Thursday July 23, 2009 MS&E247s International Investments Handout #13 Page 1 of 16

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1 MS&E247s Inernaional Invesmens Handou #13 Page 1 of 16 Reading Assignmens for his Week TTh 3:15-4:30 Gaes B01 Thursday, July 23, 2009 Final Exam MS&E 247S Fri Aug :15PM-3:15PM Gaes B01 Or Saurday Aug :15PM-3:15PM Gaes B01 Remoe SCPD paricipans will also ake he exam on Friday, 8/14/09 Please Submi Exam Procor s Name, Conac info as SCPD requires, also c.c. o ffuy@sanford.edu a week before he exam. Local SCPD sudens please come o Sanford o ake he exam. Ligh refreshmens will be served on Aug 14, Handou #13 Inernaional Asse Porfolios Bond Porfolios hp://sanford2009.pageou.ne Levich Luenberger Solnik Fabozzi Wooldridge Scan Read Chap 14 Pages Bond Porfolios Chap Pages Chap Pages Chap 22 Pages , esp Acive Bond Porfolio Mgm Sraegies Chap Pages 14-2 Inernaional Asse Porfolios Bond Porfolios MS&E 247S Inernaional Invesmens Yee-Tien Fu Reurn and Risk in Naional Bond Markes We assume ha our invesor reas he US$ as his base currency (he numeraire currency used by he invesor for measuring performance). In general, he reurn on a foreign bond, as measured in US$ erms, has 3 componens: 1 Ineres income earned or accrued. 2 The capial gain or loss on he bond, resuling from he inverse relaionship beween ineres raes and bond prices. 3 The foreign exchange gain or loss, applied o he above wo iems Calculaing Unhedged Reurns in US$ Terms B - he iniial purchase price of he bond in foreign currency (FC) erms S - he spo exchange rae, in $/FC erms, on he purchase dae Afer one monh: B +1 - he value of he bond afer one monh, represening he iniial bond price plus he price change over he monh ( +1 ) plus accrued ineres (C +1 ) Calculaing Unhedged Reurns in US$ Terms Therefore: B S - he US$ purchase price of he foreign bond B +1 S +1 - he value of he bond afer one monh in US$ erms, where B 1 B 1 C 1 Noe ha: If ineres raes rise, bond prices fall ( +1 < 0). If ineres raes fall, bond prices rise ( +1 > 0). 14-6

2 MS&E247s Inernaional Invesmens Handou #13 Page 2 of 16 Yield o Mauriy Ineres rae ha makes he presen value of he bond s paymens equal o is price Solve he bond formula for r T C P ParValue B (1 r ) (1 r T ) 1 T 14-7 Calculaing Unhedged Reurns in US$ Terms The coninuous rae of reurn on he foreign bond measured in US$ and on an unhedged basis is: B S B S R U B FC S $, ln( ) ln( ) ln( 1 ) US$,FC (14.1) B S B S Therefore he unhedged US$ reurn on he foreign bond has wo pieces: 1 he reurn on he bond in foreign currency erms (B FC ); and 2 he reurn on he foreign currency used o buy he bond S US$,FC ) Calculaing Unhedged Reurns in US$ Terms Calculaing Unhedged Reurns in US$ Terms Noe ha he reurn on he bond in foreign currency erms is uncerain because of he possible capial gain or loss on he bond. Bu he reurn measured in US$ has an addiional source of uncerainy, he foreign exchange gain or loss. The variance of he reurns in equaion (14.1) reflecs he variance of each erm and he covariance beween he reurns on he foreign bond and he reurns on spo foreign exchange, or: ( ) ( B ) ( S ) 2Cov( B ; S (14.2) R$, U FC US$,FC FC US$, FC) Noe ha he covariance erm can be eiher posiive or negaive, as shown in Table Currency and Bond Marke Reurns Combinaions Currency Marke Reurns and Bond Marke Reurn Combinaions Bond Marke Reurns Table 14.2 Pg 496 Negaive Posiive Currency Marke Reurns Negaive FC ineres raes Spo FX (A) FC ineres raes Spo FX (D) Posiive FC ineres raes Spo FX (C) FC ineres raes Spo FX (B) Spo FX has he dimension of $/, hence measures he value of Cases A and B have a Fisherian foundaion. For Case A, a forecas of fuure inflaion may raise ineres raes (bond marke losses), Fisher Effec (Fisher Closed) i DM = r DM + E( P Germany) and depress he foreign exchange rae (currency marke losses). Inernaional Fisher Effec (Fisher Open) i $ - i DM = E( Spo) 14-12

