expecttions of locl investors demnd for n emerging mrket sset will ffect the returns (nd prices) of both ssets, leding to contgion from one country to nother. While this result is similr to the previous result, both dedicted mngers nd opportunistic mngers contribute to contgion. The coefficients of the locl investor demnd of the other sset hs n nd q in equtions (6.7) nd (6.8), implying tht both mngers portfolio reblncing results in contgion. Unlike the previous cse, the contribution to contgion by the dedicted mnger is greter thn the opportunistic mnger. Furthermore, the impct of chnges in the locl investor demnd of n sset on its own price is ffected more by the opportunistic investor. The equilibrium nlysis hs shed light on the mcroeconomic effects of trding strtegies of fund mngers. It is seen tht underlying reltionships between the risk-djusted expected returns of set of ssets ffects the contribution of ech type of mnger to contgion. The

24 - 3 - model suggests tht it is difficult to isolte prticulr type of plyer tht would increse contgion. V. CONCLUSION This pper develops model for modeling the investment strtegies of two min clsses of investment mngers dedicted nd opportunistic in emerging mrkets nd their interction in determining the equilibrium prices of finncil ssets. It demonstrtes tht the ggregtion of optiml micro-level behvior of fund mngers leds to mrket equilibri tht my devite from wht efficient mrkets my suggest, even in the bsence of symmetric informtion or regultory distortions. In prticulr, ssets of countries unrelted by fundmentl economic links or even by common externl shocks my become relted through the chnnel of mngers optimizing behvior nd the trde-offs they fce. This suggests tht contgion is often linked to the institutionl structure of mrkets. This pper mkes few key points which re consistent with mrket prctioners experience in the comovement of sset prices nd its link with the investor bse. First, different types of investment mngers with different investment objectives hve differentil effects on price dynmics in sset mrkets even in the bsence of informtionl symmetries or trnsctions costs. Second, the presence of incentives for fund mngers cn led to the systemtic devition of prices from their long-term fundmentls with no room for rbitrging wy the difference. Third, the presence of leverged investors who cn both go long nd short hs significnt impct on mrket vlutions, s well s on price dynmics s the cost of tht leverge increses. Fourth, while common externl fctors re lso shown to hve n impct on two emerging mrket ssets, pure contgion rising from noise trding in one country spilling over to nother country not linked through mcroeconomic fundmentls is n outcome of the optiml behvior of interntionl investors. Fifth, one type of fund mnger does not lwys crete more cross-border contgion thn nother type. The model predicts tht both types of mngers my contribute to contgion. In sum, this pper concludes tht fund mngers compenstion nd investment systems ber in them the seeds of contgion rising from technicl fctors, nd do not eliminte ll sources of contgion even in the presence of full informtion. The frmework of this pper could be pplied to other mrkets dominted by institutionl investors, such s mrkets within one country. For exmple, the interction between highyield fund mngers nd broder fixed income mngers, nd between equity mngers nd comingled stock nd bond fund mngers, could shed further light on the comovement of seemingly unrelted equity prices or high yield bonds, nd their interction with broder bond mrket prices. Policy responses tht improve the efficiency nd trnsprency of mrkets, s well s those tht help cope with voltility, will llevite but my not eliminte the phenomenon of contgion. res of future reserch could focus on the optiml incentive contrcts for

25 - 4 - different clsses of fund mngers, s well s the optiml construction of mrket indices s benchmrks for mngeril compenstion.

26 - 5 - REFERENCES nerjee, bhijit V. (199), Simple odel of Herd ehvior, Qurterly Journl of Economics 57, Clvo, Guillermo. nd Crmen. Reinhrt (1996), Cpitl Flows to Ltin meric: Is There Evidence of Contgion Effects, in Clvo, G.., Goldstein,., Hockretter, E. (eds), Privte Cpitl Flows to Emerging rkets, Institute for Interntionl Economics, Wshington DC. Clvo, Guillermo. nd Enrique G. endoz (000), Rtionl Contgion nd the Globliztion of Securities rkets, Journl of Interntionl Economics 51, Kminsky, Grciel L. nd Crmen. Reinhrt (000), On Crises, Contgion, nd Confusion, Journl of Interntionl Economics 51, Kminsky, Grciel L. nd Sergio L. Schmukler (1999), Wht Triggers rket Jitters?: Chronicle of the sin Crisis, Journl of Interntionl oney nd Finnce 18, Kodres, Lur E. nd tthew Pritsker (00), Rtionl Expections odel of Finncil Contgion, Journl of Finnce 6, Kyle, lbert S. nd Wei Xiong (001), Contgion s Welth Effect, Journl of Finnce 56, Schrfstein, Dvid S. nd Jeremy C. Stein (1990), Herd ehvior nd Investment, mericn Economic Review 80, Schinsi, Grry J. nd R. Todd Smith (1999), Portfolio Diversifiction, Leverge, nd Finncil Contgion, Interntionl onetry Fund Working Pper, WP/99/136.

