Financial markets behavior changes

Transcription

1 PETER NYSTRUP is an indusrial PhD suden a Sampension in Hellerup, Denmark and in he deparmen of applied mahemaics and compuer science, Technical Universiy of Denmark in Lyngby, Denmark. pnys@du.dk BO WILLIAM HANSEN is he head of invesmen analysis a Sampension in Hellerup, Denmark. bwh@sampension.dk HENRIK MADSEN is a professor and head of he secion for dynamical sysems in he deparmen of applied mahemaics and compuer science a Technical Universiy of Denmark in Lyngby, Denmark. hmad@du.dk ERIK LINDSTRÖM is an associae professor a he Cenre for Mahemaical Sciences, Lund Insiue of Technology in Lund, Sweden. erikl@mahs.lh.se Regime-Based Versus Saic Asse Allocaion: Leing he Daa Speak PETER NYSTRUP, BO WILLIAM HANSEN, HENRIK MADSEN, AND ERIK LINDSTRÖM Financial markes behavior changes abruply. Alhough some changes may be ransiory, he new behavior ofen persiss for several periods afer a change. The mean, volailiy, and correlaion paerns in sock reurns, for example, changed dramaically a he sar of, and coninued hrough he global financial crisis of 007 o 008. Similar regime changes, some of which can be recurring (recessions versus expansions) and some of which can be permanen (srucural breaks), are prevalen across a wide range of financial markes and in he behavior of many macro variables (Ang and Timmermann [01]). Observed regimes in financial markes are relaed o he phases of he business cycle (see Campbell [1998] and Cochrane [005]). The link is complex and difficul o exploi for invesmen purposes, due o he large lag in he availabiliy of daa relaed o he business cycle. Our inenion is o le he daa speak by focusing on readily available marke daa, insead of aemping o esablish he link o he business cycle. Regime changes presen a big challenge o radiional sraegic asse allocaion (SAA). In he presence of ime-varying invesmen opporuniies, porfolio weighs should be adjused as new informaion arrives. Tradiional SAA approaches seek o develop saic, all-weaher porfolios ha opimize efficiency across a range of economic scenarios. If economic condiions are persisen and srongly linked o asse class performance, however, hen a dynamic sraegy should add value over saic weighs (Sheikh and Sun [01]). The purpose of a regime-based sraegy is o ake advanage of favorable economic regimes, wihsand adverse economic regimes, and reduce poenial drawdowns. Regime-based invesing is disinc from acical asse allocaion (TAA). While he laer is shorer erm, higher frequency (i.e., weekly or monhly), and driven primarily by valuaion consideraions, regime-based invesing arges a longer ime horizon (i.e., a year or more) and is driven by changing economic fundamenals. A regime-based approach has he flexibiliy o adap o changing economic condiions wihin a benchmark-based invesmen policy, which can involve more han one rebalancing wihin a year. I sraddles a middle ground beween sraegic and acical (Sheikh and Sun [01]). LETTING THE DATA SPEAK This aricle examines wheher regimebased asse allocaion (RBAA) can effecively respond o financial regimes, in an effor o provide beer long-erm resuls when compared o saic approaches. Dopfel [010] showed he poenial ouperformance of a RBAA sraegy, assuming complee informaion abou he prevailing regime and fuure IT IS ILLEGAL TO REPRODUCE THIS ARTICLE IN ANY FORMAT FALL 015 THE JOURNAL OF PORTFOLIO MANAGEMENT 103 Copyrigh 015