3 MS&E247s Inernaional Invesmens Handou #13 Page 3 of 16 Currency and Bond Marke Reurns Combinaions Cases C and D resul in negaive covariance beween currency and bond marke reurns. Case C corresponds o a igh moneary policy ha raises ineres raes (bond marke losses) bu aracs foreign capial and appreciaes he exchange rae (currency marke gains). Case D suggess a low ineres rae environmen (bond marke gains) ha encourages an ouflow of funds and a weaker currency marke (currency marke losses) Currency and Bond Marke Reurns Combinaions If foreign ineres raes are headed down, he manager may wan o buy foreign bonds. Bu if lower ineres raes imply a weaker currency (case D), he manager mus weigh his possibiliy and consider a hedge o limi currency losses Calculaing Currency-Hedged Reurns in US$ Terms Afer buying he foreign bond a a price B, one possible sraegy is o sell all fuure coupon paymens forward in exchange for US$ as well as sell he final reurn of principal forward. This sraegy is much like a currency swap ha eliminaes all currency risks and ransforms his foreign bond ino a US$ bond The Basic Cash Flows of a Currency Swap Firms A and B can each issue a 7-year bond in eiher he US$ or SFr marke. Firm A Firm B US$ finance 10% 11.5% SFr finance 5% 6% Difference (A-B) -1.5% -1.0% -0.5% Firm A has a comparaive advanage in borrowing US$ while firm B has a comparaive advanage in borrowing SFr. By borrowing in heir comparaive advanage currencies and hen swapping, lower cos financing is possible. Figure 13.2 Pg The Basic Cash Flows of a Currency Swap A Borrows $ a 10% $ a 0 SFr a % (US$) 5.5% (SFr) $ a 7 SFr a 7 Togeher, A and B save 0.5 percen. Noe ha if a bank or swap dealer inermediaes he ransacion and charges a fee, he aggregae ineres savings will be reduced. Figure 13.2 Pg 453 B Borrows SFr a 6% Suppose our invesor sells a one-monh forward currency conrac (priced a F ) for an amoun equal o nex monh s esimaed value of he bond wih accrued ineres,, where : Bˆ 1 Bˆ B ˆ C If our invesor guesses righ, and B 1 Bˆ 1, hen he has made a perfec hedge. The US$ value of his foreign bond is Bˆ 1 F and he coninuous rae of reurn measured in US$ is: Bˆ ˆ 1F B 1 F R ln( ) ln( ) ln( ) ˆ $, H * BFC FUS$,FC (14.3) BS B S where he H * subscrip indicaes a perfec hedge

4 MS&E247s Inernaional Invesmens Handou #13 Page 4 of 16 The reurn also has wo pieces: R $,H * The reurn on he bond in foreign currency erms ( ˆB FC ) plus he one-monh forward premium ( F US$,FC ). The variance of reurns in equaion (14.3) is: 2 2 ˆ 2 ( R ) ( ) ( ) Cov( ˆ $, H * BFC FUS$,FC 2 BFC; FUS$, FC) (14.4) 2 As an empirical maer, ( R$, H* ) should be less 2 han ( R ) because he volailiy of he $,U forward premium is far smaller han he volailiy of exchange rae changes Levich Figure 5.8A Forward Premium and Spo Rae Change $/DM One-Monh Forward Raes: Jan Jul Forward Premium and Spo Rae Change $/DM Three-Monh Forward Raes: Jan Jul 1990 Mos likely, our invesor canno perfecly predic he fuure price of he foreign bond. We define he predicion error as he acual minus he expeced bond price, or: B Bˆ ˆ The erm and is volailiy represen he ineres rae risk in he foreign bond marke. If 0 1, our hedge amoun was oo small and he unexpeced (posiive) excess value of he bond is valued a S +1 and we need o sell he unexpeced addiional funds in he marke a S +1. Levich Figure 5.8B Conversely, if 1 0, our hedged amoun was oo large (we oversold foreign currency forward) and we need o buy unexpeced addiional funds in he marke a S +1. In general, once he value of he fuure exchange rae is known, we measure he coninuous rae of reurn on he foreign bond measured in US$ and on a currency-hedged basis as: Bˆ 1F 1S 1 R$, H ln( ) ln( ) BS BS Bˆ 1 F 1S 1 ln( ) ln( ) ln( ) (14.5) B S BS ˆ 1S 1 BFC FUS$,FC ln( ) B S Bˆ 1F 1S 1 R$, H ln( ) ln( ) BS BS Bˆ 1 F 1S 1 ln( ) ln( ) ln( ) (14.5) B S BS ˆ 1S 1 BFC FUS$,FC ln( ) B S In order o allow for he possibiliy ha 1 may be negaive, we need o modify he definiion of he hedged US$ reurn in equaion (14.5) on page