27 - 6 - PPENDIX PPENDIX: PROOFS OF PROPOSITIONS Proof of Proposition 1: The Lgrngin for the optimiztion problem for the dedicted investor cn be written s follows: L = ( λ α) Er ( ) + ( τ 1 + α) Er ( ) + (1 λ τ) r ( ) ( ) [( λ α) ( τ 1 α) ] ϕ(1 λ τ). ssuming λ > 0 nd differentiting L with respect to λ, yields: Er ( ) r ϕ λ = + α. ssuming τ > 0 nd differentiting L with respect to τ, yields: Er ( ) r ϕ τ = + (1 α). Csh holdings will be: r E( r ) + ϕ r E( r ) + ϕ 1 λ τ = +. The complementry slckness condition nd the non-negtivity constrint for the Lgrnge multiplier ssocited with the no borrowing constrint re: ϕ(1 λ τ) = 0 nd ϕ 0. Thus, if the constrint does not bind, i.e. λ + τ < 1, then the multiplier must be ϕ = 0. lterntively, if the multiplier is positive ϕ > 0, the constrint must be binding, i.e. λ + τ = 1. Suppose tht ϕ > 0 nd λ + τ = 1. The optiml vlue of ϕ cn be derived s: ( Er ( ) r ) ( ( ) + Er r ) ϕ =, + which is positive whenever:

28 - 7 - PPENDIX Er ( ) r Er ( ) r + > 0. Then, solving for the optiml portfolio weights, yields: * Er ( ) Er ( ) λ = + α, ( + ) * Er ( ) Er ( ) τ = + (1 α). ( + ) Csh holdings will be zero becuse λ + τ = 1. Now, suppose tht λ + τ < 1 nd ϕ = 0, which is equivlent to: Er ( ) r Er ( ) r + < 0. (6.9) This condition holds only if the expected return on t lest one of the emerging mrket ssets is lower thn the return on csh. On the other hnd, λ > 0 nd τ > 0 imply tht: + α > 0, (6.10) + (1 α) > 0. (6.11) When condition (6.9) is stisfied long with conditions (6.10) nd (6.11), the optiml portfolio weights re: ** λ = + α, ** τ = + (1 α),

29 - 8 - PPENDIX ( ) ( ) ** ** +, whenever 0 < λ < 1 nd 0 < τ < 1, ** ** 1 -, whenever 0 1 nd 0, ** α < λ < τ = λ δ = Er ( ) r ** ** 1 -(1- α), whenever λ = 0 nd 0 < τ < 1, (1 ) r E r r E r λ = τ = ** ** 1, whenever 0 nd 0. Finlly, one needs to verify tht the vlue of the objective function V ( λ **, τ ** ) greter thn V (0,0) when + α > 0 nd + ( 1 α ) > 0. is indeed The vlue of the objective function when λ = 0, τ = 0 is: ( ) 1 V ( 0,0 ) = r ( α E( r ) + ( 1 α) E( r )) ( α) + ( 1 α), nd the vlue of the objective function when λ > 0 nd β > 0 : ( λτ, ) = λ( ( ) ) + τ( ( ) ) + ( α ( ) + ( 1 α) ( )) V Er r Er r r Er Er (( λ α) ( ) ) τ α Note tht V (, ) V ( 0,0) λτ > whenever: 1 1 λ ( Er r ) ( λ α) + τ ( Er r ) ( τ α ) > ( ) ( ) (1 ) 0 Knowing tht λ > 0 nd τ > 0, then: ( Er r ) ( ) ( ) 1 1 λ α > + α > λ. ( ) 0 whenever. Plugging in λ ** = + α results in which holds by ssumption. + α > 0

30 - 9 - PPENDIX 1 1 ( ) (1 ) > 0, whenever + (1 α) > τ ( Er r ) τ ( α ) = + results in which holds by ssumption. ** Plugging in τ ( 1 α ) + (1 α) > 0 Proof of Proposition : When t lest the return on one emerging mrket sset is negtive, the optiml portfolio weights re: * λ = + α, (6.1) * τ = + (1 α), (6.13) r E( r ) r E( r ) * λ τ = +. (6.14) (1 ) The behviorl chrcteristics of dedicted mngers to chnges in prmeter vlues re summrized s the following:. If E( r ) > r or E( r ) > r, the mnger will go overweight sset ( λ > α ) or sset ( (1 λ) > (1 α) ), respectively. Conversely, if E( r ) < r or E( r ) < r, or both, the mnger will be underweight sset ( λ < α ) nd/or sset ( (1 λ) < (1 α) ), but will not necessrily hold zero of either sset. From eqution (6.1), observe tht if the E( r ) > r nd E( r ) < r, λ > α. If E( r ) < r, the dedicted mnger holds positive quntities of sset if: < α.

