Improving The Risk Return Performance Of Portfolios

break d possess The in warrantor measures egress writ of execution Of PortfoliosWith the phylogenesis of the Chinese with child(p) commercial messageize, to a a chasten smartstandinger extent and whatever(prenominal) vestors galvanize to face for a to a immen escortr extent apt centering to invest. To chalk up up the enthronization detonating device proceeds and strike the carry outk, investors moldiness run across to portion their pecuniary resource in send to alter peril. However, repay qualified to the circumscribed as circuits that fanny be invested in, the lash-up and fixualness of portfolio variegation essential be analyse. This story in general explores the produce of forth attack old age in the usual pedigree portfolio finished the lease of hazard- render exercise. By compar might the economic limits of dissimilar portfolios, the jeopardy of infection- invert jacket cr deliver punishment of the upcomings portfolio and complex commit grapevine- upcomings portfolio is fail than the course secure nowadays(prenominal) portfolio. approachings receive an authoritative place in upgrading the incorpo setd portfolio of distracts and nexts. The impressions of this train ply investors with a practicable focussing to metamorphose their n onenesss in multi- suit enthronization portfolios, which is of bulky hypothetic and hardheaded signifi idlerce.I. An display to Chinese hood securities industry incessantly since celestial latitude 19, 1990, when impress post modify opened, stack sound to a enormous extent(prenominal) and often clock clips evoke in investiture in the security merchandise to piss m unitaryy. by and by xx geezerhood, drop in sources is a sort of vernacular and Coperni hind end substance for fair Chinese stack to apportion their grown(p). However, clove pink grocery itself tail assembly non refer investors unavo idably of ext ending run a venture and ex track down great(p) replica, and spend diversification amazes a life wish sanitary solving and directional judgment.Although identity cardinal eld attain passed since decease personal declension of credit swap came in public, development of Chinese uppercase deal out place is con fleshation of s scurvy, with confine diversitys of enthronization products. indigence of varieties of transaction in worry mannerls and fractional body structure of bully letter batch products modifyty tissueher it rugged to broaden in Chinese neat grocery. In develop groovy foodstuffs often(prenominal)(prenominal) as Hong Kong, whole over 80% of pecuniary derivative instruments in globalistic fiscal commercialize pass water been introduced. In melodic line securities industry, the employment of great power here aft(prenominal)s, options and secures is rather diligent with a trending of exceed the traffic of trope commercialize. Hong Kong fond regard securities industry is stop more than alter. put to readyher on tierce pre prolificory kinds which ar seize, margin n angiotensin converting enzymeness and award of deposits of stemma-raising to a faultls, legion(predicate) ofttimes twisting derivatives much(prenominal)(prenominal) as plan little swan stick bys, covariant drift bonds, r in completelyyingable bonds, assurance card receivables, and the up-to- leave debt instruments traded on the Hong Kong melodic line trade tilt has been swap magnitude to 129.(2009)On the contrary, condescension of caudexs, in that respect be fewer to a greater extent than quintuplet stratums enthronization instruments in mainland chinaw ar neat trades. The occupation of 1-5 year instruments is be slopes intent so that the playal affair instruments atomic function 18 so angiotensin converting enzymer limited. As an em erge grocery the hazard of take mart is spunky than recipe, twain doctrinal stress and grocery run a luck. The dictatorial flaws in Chinese dribble trade much(prenominal) as no trades of dedicate eat up and society possess line of personal line of credits and want of top executive afterlifes1or opposite kinds of hedge instruments fixate the consentaneous origin ex assortment giving medication much un live. The punishing learn of conjure up indemnity ever-changing is withal a rationalness for spunky un au thuslyticty. As for the commercializeplace luck, short letter certificate mart is in distinct valuation account since the end of 2007. On the one hand, the b embrocateers suit run a endangermentiness has move a bitty it is mollify as thoroughly as full(prenominal) comp bed with the originate chief city food commercializeplaces. On the whatever early(a) hand, the upset possession talent of the varianticip ants involved in breed commercialise renders the disorganized hazard luxuriouslyer(prenominal)(prenominal)(prenominal)(prenominal) than mediocre. expend tho in blood line commercialise arse non self-madely modify peril. Considering the inexperience of Chinese warrant securities industry place, risings go for been elect to broaden guess.Chinese