2 regime shifs is available. Dopfel [010], however, concluded ha an invesor who does no possess excepional forecasing skill is beer off holding a saic porfolio ha is hedged agains he uncerainy associaed wih regime shifs. This conclusion conrass wih he large number of sudies ha have documened he profiabiliy of dynamic asse allocaion (DAA) sraegies based on regime-swiching models. See, for example, Ang and Bekaer [00, 004], Guidolin and Timmermann [007], Bulla e al. [011], and Krizman, Page, and Turkingon [01]. The invesor should accep his profiabiliy wih cauion, as no all he sudies accoun for ransacion coss when comparing he performance of dynamic and saic sraegies. This is imporan, as frequen rebalancing can offse a dynamic sraegy s poenial excess reurn. Furhermore, he in-sample performance generally exceeds he ou-of-sample performance if he sraegies are a all esed ou of sample. Inspired by he apparen profiabiliy of regimeswiching sraegies, his aricle challenges Dopfel s [010] conclusion by leing he daa speak. In an invesmen universe consising of a global sock index (MSCI ACWI) 1 and a global governmen bond index (JPM GBI), we compare he performance of a RBAA sraegy o ha of a sraegy based on rebalancing o saic weighs. Exhibi 1 shows he developmen in he wo indices over he 0-year daa period. Our inenion is o idenify regimes in he sock reurns using a regime-swiching model and le he asse allocaion depend on he idenified regime. The focus on E HIBIT 1 The invesmen universe modeling he sock reurns is naural, as porfolio risk is ypically dominaed by sock marke risk. In addiion, he sock markes generally lead he economy (see Siegel [1991], for example). The goal is no o predic regime shifs or fuure marke movemens, bu o idenify when a regime shif has occurred and hen benefi from he persisence of equilibrium reurns and volailiies. The regime-swiching process can be inerpreed as a momenum process when i is more likely o coninue in he same sae han o ransiion o anoher sae (see Ang and Bekaer [00]). Exhibi shows he sock index s daily log-reurns. 3 The volailiy forms clusers, as large price movemens end o be followed by large price movemens and vice versa, as Mandelbro [1963] noed. 4 The RBAA sraegy aims o exploi he volailiy s persisence, as risk-adjused reurns, on average, are subsanially lower during urbulen periods, irrespecive of he source of urbulence, as Krizman and Li [010] showed. Our purpose is no o ouline he opimal sraegy, bu raher o discuss he profiabiliy of an RBAA approach. THE HIDDEN MARKOV MODEL Imagine knowing a person s hear rae. While he person sleeps, we see a low average hear rae wih low volailiy. When he person wakes up, we see a sudden rise in he hear rae s average level and volailiy. Wihou acually seeing he person, we can reasonably conclude wheher he or she is awake or sleeping, ha is, which sae he person is in. E HIBIT Volailiy clusering in he daily log-reurns 104 REGIME-BASED VERSUS STATIC ASSET ALLOCATION: LETTING THE DATA SPEAK FALL 015

3 Reurns are he hear rae of a financial marke. The use of hidden Markov models (HMMs) o infer he sae of financial markes has gained populariy over he las decade. The HMM is a black-box model, bu he inferred saes can ofen be linked o business cycle phases (see Guidolin and Timmermann [007], for insance). The possibiliy of inerpreing he saes, combined wih he model s abiliy o reproduce sylized facs of financial reurns, is par of he reason ha HMMs have become increasingly popular. In a hidden Markov model, he probabiliy disribuion ha generaes an observaion depends on he sae of an unobserved Markov chain. A sequence of discree random variables { } is said o be a firs-order Markov chain if, for all N, i saisfies he Markov propery: Pr,, 1 = Pr +1 1 (1) +11 The condiional probabiliies Pr( +1 = j = i) = γ ij are called ransiion probabiliies. As an example, consider he wo-sae model wih Gaussian condiional disribuions: where Y ~ N μ, 1 if = 1, μ = μ, if =, Γ = 1 γ γ γ 1 γ μ,σ μ σ = 1 σ, if = 1, σ, if =, and When he curren sae is known, he disribuion of Y depends only on. The sojourn imes are implicily assumed o be geomerically disribued: 1 Pr ( ) = γ ( γ ) () The geomeric disribuion is wihou memory, implying ha he ime unil he nex ransiion from he curren sae is independen of he ime spen in he sae. HMMs can mach financial markes endency o change heir behavior