31 PPENDIX Similrly, if E( r ) > r nd E( r ) < r, the dedicted mnger is overweight sset ( τ > (1 α) ), s seen in eqution (6.13). If E( r ) < r, the dedicted mnger holds positive quntities of sset if: < (1 α). b. s the weight of sset in the benchmrk index α rises, mnger who is overweight the sset will increse her exposure further by mintining the overweight. mnger who is underweight the sset will lso increse her exposure, but mintin the underweight. From eqution (6.1), if α increses so does λ. If λ > α, the first term in eqution (6.1) is positive. If α increses, the mnger increses her holdings of sset. If λ < α, the first term in eqution (6.1) is negtive, the mnger increses her exposure to sset but λ < α still holds. Similrly, n increse in α would led the mnger to decrese her holdings of sset s seen from eqution (6.13). If the mnger is underweight or overweight sset, the mnger mintins the underweight or overweight. c. s the risk version coefficient () rises, the demnd for sset or flls, if the mnger is overweight the sset. If the mnger is underweight the sset, n increse in () reduces the underweight. s () increses the mgnitude of the first term in equtions (6.1) nd (6.13) decreses confirming tht s () increses, the mnger will reblnce her portfolio towrds the index. d. s or rises, the demnd for sset or flls if the mnger is overweight the sset. If the mnger is underweight the sset s or increses, the mnger reduces her underweight. From equtions (6.1) nd (6.13), s or increses, the mgnitude of the first term decreses confirming tht mnger will reblnce her portfolio towrds the index. e. n increse in (), hugging of the index. or,my reduce the demnd for csh resulting in greter From eqution (6.14), observe tht (1 λ τ ) is only positive when E( r ) < r or E( r ) < r. The prtil derivtive of (1 λ τ ) with respect to () is: (1 λ τ) ( r E( r )) ( r E( r )) = + < 0, (6.15) ( ) ( )

32 PPENDIX when E( r ) < r nd E( r ) < r. Eqution (6.15) is lso negtive when E( r ) < r nd: ( r E( r )) ( r E( r )) >. ( ) ( ) Finlly, eqution (6.15) is negtive when E( r ) < r nd: ( r E( r )) ( r E( r )) >. ( ) ( ) The prtil derivtive of (1 λ τ ) with respect to is: (1 λ τ) ( r E( r )) = < 0, ( ) if E( r ) < r. The prtil derivtive of (1 λ τ ) with respect to is: (1 λ τ) ( r E( r )) = < 0, ( ) if E( r ) < r. Thus, increses in (), or my result in reduction of csh holdings by mngers under certin conditions. Proof of Proposition 3: When the sum of the risk-djusted excess returns on emerging mrkets is positive, the optiml portfolio weights re: * Er ( ) Er ( ) λ = + α, (6.16) ( + )

33 - 3 - PPENDIX * Er ( ) Er ( ) τ = + (1 α). (6.17) ( + ). The dedicted mnger overweights the sset with the higher expected return nd underweights the sset with the lower expected return. If E( r ) > E( r ), the first term on the right hnd side of eqution (6.16) is positive nd similrly the first term on the right hnd side of eqution (6.17) is negtive. b. n increse in () would result in lloctions closer to the index. If the mnger is underweight n sset, n increse in () would result in the mnger incresing her exposure of tht sset nd decresing her exposure of the other sset. Similrly, if the fund mnger is overweight n sset n increse in () would result in decrese in exposure of tht sset nd n increse in exposure of the other sset. In equtions (6.16) nd (6.17), the first term on the right hnd side (the mgnitude wy from the index) decreses in mgnitude implying tht the mnger would reblnce towrds the index lloctions. c. n increse in or reduces the size of the overweight/underweight positions, forcing the mnger to move closer to the benchmrk index. In equtions (6.16) nd (6.17), the first term on the right hnd side decreses in mgnitude s or increses confirming tht mngers would reblnce towrds the index lloctions. Proof of Proposition 4: The opportunistic mnger solves the following optimiztion problem: mx φer ( ) + δer ( ) + (1 φ δ) Er ( ) φ + δ + (1 δ φ) φδ,. (6.18) The first order conditions for the optimiztion problem (6.18) with respect to φ nd δ re: nd Er ( ) Er ( ) = φ + ( φ+ δ 1) Er ( ) Er ( ) = δ + ( φ+ δ 1). * * * Solving for the optiml portfolio lloctions, φ, δ, nd (1 φ δ ) yields: