Portfolio Strategies for hedging against Rand weakness

Transcription

1 Portfolo Strateges for hedgng aganst Rand weakness GDI Barr, C Holdsworth and BS Kantor* Unversty of Cape Town November 2006 * respectvely, Professor n the department of Statstcal Scences, graduate researcher n the department of Statstcal Scences and Professor of Economcs.

2 1. Introducton and Summary Barr, Holdsworth & Kantor Portfolo Strateges for hedgng aganst Rand weakness (Nov 2006) ~2~ The volatlty of the Rand over the last twenty-fve years has made most South Afrcans aware of the rsk of holdng Rand denomnated assets. In ths paper we show how optmsed strategc equty postons on the Johannesburg Stock Exchange (JSE) may gve protecton aganst Rand weakness. We frst consder how portfolo strateges may be used to hedge aganst South Afrcan exchange rate volatlty n general (wth a partcular focus on the dollar Rand exchange rate) as well as how strateges may be used to optmse portfolos under expectatons of ether future strengthenng or weakenng of the Rand. However, snce the prmary focus has been on protecton aganst Rand weakness we then formulate, test and compare the Rand hedge characterstcs of JSE portfolos (usng Top40 components) whch are optmsed to mantan foregn currency value n the face of Rand deprecaton aganst well known Rand hedge portfolos such as the ITRIX exchange funds whch track the FTSE100 n rand terms. The portfolos were re-estmated annually each July from 2003 to 2005 usng the prevous four and a half years of monthly data and were evaluated over the next 12 months, both for the entre 12 months and for subsectons of the 12 months. The results showed that t s possble to form domestc portfolos that gve consstent protecton aganst a R/$ deprecaton. 2. The Hstory of SA exchange rate movements South Afrca over the last twenty-fve years has been charactersed by perods of exchange rate volatlty and, apart from a recent perod from early 2002 to late 2005, long perods of nomnal and real Rand weakness. In Fgure 1, we demonstrate and compare the behavour of the real R/$ exchange rate and the nomnal R/$ exchange rate over the perod when the rand has traded as a managed float and over some sub-perods wth an assocated freely traded Fnancal Rand. In August 1985, t s seen that the rand was subject to a severe real and nomnal shock when the former Natonalst government ressted any change to democratc rule n South Afrca and severely dsapponted fnancal markets. As a result foregn captal was wthdrawn on a very large scale, and the exchange rate weakened sharply. An exchange rate shock of equvalent magntude to that experenced n 1985 occurred n

3 ~3~ November and December of 2001 when the rand fell sharply but n ths case the explanaton for the shock was much less obvous and has largely defeated offcal attempts to explan t. 1 The volatlty of the nomnal and the real rand over the more recent perod; s of partcular nterest. Over ths perod the nomnal (and real) Rand frst collapsed and then systematcally recovered. Note that snce the dfference n the rates of nflaton between South Afrca and ts tradng partners has generally been of the order of 5% (or lower) over ths perod, the actual dfference (n percentage changes) between the real and nomnal exchange rate has been small. Ths leads to the mportant realsaton that most of the exchange rate movement (agan nomnal or real) represents movements whch one could classfy as real shock, rather than stemmng from nflaton rate dfferences. By defnton, such real shocks consttute unexpected movements n the exchange rate and ths s exactly the type of movement that portfolo strategsts would want to hedge aganst. Fgure 1: Real and nomnal rand exchange Rates Source: South Afrcan Reserve Bank 1 See the Myburgh Commsson of Enqury nto the collapse of the rand n (The commsson s report s avalable at We have ascrbed the rand s collapse to a panc demand for foregn exchange from wealthy ndvduals wth newly found access to hard-currency assets made avalable through the asset swap mechansm. Effectvely the only lmts mposed on these demands for US dollars were the Rands ndvduals could muster for the purpose. We descrbe ths panc demand for US dollars as one of the unntended effects of partal exchange control reform (see Kantor and Marchett (2003).

4 R/$ (n Fn. Rand where applcable) JSE Index Barr, Holdsworth & Kantor Portfolo Strateges for hedgng aganst Rand weakness (Nov 2006) ~4~ 2.1 The lnk between the Rand exchange rate and the JSE The level of the JSE n current prces and the Rand exchange rate are obvously lnked because both are smultaneously affected by South Afrcan nflaton. If one consders the relatonshp snce 1980 t s seen that the JSE has tracked the R/US$ exchange rate qute closely over the perod untl recently, mplyng a farly long-run equlbrum value of the JSE measured n US dollars over the 26 year perod examned. It s worth notng that at year-end 2002 the JSE was only about 20% hgher n dollars than n the early eghtes and snce the real exchange rate n dollars has declned about 20% over the same perod, the JSE had barely kept up wth nflaton up to In comparson, the US market has shown spectacular real growth over the same perod. However, snce 2002 the JSE has more than trpled n Rand value and has ncreased fve fold n dollar terms, closng the gap on the US market. Rand/$ exchange rate & the JSE All-share Index Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92 Jan-94 Jan-96 Jan-98 Jan-00 Jan-02 Jan-04 Jan-06 R/$ (n FR where applcable) JSE All-share Fgure 2: Rand/$ exchange rate and the JSE All-share Index Source: South Afrcan Reserve Bank Not all sectors of the JSE respond to exchange rate nnovatons n the same way and ndvdual companes are clearly affected n lne wth the market s perceptons on how real exchange rate changes would mpact on company operatng profts and dvdend flows. We frst examne how the ndvdual operatng characterstcs of lsted companes would determne the way n whch ther proftablty, and hence ther share prce, would be affected

5 ~5~ by exchange rate changes. We may n fact segment shares on the JSE nto four broad categores followng Barr and Kantor(2005); Rand leverage companes, that s those companes wth SA based operatons who sell nto foregn markets; Rand hedge companes, that s those companes wth foregn based operatons who sell nto foregn markets; Rand play companes, that s those companes wth SA based operatons who sell prmarly nto the SA market; Mxed companes, that s those companes whch have a mx of the above and are not clearly classfed nto ether of the three categorsatons above. The economc detals relatng to ths categorsaton s not central to ths paper but s gven n the appendx to ths paper. 3. Lterature Revew Barr and Kantor (2005) provded the framework for classfyng shares accordng to ther theoretcal exposure. They grouped shares nto three categores; Rand Play, Rand Hedge and Rand Leverage. Rand Plays had ther revenue stream and costs based domestcally (n Rands), Rand Hedges had ther revenues and costs prmarly based offshore (n foregn currency), Rand Leverage shares revenues were n foregn currency wth ther costs n Rands. Barr and Kantor then tested the followng regresson model for each share n the Top40 ndex: Rt 1 I1 t 2I2t where I 1t denotes the log percentage change on the R/$ exchange rate for tme t I 2t denotes the log percentage change on the Top40 ndex for tme t

6 ~6~ They found that, n general, the sgn of the R/$ corresponded to the drecton gven by the a pror classfcaton of share. Ths s an mportant result as t enables the a pror selecton of shares wth potentally postve R/$ Betas, mplyng beneft from a Rand deprecaton. Benson and Faff (2003) examned the exchange rate exposure of unlsted, Australan nternatonal equty funds from 1989 to 1999, a perod charactersed by large volatlty n the Australan Dollar (AUD). These funds typcally had more than 90% of ther assets nvested n nternatonal shares. Benson and Faff found weak evdence of exposure to the trade-weghted exchange rate. When blateral exchange rates were used nstead, the exposure to ndvdual currences was revealed and t was found that exposure was more prevalent for each of the currences than had prevously been estmated. The reason the trade-weghted exposure had been neglgble was that the exposure to the U.S. Dollar was n general the opposte sgn to the exposure to the other currences. Benson and Faff also found exchange rate exposure to be nconsstent between tme perods and reasoned that the decreasng exposure could be due to ncreased hedgng by frms as the AUD became more volatle. Ths research s useful n the South Afrcan context as t suggests that one s more lkely to fnd foregn exchange exposure n South Afrcan shares by usng an mportant blateral rate than by usng a trade weghted exchange rate. Ths dea was also tested by Domnguez and Tesar (2001), who usng multple blateral exchange rates nstead of a trade-weghted exchange rate to avod the possblty of averagng out exposure, found consderable exchange rate exposure when examnng companes based n Chle, France, Germany, Italy, Japan, The Netherlands, Thaland and the Unted Kngdom. They used. Loudon (1993) nvestgated the exchange rate exposure of 141 Australan companes, usng monthly data from 1984 to He found cross-sectonal dfferences n exposure, wth Resource companes beneftng from exchange rate deprecaton and Industrals ganng from an apprecaton. Ths confrms the noton of beng able to categorse shares wth respect to ther exposure to the exchange rate. Joron (1990) was arguably the frst to emprcally examne the exchange rate as an explanatory varable when modellng share returns. He examned the exposure of U.S.

7 ~7~ multnatonals to a trade-weghted exchange rate from 1971 to Although he was unable to fnd wdespread sgnfcance, Joron (1990) was able to reject the hypothess that exposure, measured by the exchange rate Beta, was zero for all multnatonals. 3.1 Model Formulaton and Nomenclature The focus of ths paper s the mplementaton of a methodology to hedge aganst a deprecaton n the exchange rate aganst the dollar by nvestng locally, specfcally n the JSE, and hence the problem s one of portfolo selecton. Gven the focus on the exchange rate, asde from the market, t was necessary to nclude a term for the R/$ exchange rate when modellng share returns. Followng Barr and Kantor (2005), ths paper reles on regressng the log returns of each of the Top40 shares aganst the log returns of the Top40 Index and R/$ exchange rate. In order to avod the problems assocated wth multcollnearty, the Top40 returns are orthogonalsed relatve to the R/$ exchange rate. Although the absence of multcollnearty s not a strct assumpton of Ordnary Least Squares regresson, multcollnearty can lead to nstablty n coeffcents, wth hgher assocated varances. Instablty of the R/$ would be a partcular problem n ths nstance as dfferent perods are used to form estmates of the betas and nstablty due to multcollnearty could make t very dffcult to examne the consstency of exchange rate exposure. The relatonshp between Top40 returns and nnovatons n the exchange rate can be represented as equaton (1). R Tt 0 1 R$ t c t (1) Where R $ t s the log return of the R/$ exchange rate at tme t R Tt s the log return of the orthogonalsed top40 ndex at tme t Regressng the top40 onto the exchange rate gves equaton (2)

8 ~8~ ˆ R Tt ˆ0 ˆ1 R$ t (2) R ˆ, denoted as R' Tt s orthogonal to the exchange rate and represents the fluctuatons Tt R Tt n the top40 not explaned by the exchange rate. Ths allows the log return on each share to be related to the movements of the exchange rate and the Top40 Index n the followng manner: Where R t s the log return of share at tme t R t 1 R R' $ t 2 Tt e t (3) Ths s a two-ndex model, where ndex means term and s not ndcatve of an actual ndex beng used, and s subject to the condtons, as shown n Elton, Gruber, Brown and Goetzmann (2000) and Sharpe (1970) 1) corr( e, e ) 0 t 2) corr( R, e ) 0 $ t 3) corr(r' Tt $ t jt t 4) corr( R,R',e ) 0 t Tt ) 0 j j Ths s very close to a prespecfed, two-ndex APT model. However, the methods used n ths paper do not requre the prcng of exchange rate exposure or the prcng of the Top40. All that s requred s the ablty to, a pror, select hedge shares, whch Barr and Kantor (2005) have shown to be possble and thus the prcng factors reman n the alpha term. For any gven portfolo where share consttutes (100*w )% of the portfolo, equaton (4) relates the log return of the portfolo to the log returns of the exchange rate and the orthogonalsed Top40 ndex.

9 ~9~ R pt p p1r$ t p2 R' Tt e pt (4) Where R pt s the log return of portfolo p at tme t p w p 1 w 1 p 2 w 2 w 1 The varance of portfolo p s gven by : w' w Where w s the vector of weghts assocated wth portfolo p s the covarance matrx of the log returns of the shares. Equaton (1) s estmated va Ordnary Least Squares regresson for each share. Ths gves: R ˆ t 1 R R' $ t 2 Tt The estmated return on portfolo p can then be expressed as equaton (5).

10 ~10~ R ˆ pt ˆ R p p1 $ t p2 R' Tt (5) Where p w p 1 w 1 p 2 w 2 w 1 The expected return of portfolo p s: R pt p p1r$ t p2 R' Tt (6) Where R t s the expected log return of share at tme t R $ t s the expected log return of the R/$ exchange rate at tme t R' Tt s the expected log return of the orthogonalsed top40 ndex at tme t Elton, Gruber, Brown and Goetzmann (2000) have provded a summary of the research conducted both n usng Indces formed from shares and usng Fundamental factors n mult ndex models. One of the more mportant papers they revewed was by Chen, Roll and Ross (1986) who ntroduced a set of non-equty factors to explan share prce movement. Ther model was successful n that they found certan factors to be sgnfcant, showng that factors affectng the future ncome of the frm have an effect on the returns n the share prce. Others have looked at formng ndces of companes to act as factors but the results n ths feld have been mxed wth no clear domnance of mult-factor models over sngle-ndex models, ths was clearly shown by Elton Gruber (1973) who found the sngle ndex model to be better at predctons as the mult-ndex model ntroduced too much nose. Elton et al. (2000)

11 ~11~ concluded that whle mult-ndex models have nce smplfcaton propertes, more research needs to be completed before mult-ndex models wll be able to domnate smpler models. 4. Data and Methodology The data used n ths nvestgaton were sourced from DataStream and McGregor and for all of the analyss, monthly data was used. Followng the lterature, t was decded to use the blateral R/$ exchange rate nstead of the trade-weghted exchange rate. Ths s as a result of the possblty that a trade-weghted exchange rate mght bas down the exchange rate exposure as t could nclude exchange rates that ndvdual companes are not be exposed to. The R/$ exchange rate was used as the blateral exchange as resource prces are typcally prced n U.S. Dollars and most of the tradtonal Rand-hedges that are not resource companes are lsted n England and the Brtsh Pound s hghly correlated wth the Amercan Dollar. Returns for the exchange rate were defned such that a deprecaton of the Rand aganst the dollar resulted n a postve return and an apprecaton resulted n a negatve return. In the nterests of lqudty and allowng the portfolos to be applcable to the nvestment communty the unverse of shares avalable for the portfolos was restrcted to the consstent consttuents of the Top40 ndex over the past few years. It was decded to set a mnmum number of avalable entres for the estmaton of the portfolos at 30 to prevent short-term movements dctatng the consttuents of the portfolo. Ths constrant elmnated the possblty of certan shares beng placed n the portfolos, due to ther date of lstng dsallowng 30 ponts n the tme perod. Ths meant that Telkom was excluded from the study. The Itrx 100 was chosen to provde a benchmark to compare the effectveness of the Rand hedges. The Itrx 100, owned by the JSE, Deutsche Securtes and Sanlam, s effectvely an ndex of the 100 largest stocks lsted on the LSE. It was lsted n South Afrca very recently, October 2005, and n order to have suffcent data ponts to analyse t, ts performance was smulated. Ths was acheved by takng the prces for the FTSE 100 and multplyng them by the Rand/Pound exchange rate. Ths allowed suffcent ponts for the test perod.