5 MS&E247s Inernaional Invesmens Handou #13 Page 5 of 16 ˆ ln B 1F 1S 1 R $, H (14.5a) BS BS ˆ B 1F ln 1S 1 1 (14.5b) B ˆ S B 1F ˆ B 1F ln ln 1S 1 1 (14.5c) ˆ BS B 1F Using equaion (14.5c), we can allow for cases where 0 1. The formula produces sensible answers, and i is sill valid o hink of he hedged reurn as he sum of hree pieces: he prediced price change of he bond, he forward premium, and he residual unprediced price change of he bond. Wih 0 1, we sill have he resul ha he perfecly hedged porfolio earns a consan (known reurn) and no error variance Equaion (14.5) shows he reurn on a currencyhedged foreign bond. This reurn has hree pieces: (1) he reurn from he prediced price change on he bond in foreign currency erms, (2) he forward premium (or discoun) on he foreign currency used o buy he bonds, and (3) a residual erm represening he unprediced price change in he foreign bond ha is valued a he fuure uncerain spo exchange rae. Noice ha he US$ reurns on he firs wo pieces are cerain, because he prediced end-of-monh value of he bond has been sold forward a a price F. The primary source of uncerainy ( 1 ) sems from our inabiliy o predic B and 1 1 wih cerainy because of ineres rae risk in he foreign bond marke. The variance of reurns for he currency-hedged bond in equaion (14.5) is now: R S 1 2 ) ( BS 2 ( $, H 1 2 ) (14.6) Equaion (14.6) is a condiional variance, 2 condiional on S. In general, 1 S 1 ( R$,H ) 2 depends on he combined effecs of ( and 1) 2 ( S. 1) 2 2 S 1 2 ( R ) ( $, H 1) (14.6) ( BS ) If here were no ineres rae risk, hen he predicion of B is perfec, and In his special case, here is no residual elemen associaed wih ineres rae risk. Thus, he US$ reurns on he currency-hedged bond are given wih cerainy. Variance of reurns in his case is zero Calculaion of Prices and Reurns for a Five-Year German Bund on an Unhedged Invesmen The 5-year German Bund is priced a par wih a 4.00% coupon paid annually. The iniial spo exchange rae S 0 = $0.65/DM, so he purchase of a DM1 million bond requires an oulay of 1,000,000x0.65 = $650,000. A he end of year 1: Suppose i DM falls o 3.75%, spo DM weakens o $ Each coupon paymen is 1,000,000x.04 = DM40,000. DM bond price 40, , , , 000 1, 000, , 009, Box 14.1