abruply, as well as he new ii behavior s endency o persis for several periods afer a change. They are well suied o capure he sylized behavior of many financial series, including volailiy clusering and lepokurosis, as shown by Rydén, Teräsvira, and Åsbrink [1998]. Subsequen aricles have exended he classical Gaussian HMM by considering sojourn ime disribuions oher han he memory-less geomeric disribuion (Bulla and Bulla [006]), condiional disribuions oher han he Gaussian disribuion (Bulla [011]), and a coninuous-ime formulaion as an alernaive o he dominaing discree-ime models (Nysrup, Madsen, and Lindsröm [015a]). In Nysrup, Madsen, and Lindsröm [015b], he auhors found ha he need o consider oher sojourn ime disribuions and oher condiional disribuions can be eliminaed by adaping o he daa process s ime-varying behavior. An HMM s parameers are ypically esimaed using he maximum-likelihood mehod. Every observaion is assumed o be of equal imporance, no maer he sample period s lengh. This approach works well when he sample period is shor and he underlying process does no change over ime. The parameers ime-varying behavior, documened in previous sudies (Rydén, Teräsvira, and Åsbrink [1998], Bulla [011], and Nysrup, Madsen, and Lindsröm [015b]), calls for an adapive approach ha assigns more weigh o he mos recen observaions while keeping in mind he pas paerns a a reduced confidence. Nysrup, Madsen, and Lindsröm [015b] oulined an adapive esimaion approach based on weighing observaions wih exponenially decreasing weighs in oher words, using exponenial forgeing. This aricle pursues he same approach. The regime-swiching model is sill a wo-sae HMM wih Gaussian condiional disribuions, bu one ha adaps o he imevarying behavior of he underlying process in an effor o produce more robus sae esimaes. EMPIRICAL RESULTS We perform esing one day a a ime in a livesample seing, o make i as realisic as possible. The model is fied o he firs observaions, assigning he mos weigh o he mos recen observaions. Based on he esimaed parameers, we calculae he probabiliy ha on day he marke was in he high- or low-volailiy sae, respecively, along wih he prediced sae FALL 015 THE JOURNAL OF PORTFOLIO MANAGEMENT 105

4 probabiliies for day + 1. As he saes are highly persisen (γ ii 0.5), he sae ha is prediced o be mos likely on day + 1 will be he same sae idenified o be mos likely on day. If he sae prediced o be mos likely on day + 1 is differen han he sae on which he asse allocaion on day is based and he confidence in he predicion is above 95% 5, hen we change he allocaion based on he closing price a day + 1, i.e., we assume a one-day delay in he implemenaion. Oherwise he asse allocaion remains unchanged. We hen include he log-reurn on day + 1 in he sample, re-esimae he model, and calculae he sae probabiliies based on he new parameers. We repea his procedure sequenially by including he observaions, one a a ime, from January 1, 1996 all he way hrough he sample. 6 We compare he performance of wo regime-based sraegies (Socks Bonds and Long Shor) o he performance of he wo indices and ha of a saic porfolio wih a fixed allocaion of 49% o socks, as shown in Exhibi 3. The firs sraegy is fully invesed in he sock index in he low-volailiy sae and he bond index in he high-volailiy sae. The average allocaion o he sock index over he period was 49%. The second sraegy is long he sock index in he low-volailiy sae and shor he sock index in he high-volailiy sae. Exhibi 4 shows he developmen of he sraegies and he indices. In he shaded periods, he allocaion was based on being in he high-volailiy sae. The idenified regimes seem inuiive when we look a he log-reurns a he boom of Exhibi 4. There have been a oal of 16 regime changes over he 17-year period. The lengh of he idenified regimes varies considerably, from a few weeks up o six years. This is differen from wha we would expec if he regimes