12 4.1 Methodology Barr, Holdsworth & Kantor Portfolo Strateges for hedgng aganst Rand weakness (Nov 2006) ~12~ Gven the lterature on Mult-ndex models t was decded to use a two-ndex model to estmate the return generatng process of the portfolos. The two ndcess were the return of the R/$ exchange rate and the return of the Top40 ndex. The reason for ths specfcaton was that t allowed for an expectaton of the movement of the exchange rate to have an mpact on the expected return of a portfolo. Ths specfcaton was also consstent wth the lterature regardng exchange rate exposure. As mentoned above a requred assumpton for ndex models s that the ndces have to be ndependent. The correlaton between the returns n the R/$ exchange rate and the top40 for the frst, second and thrd perods was 0.25, 0.28 and 0.38 respectvely. The sgnfcance of these values was nvestgated usng the Fsher z- transformaton and the p-values aganst a two-sded alternatve were 16%, 12% and 2% respectvely. Gven the fact that the correlaton was relatvely consstent and sometmes sgnfcant t was decded to orthogonalse the two ndependent varables. Ths s also common n the lterature for example, Benson & Faff (2003), Youguo & Mbodja (1996), Cho & Prasad (1995) and Joron (1991) who orthogonalsed the exchange rate relatve to the market. Usually n the lterature the market effect s removed from the exchange rate, but snce the purpose of the paper s to protect aganst a predcted exchange rate movement t was decded to rather remove the exchange rate effect from the market through equaton (2). As shown n Glbetro (1985) the Top40 Beta s equal n value to the orthogonalsed Top40 Beta. Ths allows the possblty of stll examnng the market rsk of a portfolo, whle obtanng ndependent explanatory varables. The orthogonalsed Betas were estmated for each of the shares n the Top40 usng ths twostep approach. Frst the Top40 Index was orthogonalsed relatve to the exchange rate usng equaton (2) and then equaton (3) was run, gvng the requred estmated Betas. Once ths had been completed t was possble to nvestgate the two portfolo estmaton technques The Naïve method The frst technque was to estmate the exchange rate and orthogonalsed Top40 Betas usng equaton (4). Excel s solver was then used to construct a portfolo from the avalable shares that maxmsed the portfolo s exchange rate Beta. To dsallow portfolos that were overly weghted n one share or nvested tny amounts n shares a constrant was added that forced

13 ~13~ an nvestment n a share to ether be 0 or consttute between 5 and 25 percent of the portfolo. The constrants allowed for only one portfolo to be optmal and t had to nclude at least 4 shares. Ths effectvely meant that the 4 shares wth the hghest R/$ beta were selected. Ths method would correspond wth an nvestor antcpatng a R/$ deprecaton, or tryng to hedge aganst one, wth the assumpton that f a share had a relatvely hgh R/$ beta over the estmaton perod then t would stll have a postve R/$ beta over the test perod. The portfolo s Top40 beta was used to gauge the market rsk of the portfolo The Effcent fronter method The concept behnd the second method was to calculate an effcent fronter allowng for not only movements n the market but also the exchange rate. Ths s the reason behnd the multndex approach. Equaton (6) reduces the problem of estmatng the return for each portfolo to a matter of estmatng expected returns for the orthogonalsed Top40 ndex and the exchange rate. The expected return on the Top40 ndex was taken as the average annual return over the estmaton perod. Snce the Top40 has performed remarkably well over the past few years, the average s unlkely to be a good ndcator for future performance. An expected return of the Top40 of the long term bond yeld, measured by the R153, plus 4% was examned as well. Ths left only an expected return for the exchange rate to be estmated. Snce the purpose of ths paper s to provde a method of hedgng aganst a possble R/$ deprecaton, varous expected returns for the exchange rate were used. The expected returns examned were a 5%, 10%, 15% and 20% deprecaton n the R/$ exchange rate. These expectatons need not be accurate as effectvely the nvestor s requrng a lst of shares to nvest n for a gven antcpated deprecaton. The effect of changng the expected return of the exchange rate s examned later. Once the expected return for the Top40 Index and the R/$ exchange rate are fxed t s possble to calculate the expected return of the orthogonalsed Top40 through equaton (2). The problem then becomes one of fndng the mnmum varance portfolo, assumng a return n the market wth an expected deprecaton of the Rand relatve to the Dollar for each possble return on a portfolo. Thus one s estmatng the return on the market and examnng how the effcent fronter changes for each estmated return on the exchange rate. Graphcally one s lookng at the followng pcture:

14 ~14~ Fgure 1: Effcent fronter for dfferent expected deprecatons Where Rp s the return on a portfolo p s the standard devaton of a portfolo E(R $ ) s the expected change n the exchange rate The shaded regon s an effcent fronter for dfferng values of E(R $ ). The dea s to see how the consttuents of the portfolos on the effcent fronter change as the expected return on the R/$ rate changes. In ths case only postve values of E(R $ ) are examned, these correspond to deprecatons n the Rand relatve to the dollar. Instead of the usual effcent fronter, where one examnes whch portfolo of shares would have been optmal over the estmaton perod, ths specfcaton mples one s examnng whch portfolo of shares wll be optmal f the market performed accordng to an expectaton and the exchange rate does somethng specfed, such as deprecate by 5%. Though ths may seem to be mposng a specfc relatonshp between the Top40 and the exchange rate, ths assumpton can be dropped later. In order to examne the effects of dfferng expectatons of the R/$ on the effcent fronter four cross sectons along the E(R $ ) axs n Fgure 1 were examned, these were for 5%, 10%,