6 MS&E247s Inernaional Invesmens Handou #13 Page 6 of 16 Calculaion of Prices and Reurns for a Five-Year German Bund on an Unhedged Invesmen So, in DM erms, he reurn for he firs year 1,009, ,000 ln % 1,000,000 Since he spo DM has weakened o $0.625, he bond s US$ value is 1,009,128.46x0.625 = $630,705.29, and he coupon value is 40,000x0.625 = $25,000. So, in US$ erms, he firs year reurn ha reflecs he coupon and exchange rae loss 630, ,000 ln % 650,000 Calculaion of Prices and Reurns for a Five-Year German Bund on a Currency-Hedged Invesmen The 5-year German Bund is priced a par wih a 4.00% coupon paid annually. The DM is a roughly a 1% forward premium, and slighly larger when DM ineres raes fall. Esimae of he expeced fuure bond price = previous value of he bond plus he coupon paymen. Box Box Calculaion of Prices and Reurns for a Five-Year German Bund on a Currency-Hedged Invesmen German Spo Forward Year Ineres Rae Rae % % % % For he firs year: The iniial bond value = DM1,000,000. Wih DM40,000 of ineres expeced, he invesor hedges by selling DM1,040,000 forward a $0.6560/DM, resuling in 1,040,000x = $682,240. Box Calculaion of Prices and Reurns for a Five-Year German Bund on a Currency-Hedged Invesmen Because DM ineres raes dropped, he bond price rose o DM1,009,128 (underhedged by he amoun of DM9,128). The addiional DM9,128 mus be marked o marke a he curren spo rae, which gives a US$ value of 9,128x0.625 = $5,705. The oal rae of reurn over he firs period is hus Box , ln % 650, Cenral Bank Risk vs Ineres Rae Risk Ineres rae risk refers o uncerainy abou fuure ineres raes ha inroduces he possibiliy for capial gains and losses on longerm bonds. Cenral bank risk refers o uncerainy abou he naional moneary auhoriy o deliver moneary policy ha resuls in a paricular level of ineres rae risk Acive Hedging vs Passive Hedging Sraegies Wha are he heir advanages? In a passive hedging sraegy, he invesor follows he same hedging plan over ime independen of marke condiions. For example, rules whereby he invesor always hedges 100%, or always hedges 10%. Wih acive hedging, he amoun hedged flucuaes. A passive sraegy is a low-cos means of reducing exposure o risks. The invesor is sure o be proeced agains large negaive shocks, bu he also forgoes he opporuniies of large gains from posiive shocks. In an acive sraegy, he invesor reains risks during cerain periods. This offers he possibiliy of higher reurns if he invesor has experise in judging when o hedge and when no o hedge

7 MS&E247s Inernaional Invesmens Handou #13 Page 7 of 16 Three Types of Acive Sraegies Currency-driven invesmen sraegy places he focus on finding good performing currencies and buy safe asses (e.g., governmen bonds) denominaed in ha currency. The obvious way o speculae on a currency view is o ake a posiion in foreign exchange spo, forward, or fuures conracs. If he currency forecas is correc, he speculaion will be profiable Three Types of Acive Sraegies A second sraegy is o ignore currency when making inernaional invesmens, based on he premise ha he currency effecs cancel ou over he long run. If he invesor has experise in picking good socks or bonds, his experise will be awarded. Wha if he socks or bonds are denominaed in a foreign currency? If he forward rae and fuure spo rae are equal, on average, he invesor can hedge his currency risk wihou sacrificing longerm reurns Three Types of Acive Sraegies A final sraegy is he ulraselecive approach, in which he invesor picks only hose siuaions where boh posiive foreign bond and currency reurns are expeced. This calls for eiher shor posiions in unhedged bonds (Case A in Table 14.2), when boh bonds and currency are expeced o weak, or long posiions in unhedged bonds (Case B), when boh bonds and currency are expeced o srenghen. Currency Marke Reurns and Bond Marke Reurn Combinaions Bond Marke Reurns Negaive Posiive Currency Marke Reurns Negaive FC ineres raes Spo FX (A) FC ineres raes Spo FX (D) Posiive FC ineres raes Spo FX (C) FC ineres raes Spo FX (B) Table 14.2 Pg While his approach may be successful, i is far oo limiing. The invesor passes up favorable bond markes when he currency is expeced o weaken (Case D), and passes up favorable currency plays when profiable foreign socks or bonds canno be idenified (Case C). Our analysis demonsraes ha he currency and ineres rae risk dimensions of an inernaional bond porfolio are separable invesmens. We show his in Table 14.5 for a world wih hree counries and hree currencies. An invesor who waned o inves in U.S. bonds bu hold an exposure o currency risk would buy U.S. Treasuries and currency hedge hem ino (cell A) by selling US$ forward for Ineres Rae Risk Table 14.5 Pg 508 The Expanded Opporuniy Se of Naional Bond Markes Currency Risk and Ineres Rae Risk Dimensions Unied Saes Germany Japan Currency Risk US$ DM U.S. Treasury Bond German Bund: Currency hedged o $ JGB: Currency hedged o $ U.S. T-Bond: Currency hedged o DM German Governmen Bond (Bund) JGB: Currency hedged o DM U.S. T-Bond: Currency hedged o German Bund: Currency hedged o Japanese Governmen Bond (JGB) 14-42