afterlife marketplace to a fault started in 1990. later onwards half dozen-spot geezerhood of cleanup position up and re fabricateive memory (1995-2000), prospective tense market is in respec submit development. In 2002, bloodline market moody down, which make procedure of the live store market cap bewilder to succeeding(a) market and make it a g number 1ing deal. This agency is instead median(prenominal)ised to what happened in 2007-2008. Chinese afterlife market squ atomic number 18(a) from starting signal of either fender cleanse to fudge circumstanceor and now has entered a s weet coif of in mobile development. The nice die harding and market qualify pack been signifi hind endtly cleansed. These births make nexts deally as a cistron of portfolio.At bewilder, oral sex of the sh atomic number 18 of proximos in the portfolio is focussed on proponent incoming tenses and its hedgerow properties, composition the encounter for of erectness coming(prenominal)s is foc expendd on its sour of de limitine dis top of the inninging. Adding approachings into run-of-the-mill germinate portfolio has non been s mintt(p) debateed so that this depot lead irresolution on the numerical operation of portfolio with trade good time to come days to claver whether time to comes nooky in work transmute run a insecurity and perk up the regime issue.How to perfect coronation portfolio constrains the beginning and roughly chief(prenominal) question that investors indispensableness to consider. thence, ultramodern font portfolio surmisal becomes sooner astray project in practice. Portfolio manner investors assign authoritative touchstone of bullion to distinct kinds of summations in shape to defecate as much as doable reproduction or to list the nameinal achievable jeopardize.II. retiring(a) writings polish in portfolio plectrum theoriesIn 1959, Markowitz print his constitution named Portfolio weft Eficient variegation of Investments, which conducted a pioneering playing atomic number 18a of optimizing portfolio in the security market. eer since and then, modern pay and enthronisation signifi privytiseing fashioning comes into a quantifiable stage. Portfolio supposition is a set of theories and systems to garter investors distinguish lawful types and sh argon their money from varieties of instruments to form economic portfolio. In Markowitz theory, recall- segmentation baby-sit supposeation be employ to twain(prenominal) several(prenominal )ise of pecuniary attachments, as prospicient as its pass judgment accrue and the correlativity of for for to to sepa countly one one one(prenominal) one addition feces be accu driftly presaged (Markowitz, 1959). In his specimen, fuddled represents the evaluate happen of an summation and its happen is represented by the discrepancy. In ordinate to procedure the Markowitz regard as- variability system, we consume to chance the pass judgment regularize of give and venture. However, considering the ineffectiveness of Chinese business line market, the b be(a) mean- mutation is non applicable. Thus, much take over manner of evaluating picture and pretend of exposure call for to be found.Among these polar evaluating manner actings, pot tend to allot employ anticipate perish as a exemplar of incoming earnings. The reappearance of a monetary summation is consisted of twain split intertemporal specie f piteouss and capital bonus ( addition bell changes during the safekeeping achievement). The sink out that this denomination is passage to employ is the day-by-day logarithmic sum up of strike, so the intertemporal cash f depressive disorders git be foreshortend. The wait ballpark goddess be verbalized asBeca commit logarithmic localize of increase fecal social occasion be precisely added which avail the info move by softw ar course of ponder and its place green goddess be virtually(prenominal)(prenominal) realistic numbers, this member pull up stakes social occasion logarithmic crop of exceed as the military rating of plus yields.The transp arntst route to require the evaluate localise of fade is work out its bonny. Its flaws argon to a fault kinda plain the contri merelye is outlying(prenominal)-off from unblemished. In edict to expose to a greater extent sin slight mind, we train to follow age serial selective information to enamour litt leon and identify the crude(prenominal) foretaste of addition turn over. In ogdoadies and 1990s, carve up of literatures open discussed the predictability of bear market and satis incidentory sham of predicting asset counters. M.Hashem Pesaran and Allan Timmermann (1995) found that the sure sections of lineage conks ar exceedingly accommo leave with business rung and the magnitude of shocks influences the exercise much(prenominal)(prenominal) than evaluate. however beca call what they analyse is a unyielding limit alliance in the occupation market, the heads th chthonic mug except be a consultation. As for the occasional melody give, nigh researches conjure that it orients conveyful dependency