15 ~15~ 15% and 20% expected annual deprecatons n the R/$ exchange rate. Ths gave four effcent fronters for each wndow perod. Once the effcent fronter was determned the portfolo that maxmsed the Sharpe rato was selected for testng. The average yeld of the R153 was taken as the rsk-free rate. Smlarly to the prevous method constrants were placed on the mnmum and maxmum possble allocatons to each possble share wth 5% beng the mnmum and 25% beng the maxmum. A constrant was added that ensured that the Top40 Beta was wthn 0.15 of 1 to ensure that the portfolo was able to mantan exposure to the market whle hedgng aganst a deprecaton. Only shares wth consstently postve R/$ Betas were looked at, ths gave 16 shares to pck from, namely Anglo Amercan PLC (AGL), Anglo Platnum (AMS), Anglogold Ashant Ltd (ANG), BHP Bllton PLC (BIL), Gold Felds Ltd (GFI), Harmony Gold Mnng Ltd (HAR), Impala Platnum Holdngs Ltd (IMP), Kumba Ltd (KMB), Lberty Internatonal PLC (LBT), Rchemont Securtes AG (RCH), Remgro Ltd (REM), SAB Mller PLC (SAB), Sapp Ltd (SAP), Stenhoff Internatonal Holdngs Ltd (SHF) and SASOL Ltd (SOL) The performance of the selected portfolo was examned for the 12 months after the estmaton perod, wth the assumpton that the portfolo was rebalanced monthly to the allocaton set out n the estmaton perod. Both methods used 54 months of data to estmate ther portfolos for the next 12 month perod, at the end of 12 months the portfolos were re-estmated. Ths gave three portfolo test perods for each method, July 2003-June 2004, July 2004-June 2005 and July 2005-June These corresponded to the three estmaton wndows January 1999-June 2003, January 2000-June 2004 and January 2001-June Estmaton There were three test perods to evaluate for each of the methods. Each method was evaluated on two aspects, the orthogonalsed R/$ beta and the rsk-adjusted return durng the test perod. Snce the objectve s to hedge aganst a R/$ deprecaton, the return durng the months that the R/$ deprecated s also looked at separately from the perods when the Rand apprecated aganst the dollar.

16 ~16~ The method usng the maxmsaton of the R/$ beta produced the followng portfolos durng the three constructon perods, only shares that were selected n a portfolo are dsplayed. N1, N2 and N3 represent the portfolo for the frst, second and thrd test perod respectvely. Portfolo allocatons N1 N2 N3 IMP 25% 25% 0% AMS 25% 25% 25% SOL 25% 25% 25% LBT 25% 25% 0% HAR 0% 0% 25% AGL 0% 0% 25% R/$ beta Top 40 Beta Start 1999/01/ /01/ /01/31 End 2003/06/ /06/ /06/30 Table1: Portfolo allocatons for maxmsng R/$ Beta Even though all of the top40 shares were avalable to pck from only sx were selected over the three perods, and thus the portfolos are smlar. Ths shows the stablty of the rankng of the R/$ Betas, the four hghest R/$ betas n the second perod belong to the same set of shares wth the four hghest R/$ betas n the frst perod. Two of those four have are n the top four n the last perod. Ths shows that by selectng the set of share wth the hghest R/$ betas allows for relatvely consstent portfolos wth respect to ther consttuents. The followng table represents the actvty of the portfolos durng the test perod. N1 N2 N3 R/$ beta Top 40 Beta Start 2003/07/ /07/ /07/31 End 2004/06/ /06/ /06/30 Table 2: Orthogonalsed Betas of portfolos durng test perod.

17 ~17~ Ths table shows that whle the R/$ beta s not consstent wth respect to the value durng the portfolo constructon perod and the test perod, at least the sgn remans consstent. In addton to ths table, t s mportant to see how the portfolos performed wth respect to returns durng perods when the R/$ deprecated and when t apprecated. Ideally one would lke the portfolo to perform better when the R/$ deprecated. These values are dsplayed n the tables on the followng page (Tables 3-5). It s evdent from the tables that over the perods of nvestgaton R/$ deprecaton has not been as pronounced as n prevous years. Ths can be seen by lookng at the values for the annual R/$ return and the fact that n each of the years examned there were more months where the Rand apprecated relatve to the Dollar than there were where the Rand deprecated aganst the dollar. The mportant statstcs n the tables are that of the performance of the portfolo when the R/$ deprecated and when t apprecated. As can be seen n the table for the frst two perods the portfolo selecton method was successful n that the portfolo performed better when the R/$ deprecated than t dd when the R/$ apprecated and the dfference s qute large. The last perod s dfferent n that the portfolo performed better when the R/$ apprecated than when t deprecated. Ths s examned later.