were based on a business cycle indicaor. There appear o be large differences in he volailiy level wihin he six-year, high-volailiy regime ha begins in 1998 and includes boh he build-up E HIBIT 3 The performance of he indices and he sraegies from and burs of he do-com bubble. This suggess ha he marke saes were less persisen around his ime. The bond index has realized he highes Sharpe raio (SR), wih an annualized reurn (AR) of 6.0% and an adjused annualized sandard deviaion (SD) of only 3%. We have adjused he repored SDs for auocorrelaion using he procedure oulined by Kinlaw, Krizman, and Turkingon [015]. 7 The daa period was characerized by falling ineres raes and low inflaion, leading o a srong performance for bonds. I is unlikely ha he environmen for bonds will be as favorable going forward. The Socks Bonds sraegy has realized he second highes SR of 1.3. The annualized SD is he same as for he saic porfolio, which has he same average exposure o he sock index, bu he realized reurn is higher as long as ransacion coss do no exceed 39 basis poins per one-way ransacion. This is when we ignore he coss associaed wih rebalancing o saic weighs, so he break-even ransacion cos is higher han 39 basis poins. In addiion, he maximum drawdown 8 (MDD) for he Socks Bonds sraegy is much smaller han ha of he saic sraegy. The Long Shor sraegy has been less profiable, bu i sill ouperforms he sock index when ransacion coss are less han 130 basis poins per one-way ransacion. The ouperformance essenially happened during he financial crisis in 008. The Long Shor sraegy has a lower ail risk han ha of he sock index, bu he risk of he sraegy underperforming he index going forward seems real. This observaion is confirmed in Exhibi 5, which summarizes he performance of he indices and he regime-based sraegies, when we exclude 008 from he sample. Alhough i sill has a lower ail risk han ha of he sock index, he Long Shor sraegy underperforms he sock index. The performance of he bond index and he Socks Bonds sraegy barely changes, whereas he AR and he SR of he sock index and he saic porfolio increase. The average allocaion o he sock index when we exclude 008 is 5%, which equals he fixed allocaion o socks in he saic porfolio (Exhibi 5). The Socks Bonds sraegy s realized reurn sill exceeds ha of he saic porfolio as long as ransacion coss do no exceed 140 basis poins per one-way ransacion. SUMMARY AND DISCUSSION Our resuls indicae ha no level of forecasing skill is required for a RBAA sraegy o be more profiable 106 REGIME-BASED VERSUS STATIC ASSET ALLOCATION: LETTING THE DATA SPEAK FALL 015

5 E HIBIT 4 The developmen of he sraegies and he indices across he inferred regimes E HIBIT 5 The performance of he indices and he sraegies from han a saic sraegy. We did he esing one day a a ime in a live-sample seing o make i as realisic as possible. Our approach was based on idenifying regimes in marke reurns, using a regime-swiching model wih ime-varying parameers. As he parameers are updaed every day, he same approach should work in oher ime periods as well. The resuls are robus, as hey are based on available marke daa wih no assumpions abou equilibrium reurns, volailiies, or correlaions. Addiionally, i migh be possible o improve performance by including economic variables, ineres raes, invesor senimen surveys, or oher indicaors. The ouperformance of he sraegy ha swiched beween socks and bonds appeared o be mos reliable, as i did no jus happen during one year, as was he case wih he Long Shor sraegy. Alhough he break-even ransacion cos was more han 39 basis poins (140 basis poins when excluding 008), he sraegies will only FALL 015 THE JOURNAL OF PORTFOLIO MANAGEMENT 107