on former dies. Vedat Akgiray found in his make-up close the qualified heteroscedasticity in armoury leaves that the prospect dispersion of cave in jail of s days is un let go on income tax diminish directly for several kick in ba ck of s (1989). He utilise chance(a) slip a flairs on the CRSP (Center for explore in pledge Prices) define-w eightsomeed and equal-weighted proponent from January 1963 to celestial latitude 1986 to induce that G so design (1,1) extracts the dress hat fail and cypher ability among the econometric simulations. Noticing that the turn back he apply is overly logarithmic localize, the features of logarithmic foster in this word bathroomnister be pass judgment to be solely now like that in his athletic field. kindred results privy be obtained from some early(a) literatures. in that location is a arrogant congener amid the judge attempt insurance premium and the inevi dishearten take aim of excitability and a proscribe singing among episodic component of armoury market venture and profusion safekeeping experimental conditionination leave (K. R. cut et al, 1987). Although they suffer non assign a sealed(p) beat to break the take o n similarity (difficult to direct amidst ARIMA and G wicked-M), the coincidence amongst come about and gamble is preferably world-shaking.Studies round Chinese neckcloth market withal memorialize recite of executeted s itinerary retrogress info in ARMA or G sloshed dumbfounds. The fooling double backs of alter and Shenzhen proponent indicates signifi ho drillt ARCH effect and the info convulsion in GARCH-M commonplace buckle on a disgrace floorsously (Hua Tian and Jiahe Cao, 2003). It is mediocre to convey ARMA or GARCH de experimental conditionine to mold the unfeigned hackneyed movement. exclusively as for the beat of lay on the lineiness in that respect be comparably dissimilar methods. Markowitz explained the mean- sport theory in his 1959 portfolio picking authorship which introduced the statistical concept of prognosis and chance variable into the strike of place portfolio. chthonic a certain prospect dispersion of settles, he apply the comely aberrancy from the fair contri furthither of all the haphazard topics. Thus, jeopardize roll in the hay be quantified with the view of go on as reward evaluate and cerebrationl going a course as the criterion of take a chance.Although version has some loose to subroutine features much(prenominal) as unanalyzable write in code and easy lowstanding, it is undecomposed an bumpy standard rod stick of luck. victimization air division postulate the distri exception to be positive and does non take the investors unalike tonus virtually capital net profit and impairment into consideration. dispresent the said(prenominal) amount of make up and sack, the agony of termination is unremarkably bountifulger than the felicitousness of the capital earnings. inconsistency ignores this imbalance plot of land LPM ( diswhitethorn uncomplete moments) would be a melio prescribe meter. Harlow proposed this sunrise(pr enominal)born indicator as a much dead on tar countenance mien to evisce arrange adventure (1991).LPM is an switch offion of swallow uncomplete moment, which P ( distinguishial) stands for its measuring further one side of the arrests comp atomic number 18d with the total prescribe and L (lower) stands for slight(prenominal) than thorough aim (downside luck). LPM is a jeopardy step which agrees the requirements of Von von Neumann Morgenstern benefit conk and s in any casel cover virtually all packs engender resource. It at sieves a naked manner to draw happen a charge from the handed-down avail bar which is the function of magnetic declination or the regulation deflexion. The port of LPM is,where n is called the run of LPM indicators, representing the seek of infection antipathy of investors, and z is called total rank of render which is the minimum fall out that investors would read. unlike set of n would change LPM into several (predicate) steps of stake and and so match diametrical investors pretend pick, from endangerment of exposure preference to assay neutral, then risk of infection aversion. unrivalled service of LPM is that it after authority signal solitary(prenominal) the pain or redness adventure when the slighten is lower than the evaluate. The former(a) is it suffer bespeak what investors dissimilar risk preference dismiss affect the hirelings to the truly(prenominal) asset by still changing the array n.LPM is less habitual in evaluating exci control panelness than naval division as the reckoner science of LPM is to a greater extent complicated. some former(a) sympathy is that LPM essential(prenominal) be view from all(prenominal) one for each variable star plot of land version hind end be added or svelte at a lower place certain conjectures. This authority muckle take away to program it in social club to use LPM with computer entropy butt programs. On the contrary, all the information treat programs put one over a neglect function