18 ~18~ N1 Portfolo R/$ Top40 Portfolo when R/$ Apprecated Portfolo when R/$ deprecated Average return 13.40% % 21.20% 2.55% 45.95% Std. Devaton 19.76% 19.99% 15.45% 19.50% 21.21% Return/Std. Devaton count Table 3: Performance of P1 from 2003/07/31 to 2004/06/30 N2 Portfolo R/$ Top40 Portfolo when R/$ Apprecated Portfolo when R/$ deprecated Average return 39.52% 8.10% 36.04% 1.53% 92.72% Std. Devaton 21.16% 18.80% 16.28% 14.49% 20.26% Return/Std. Devaton count Table 4: Performance of P2 from 2004/07/31 to 2005/06/30 N3 Portfolo R/$ Top40 Portfolo when R/$ Apprecated Portfolo when R/$ deprecated Average return 70.73% 6.21% 43.91% 76.87% 62.13% Std. Devaton 31.94% 16.37% 16.16% 17.00% 48.57% Return/Std. Devaton count Table 5: Performance of P3 from 2005/07/31 to 2006/06/30 Where count refers to the number of months n the test perod that s applcable to the column label.

19 ~19~ The second portfolo constructon method produced more portfolos as for each constructon perod a portfolo was constructed for a 5%, 10%, 15% and 20% expected annual deprecaton n the R/$ rate. The followng table shows the allocatons for each estmated deprecaton n the exchange rate for the each of the frst estmaton perod. Only shares that were selected n at least one portfolo are shown Expected deprecaton of Rand relatve to Dollar 5.00% 10.00% 15.00% 20.00% IMP SOL LBT BIL GFI Table 6: Portfolo allocatons for the frst perod for each expected deprecaton n the exchange rate. The portfolos are remarkably smlar, both n terms of consttuents and n terms of allocatons. Ths shows that the level of expected deprecaton s not as mportant as expectng a deprecaton of any value. Ths s an mportant result whch suggests that there s a best set of shares to nvest n rrespectve of the level of expected deprecaton as long as a deprecaton s antcpated or needed to be hedged aganst. Gven the smlarty between the portfolos, only the results correspondng to the portfolos formed wth a 20% expected deprecaton n the R/$ exchange rate are dsplayed. Ths makes the portfolo selecton method comparable to the frst method where the R/$ Beta was maxmsed and would beneft most from a large deprecaton n the R/$ exchange rate. The next table dsplays the portfolo allocatons for the mult ndex effcent fronter method for each estmaton wndow. Portfolos are labelled M1, M2 and M3 correspondng to the frst, second and thrd test perods respectvely.

20 ~20~ Portfolo allocatons M1 M2 M3 IMP SOL LBT BIL KMB GFI REM R/$ beta Top40 beta Start 1999/01/312000/01/ /01/31 End 2003/06/302004/06/ /06/30 Table 7: Portfolo allocatons for Mult ndex optmsaton Whereas the method that maxmsed the R/$ Beta used four shares at a tme, ths method never uses less than fve, wth seven shares used over the entre test perod. The portfolos are relatvely consstent wth regard to ther consttuents, wth each portfolo sharng 4 shares wth the next perod s optmal portfolo. LBT, SOL and BIL appear n each of the portfolos, wth SOL and LBT consstently recevng hgh allocatons. Ths shows that resource stocks are not necessarly the best hedges, but rather duel lsted shares and SASOL. The tables on the followng page (tables 8-10) show the performance of the portfolo usng the same measures as before.

21 ~21~ M1 Portfolo R/$ Top40 Portfolo when R/$ Apprecated Portfolo when R/$ deprecated Average return 10.12% % 21.20% 2.60% 32.67% Std. Devaton 18.65% 19.99% 15.45% 18.34% 21.97% Return/Std. Devaton count Table 8: Performance of M1 from 2003/07/31 to 2004/06/30 M2 Portfolo R/$ Top40 Portfolo when R/$ Apprecated Portfolo when R/$ deprecated Average return 47.30% 8.10% 36.04% 22.61% 81.86% Std. Devaton 14.94% 18.80% 16.28% 12.64% 12.67% Return/Std. Devaton count Table 9: Performance of M2 from 2004/07/31 to 2005/06/30 M3 Portfolo R/$ Top40 Portfolo when R/$ Apprecated Portfolo when R/$ deprecated Average return 54.72% 6.21% 43.91% 77.24% 23.19% Std. Devaton 22.34% 16.37% 16.16% 10.76% 31.96% Return/Std. Devaton count Table 10: Performance of M3 from 2005/07/31 to 2006/06/30 Where count refers to the number of months n the test perod that s applcable to the column label.

22 ~22~ Even though ths method dffers from the naïve method the results are smlar n that the constructed portfolo performs better when the R/$ deprecates for the frst two perods but ths s not so for the last perod. The explanaton for the lower performance n the thrd perod s not necessarly obvous. Ths s a strange result as t shows that two dfferent sets of tradtonal Rand hedges performed better when the Rand apprecated than when the Rand deprecated. A possble explanaton s that ths was due to shares rsng due to postve sentment that happened to occur whle the Rand apprecated n value and ths s plausble snce the test perod was a perod of rapd share prce growth that was not assocated wth hgher R/$ volatlty. The last nvestment opton examned was the Itrx Exchange traded Fund. Snce ths s based on the FTSE 100 t should gve a natural hedge to the R/$ exchange rate as the correlaton between the Brtsh Pound and the Amercan Dollar s tradtonally very hgh. The followng table gves the beta values of the Itrx fund for the three test perods: Itrx fund I1 I2 I3 R/$ Beta Top40 Beta Start 2003/07/ /07/312005/07/31 End 2004/06/ /06/302006/06/30 Table 11: Orthogonalsed Betas Itrx durng test perods. The postve values for the R/$ Beta confrm the belef that the Itrx should act as a natural hedge aganst Rand deprecaton whle the relatvely low top40 Beta confrms that the Itrx s weak relatonshp wth the performance n the South Afrcan market. The returns for the smulated Itrx fund are dsplayed n the tables on the followng page (tables 12-14). As can be seen the Itrx fund always performs better when the R/$ deprecates than t does when the R/$ apprecates. Ths comes at the expense of a lower return for the fund, ths s due to the fact that as the shares are based n England they would not have been able to partcpate n the recent rapd growth seen on the JSE.