8 MS&E247s Inernaional Invesmens Handou #13 Page 8 of 16 Wha are he key elemens o ake ino consideraion when invesing in an inernaional bond porfolio? The firs crierion is selecing a marke wih no conrols on capial ouflows. Oher insiuional consideraions - marke size, liquidiy, axaion - play a role. Acive porfolio decisions are made on he basis of esimaed risk and reurn. The invesor can hedge a large porion of he currency risk in foreign bonds if liquid shor-erm currency forward markes are available Efficien Froniers of Unhedged and Currency-Hedged Global Bond Porfolios Average Reurn (% per annum) Figure 14.4 Pg Global Porfolio Hedged Porfolios Global Porfolio Unhedged Porfolios Dollar Porfolio Risk: Sandard Deviaion of Reurns Abou Figure The sample period is January December 1990, monhly daa. Securiies are 10-year governmen bonds issued by he Unied Saes, Canada, Germany, Japan, and he Unied Kingdom. The unhedged global porfolio is an equally-weighed porfolio of non-u.s. securiies. The hedged global porfolio is based on one-monh forward currency conrac, rolled over monhly. The end poins of he fronier represen 100 percen in U.S. bonds or 100% in global bonds. Inerior poins on he fronier represen 90/10, 80/20, 70/30, ec. combinaions Average Reurn (% per annum) Figure 14.5 Pg 510 Efficien Porfolio Froniers wih Acive and Passive Hedges Global Porfolio Hedged Porfolios + Currency Overlay Sraegy x Tacical Hedge Sraegy Unhedged Porfolios Global Porfolio Dollar Porfolio Risk: Sandard Deviaion of Reurns Abou Figure The sample period is Jan Dec. 1990, monhly daa. Securiies are 10-year governmen bonds issued by U.S., Canada, Germany, Japan, and U.K.. The unhedged global porfolio is an equally-weighed porfolio of non-u.s. securiies. The hedged global porfolio is based on one-monh forward currency conrac, rolled over monhly. The acical hedge porfolio acively hedges a percenage of he global porfolio based on he signals from 10 echnical rading rules. The overlay porfolio reflecs he performance of he hedged global porfolio combined wih a currency fund acively managed based on he signals from 10 echnical rading rules A acical hedging sraegy is one where he percenage of currency fuures o sell for currency I (P T,I ) based on he 10 echnical rules is deermined by he formula: P T,I = [10 - (N L,I -N S,I ) ] x 10%, for N L,I >= 5 = 100% for N L,I <= 4 where N L,I and N S,I are he number of echnical rules advocaing long and shor currency posiions respecively. The currency overlay sraegy is acually a combinaion of wo separae invesmens: (1) a foreign currency bond posiion ha is always hedged agains currency risk, and (2) a currency posiion governed by he rading rule P I = [(N L,I -N S,I ) ] x 10%. If all rading rules recommend a long (shor) posiion he currency overlay sraegy will be 100% unhedged (overhedged o become ne 100% shor in he foreign currency)