6 remain profiable if he marke saes persisence remains high. Volailiy clusering is no a new phenomenon, bu i can occur a differen levels of marke persisence. The esed sraegies may be based on larger changes in allocaion han mos invesors are willing o and/or allowed o implemen. Suppose your benchmark is a allocaion o socks and bonds and ha you are allowed o vary beween a and a allocaion. For he Socks Bonds sraegy, his is equivalen o allocaing 80% of he porfolio o a saic porfolio and he remaining 0% o he regime-based sraegy. The excess reurn ha you can obain is hen 0% of he excess reurn ha could be obained by allocaing he enire porfolio o he regime-based sraegy. Our resuls have imporan implicaions for porfolio managers wih medium o long-erm invesmen horizons. Even wihou any level of forecasing skill, holding a saic porfolio may no be opimal. Wih some level of forecasing skill, an RBAA sraegy s poenial ouperformance could be subsanial. I is definiely worh considering a more dynamic approach o asse allocaion, if no only o reduce he ail risk. ENDNOTES This work was suppored by Innovaion Fund Denmark under Gran [ B]. 1 The MSCI All Counry World Index, denominaed in USD, capures large- and mid-cap represenaion across 3 developed marke and 1 emerging marke counries. The difference compared o he more well-known MSCI World Index is he weigh on EM counries. The daa before 1999, where he oal reurn index began, has been reconsruced based on he price index by adding he average daily ne dividend reurn over he period from 1999 o % o he price reurns. The global J.P. Morgan Governmen Bond Index measures he performance across 13 developed, fixed-income bond markes hedged o USD. The consiuens are seleced from all governmen bonds, excluding floaing rae noes, perpeuals, bonds argeed a he domesic marke for ax purposes, and bonds wih less han one year o mauriy. The index had a modified duraion of 6.8 a he end of The log-reurns are calculaed using, r = log(p ) log(p 1 ), where P is he closing price of he index on day and log is he naural logarihm. 4 A quaniaive manifesaion of his fac is ha while reurns hemselves are uncorrelaed, absolue and squared reurns display a posiive, significan, and slowly decaying auocorrelaion funcion. 5 If he confidence hreshold is changed o 85% or 90%, here will be more regime changes, bu he resuls will only change somewha. For a given level of ransacion coss, here exiss an opimal hreshold ha balances he cos of rebalancing wih he cos of no reacing o regime shifs or delaying he reacion. 6 The log-reurns from he wo years before 1996 are used for iniializaion. 7 The adjusmen for auocorrelaion leads o slighly higher sandard deviaions and correspondingly lower Sharpe raios. The adjusmen is no imporan o he conclusions drawn, as he indices and sraegies all displayed fairly similar, low amouns of auocorrelaion. 8 The maximum drawdown is he larges relaive decline from a hisorical peak in he index value. REFERENCES Ang, A., and G. Bekaer. Inernaional Asse Allocaion Wih Regime Shifs. Review of Financial Sudies, Vol. 15, No. 4 (00), pp How Regimes Affec Asse Allocaion. Financial Analyss Journal, Vol. 60, No. (004), pp Ang, A. and A. Timmermann. Regime Changes and Financial Markes. Annual Review of Financial Economics, Vol. 4, No. 1 (01), pp Bulla, J. Hidden Markov Models Wih Componens: Increased Persisence And Oher Aspecs. Quaniaive Finance, Vol. 11, No. 3 (011), pp Bulla, J., and I. Bulla. Sylized Facs Of Financial Time Series And Hidden Semi-Markov Models. Compuaional Saisics and Daa Analysis, 51 (006), pp Bulla, J., S. Mergner, I. Bulla, A. Sesboüé, and C. Chesneau. Markov-Swiching Asse Allocaion: Do Proable Sraegies Exis? The Journal of Asse Managemen, Vol. 1, No. 5 (011), pp Campbell, J. Asse Prices, Consumpion, and he Business Cycle. Working paper 6485, Naional Bureau of Economic Research, Cochrane, J. Financial Markes and he Real Economy. Working paper 11193, Naional Bureau of Economic Research, REGIME-BASED VERSUS STATIC ASSET ALLOCATION: LETTING THE DATA SPEAK FALL 015

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