23 ~23~ I1 Portfolo R/$ Top40 Portfolo when R/$ Apprecated Portfolo when R/$ deprecated Average return 6.32% % 21.20% % % Std. Devaton 21.63% 19.99% 15.45% 13.84% 10.28% Return/std devaton count Table 12: Performance of I1 from 2003/07/31 to 2004/06/30 I2 Portfolo R/$ Top40 Portfolo when R/$ Apprecated Portfolo when R/$ deprecated Average return 25.01% 8.10% 36.04% -0.97% 61.37% Std. Devaton 12.33% 18.80% 16.28% 5.91% 11.38% Return/std devaton count Table 13: Performance of I2 from 2004/07/31 to 2005/06/30 I3 Portfolo R/$ Top40 Portfolo when R/$ Apprecated Portfolo when R/$ deprecated Average return 26.02% 6.21% 43.91% 13.23% 43.94% Std. Devaton 9.11% 16.37% 16.16% 7.99% 8.67% Return/std devaton count Table 14: Performance of I3 from 2005/07/31 to 2006/06/30 Where count refers to the number of months n the test perod that s applcable to the column label.

24 The followng tables provdes a comparson of the three possble methods of R/$ hedgng usng portfolo allocaton. Each method s compared on ts return and average regresson coeffcents over the three estmaton perods. P represents the portfolo that maxmsed the R/$ Beta. M refers to the portfolo derved from the mult ndex effcent fronter approach and I refers to the Itrx 100. Average return Average return when R/$ Apprecated Average return when R/$ deprecated N 41.22% 26.98% 66.94% M 37.38% 34.15% 45.90% I 19.12% -5.03% 70.89% Table 15: Performance of the three Rand hedge methods Formatted Average R/$ Beta Average Top40 Beta N M I Table 16: Regresson coeffcents of the three Rand hedge methods Formatted If the R153 plus 4% s used to estmate the return on the Top40 nstead of the average return over the estmaton perod then the followng results are obtaned for the effcent fronter model: Average Average return when Average return when return R/$ Apprecated R/$ deprecated M 39.69% 35.44% 52.44% Table 17: Performance of effcent fronter method wth R153+4% as expected Top40 return Average R/$ coeffcent Average Top40 coeffcent M Table 18: Regresson coeffcents of the effcent fronter method wth R153+4% as expected Top40 return These results are very smlar to the results obtaned for the effcent fronter method when the past performance of the Top40 Index was used to predct the future performance. Snce the expected returns are smlar ths suggests that the results of the effcent fronter method are not greatly affected by the expectaton placed on the Top40 Index.

25 ~25~ The Itrx provdes the hghest average return when the Rand deprecates aganst the Dollar, and the lowest of the average returns when the Rand apprecates. Ths suggests that the Itrx s the most effectve Rand Hedge of the methods surveyed. The Betas tell a dfferent story. The R/$ beta maxmsaton method comes out wth both the hghest average R/$ Beta and the hghest average top40 Beta, reflectng the hgher rsk nherent n ths method. The effcent fronter approach has a lower R/$ beta than the Itrx but an average top40 Beta that s closer to 1 and hgher than the Itrx Beta. These statstcs reveal the problem assocated wth smply nvestng n the Itrx, that of lower exposure to the South Afrcan market. Recently ths would have led to lower returns as the top40 has done extremely well recently. Ths s reflected by the fact that the Itrx had the lowest average return of the three methods nvestgated. 6. Conclusons: The results show that t s possble, n general, to hedge aganst a R/$ deprecaton by nvestng locally and that even a smple portfolo constructon technque that does not pay attenton to rsk of the portfolo s able to perform better when the R/$ deprecates than when t apprecates. In terms of hedgng aganst a R/$ deprecaton the results show that whle the Itrx fund provdes more consstent hedgng ths comes at the expense of a weak relatonshp wth the top40. Thus t would seem that the Mult-ndex effcent fronter approach s the best as t allows for hgher rsk-adjusted returns than the beta maxmsng approach, whle allowng for more correlaton wth the market than the Itrx approach. The consttuents of the mult-ndex optmsaton method show that resource stocks are not necessarly the default Rand Hedges, n some cases dual lsted shares perform better.