9 MS&E247s Inernaional Invesmens Handou #13 Page 9 of 16 Assignmen from Chaper 14 Exercises 1, Hins: Hins:

10 MS&E247s Inernaional Invesmens Handou #13 Page 10 of 16 Fixed Income Securiies: Analyics and Derivaives Individual Bond Sraegies: Barbells Sraegy Ladders Sraegy Bulles Sraegy Ladders Ladders Sraegy Ladders are a popular sraegy for saggering he mauriy of your bond invesmens and for seing up a schedule for reinvesing hem as hey maure. A ladder can help you reap he ypically higher coupon raes of longer-erm invesmens, while allowing you o reinves a porion of your funds every few years. Example: Ladder sraegy You buy hree bonds wih differen mauriy daes: wo years, four years, and six years. As each bond maures, you have he opion of buying anoher bond o keep he ladder going. In his example, you buy 10-year bonds. Longer-erm bonds ypically offer higher ineres raes Ladders Sraegy Barbell Sraegies Barbells Ladders are popular among invesors who wan bonds as par of a long-erm invesmen objecive, such as saving for college uiion, or seeking addiional predicable income for reiremen planning. Ladders have several poenial advanages: 1. The periodic reurn of principal provides he invesor wih addiional income beyond he se ineres paymens. 2. The income derived from principal and ineres paymens can eiher be direced back ino he ladder if ineres raes are relaively high or invesed elsewhere if hey are relaively low 3. Ineres rae volailiy is reduced because he invesor now deermines he bes invesmen opion every few years, as each bond maures 4. Invesors should be aware ha laddering can require commimen of asses over ime, and reurn of principal a ime of redempion is no guaraneed Barbells are a sraegy for buying shor-erm and long-erm bonds, bu no inermediae-erm bonds. The long-erm end of he barbell allows you o lock ino aracive long-erm ineres raes, while he shor-erm end insures ha you will have he opporuniy o inves elsewhere if he bond marke akes a downurn. Example: Barbell sraegy You see appealing long-erm ineres raes, so you buy wo long-erm bonds. You also buy wo shor-erm bonds. When he shor-erm bonds maure, you receive he principal and have he opporuniy o reinves i Bulles Bulles Sraegies Consrucing he Theoreical Spo Rae Curve for Treasuries Bulles are a sraegy for having several bonds maure a he same ime and minimizing he ineres rae risk by saggering when you buy he bonds. This is useful when you know ha you will need he proceeds from he bonds a a specific ime, such as when a child begins college. Example: Bulle sraegy You wan all bonds o maure in 10 years, bu wan o sagger he invesmen o reduce he ineres rae risk. You buy he bonds over four years

11 MS&E247s Inernaional Invesmens Handou #13 Page 11 of 16 Consrucing he Theoreical Spo Rae Curve for Treasuries Z 1 = 5.25/2 A defaul-free heoreical spo rae curve can be Z 2 = 5.50/2 consruced from he yield on Treasury securiies. The Treasury issues ha are candidaes for inclusion are (i) on-he-run Treasury issues, (ii) on-he-run Treasury issues and seleced off-he-run Treasury issues, (iii) all Treasury coupon securiies, and bills, and (iv) Treasury coupon srips. Afer he securiies ha are o be included in he consrucion of he heoreical spo rae curve are seleced, he mehodology for consrucing he curve mus be deermined. If Treasury coupon srips are used, he procedure is simple, because he observed yields are he spo raes. If he on-he-run Treasury issues wih or wihou seleced off-he-run Treasury issues are used, a mehodology called boosrapping is used Z 1 = 5.25/2 Z 2 = 5.50/

12 MS&E247s Inernaional Invesmens Handou #13 Page 12 of 16 Theoreical Spo Rae Curve for Treasuries Source: Fabozzi, Pages Try quesions 13 and 14 in Chaper 5 of Fabozzi Source: Fabozzi Chaper 22, Pages

13 MS&E247s Inernaional Invesmens Handou #13 Page 13 of

14 MS&E247s Inernaional Invesmens Handou #13 Page 14 of 16 Try quesions 15 and 18 in Chaper 22 of Fabozzi. Source: Fabozzi Chaper 6, Pages Try quesion 2 in Chaper 6 of Fabozzi

15 MS&E247s Inernaional Invesmens Handou #13 Page 15 of 16 Source: Fabozzi Chaper 11, Pages

16 MS&E247s Inernaional Invesmens Handou #13 Page 16 of Try quesion 20 in Chaper 12 of Fabozzi. Source: Fabozzi Chaper 12, Pages