26 ~26~ References 1) Barr, G.D.I. and Kantor, B.S. (2005) The Impact of the Rand on the Value of the Johannesburg Stock Exchange Journal for Studes n Economcs and Econometrcs, 29(2): ) Benson, K.L. and Faff, R.W. (2003) Exchange rate senstvty of Australan nternatonal equty funds, Global Fnance Journal, 14: ) Chen, N., Roll R., Ross S. (1986) Economc Forces and the Stock Market Journal of Busness ) Cho, J.J. and Prasad, A.M.(1995) Exchange rsk senstvty and ts determnants: a frm and ndustry analyss of U.S. multnatonals. Fnancal Management, 24(3): ) Domnguez, K. M. E. and Tesar, L. L. (2001), A Reexamnaton of Exchange-Rate Exposure, Amercan Economc Revew, 91(2): ) Elton E.J., Gruber M.J., Brown S.J. and Goetzmann, W.T. (2000) Modern Portfolo Theory and Investment Analyss, John Wley & Sons 7) Elton E.J., Gruber M.J. (1973) Estmatng the dependence structure of share Prces- Implcatons for portfolo selecton. Journal of Fnance 8(5): ) Glberto, M. (1985) Interest Rate Senstvty n the Common Stocks of Fnancal Intermedares: A Methodologcal Note, Journal of Fnancal and Quanttatve Analyss, 20(1): ) Joron, P. (1990) The Exchange Rate exposure of U.S. Multnatonals, Journal of Busness, 63(3): ) Joron, P. (1991) The Prcng of Exchange Rsk n the Stock Market, Journal of Fnancal and Quanttatve Analyss, 26(3): ) Loudon, G. (1993) The Foregn exchange operatng exposure of Australan stocks, Accountng and Fnance, 33:19-32

27 ~27~ 12) Sharpe, Wllam F. (1970) Portfolo Theory and Captal Markets, McGraw-Hll 13) Youguo, L. and Mbodja, M. (1996) The prcng of Foregn rsk: Evdence from ADRs Internatonal Revew of Economcs & Fnance, 5(4):

28 ~28~ Appendx Categorsaton of lsted companes on the JSE n terms of exchange rate movement response Share prces on the JSE clearly reflect the market s best attempt to fnd the present value of the expected benefts from ownng a share of the company. These benefts wll be derved from expected future earnngs and dvdends or from the sale or lqudaton of the company. These earnngs and dvdend flows from JSE lsted companes may be generated from: a) company operatons that are almost completely SA-based. We defne these companes lsted on the JSE as rand plays, e.g. retalers (such as Pck n Pay) or banks (such as Absa) wth almost all ther revenues generated and costs ncurred n South Afrca n rands; b) companes lsted on the JSE that are almost completely foregn based, generatng only foregn hard currency ncome and ncurrng only foregn costs and known as rand hedge stocks, e.g. Lberty Internatonal, a UK property owner and developer, or Rchemont; c) companes that are SA-based and ncur costs n SA but sell ther products n hard currency, e.g. resource stocks such as Harmony, whch we descrbe as rand leverage stocks. We consder the dvdend at tme t (expressed n rands) and denoted cases above: Dv t for each of the a) Rand play: Dvt s proportonal to proft at tme t, (R) Rev t (R)Cost t b) Rand hedge: Dv t s proportonal to proft at tme t denomnated n, say, US dollars and then converted nto rand to gve,

29 R /$ * $Rev t t t Barr, Holdsworth & Kantor Portfolo Strateges for hedgng aganst Rand weakness (Nov 2006) ~29~ $Cost hence the profts of a rand hedge company n dollars wll be drectly mpacted upon by the rand/us$ exchange rate; a weaker exchange rate wll ncrease the dvdend flow n rands for any gven proft n dollars. c) Rand leverage: n the thrd group (typcally resource companes), the rand prce of ther shares reacts to the dollar prces of ther traded resources as well as to the rand/us$ exchange rate. A weaker rand ncreases the rand prce of commodtes and lowers the dollar-denomnated costs of nputs, manly labour. Ths effect would, prmarly, be a short-term effect. Prces and partcularly labour costs would be expected to rse as a PPP equlbrum was re-establshed and the real rand deprecaton elmnated. Thus, a weaker rand would result n an ncrease n dollar earnngs for as long as dollar costs were below ther PPP value; as PPP s re-establshed, dollar prces of labour would rse. In ths case, as n (b) above, Dv t s proportonal to dollar proft at tme t denomnated n dollars and then converted nto rands. Although revenues are earned n dollars, costs are denomnated n rands to gve dollar proft at tme t: R /$ 1 t * $Rev t (R)Cost t * R /$ t However, rand costs rse n lne wth the consumer prce ndex. Thus, dollar costs wll be lnked to the relatve movement of the CPI and the exchange rate. At tme t+n, dollar proft wll be: CPI R /$ t n t n * $Rev 1 t n (R)Cost t * * CPI t R /$ tn Thus, assumng dollar revenues are farly stable, dollar profts n perods n the future are determned by the relatve movement of the CPI to the rand/us$ exchange rate over the n perods. For example, rand deprecaton wll lower dollar costs and create a leveraged effect on dollar profts. But, as CPI catches up over tme wth any deprecaton n the rand (or vce versa) and PPP s re-establshed, the leverage effect dsspates and the short-term

30 ~30~ mprovement n dollar profts due to the real rand deprecaton dsappears. In other words, leverage effects measured n dollars whch stem from an exchange rate deprecaton are merely short-term effects and do not fundamentally affect long term value. In rand terms, prces should reflect these leveraged dollar effects values but, assumng PPP wll hold, the long term value should prmarly be determned by expectatons of dollardenomnated resource prces and expectatons of rand/us$ exchange rates.