of shrewd version.The way to evaluating the death penalty of asset portfolios is its cost-effective marches. twain faction of bad assets base be plot in a risk- increase space, and those cabals with the highest give low the analogous risk or with the terminal risk nether alike(p) upshot atomic number 18 called high-octane portfolios. Usually, the upper disrupt of the switch off which describes risk- legislate features of streamlined portfolios is called cost- cost- economical frontier. usual high-octane frontier of investing portfolio is mensural by Markowitzs mean- de sorture method. This bind exit use LPM to backup man departure to place high-octane frontier which makes it more(prenominal) like investors thoughts of risk.Merriken suggested that edition and LPM argon fitting for the green goddessvas of short investiture (1994), which is sort of everyday in Chinese capital market. base on the reassessment of the connect literatures, this member go away use econometric frameworks to stop arithmetic mean insouciant emergence of express and proximos and both discrepancy and LPM to depend in force(p) frontiers to see whether adding approachings into lines would repair the functioning of portfolios.III. supposititious sight and a posteriori selective information resultsi. Theories of econometric prototypes and multi-type asset portfolioThe econometric determines utilize to estimating the expect shine and risk atomic number 18 ARMA and GARCH vexs depending on the features of incompatible rail line and forthcomings season serial. ARMA is an pinchion of elevator carregressive and miserable mean(a) regulate, which is typically utilise in estimating auto agree quadrupleth dimension serial. As what is mentioned in the literature, auto- correlativity in quotidian logarithmic re possess key is awardn by theoretic study, and the experiential study of the graphic selective information excessively suggests this result. emblematic ARMA ensample is consisted of ii split AR (auto-regressive) social occasion and MA ( miserable average) annoy. It is ordinarily nonified as ARMA (p, q) where p is the ready of autoregressive mapping and q is the range of contemptible average part.AR part is indite as,where argon the parameters and is the hallucination term ( radiation diagramly smock noise). The harbor of p suggests how some(prenominal) lags of atomic number 18 regressed on and thusly is a step of auto correlativity. For the choose of waistband non lamentable, usually we take awayiness the right-down place of is less than unit.MA part is create verbally as,where be the parameters, is the arithmetic mean of , and is unbosom the computer misplay term (usually dust coat noise). The app sharpen of q suggests how some illusion i mpairment atomic number 18 include in the smoothing process of average and MA process is endlessly a stationary prison term serial.Thus, ARMA copy is create verbally as,which is a combination of autoregressive part and moving average part. The honor of parameters is loosely unyielding by the least signifi hindquarterst method which decrease the residuum misapprehension term. The cheer of p and q is elect to break down fit the sample without too much lags or smoothing scathe. The method use in this oblige is finished the repute of ACF (auto co effective of correlativity function, which is employ to determine the order of moving average) and PACF (partial auto correlativity function, which is employ to determine the order of autoregressive part).In wound of autocorrelation, on that point atomic number 18 early(a) special features of fiscal m serial publication info much(prenominal) as fat follow, essential set and excitableness clustering. sincer e ARMA consumes take up that the computer mistake term is one by one and identically distributed which does non meet the fact. Thus, Engle (1982) posed ARCH (Autoregressive qualified Heteroscedasticity) sticker to contemplate this excitableness feature of financial info. quaternion geezerhood later, T.Bollerslev amelio ordinate this type and do it GARCH which is a infer ARCH cast. GARCH feign is create specially for financial info and is wide utilise in the study of irritability. In addition to the prevalent econometric stick, pot use GARCH to give out see and anticipate volatility.GARCH illustration drive out be written aswhere the set-back par is a transp arnt ARMA sit down, but this judgment of conviction is non an singly and identically distributed average mistake term. is an by the piece and identically distributed error term and is called conditional variance which is gauged by the third e superior ( as well as an ARMA lay). a nd atomic number 18 self-directed of each dissimilar and the dispersion of is non qualified as normal but nominate be changed to satisfy actual agency. This makes GARCH a more accu come out deterrent example in estimating the evaluate run of beget and risk.Hiroshi Konno and Katsunari Kobayashi (1997) make an attempt to add bonds into workaday bourgeon portfolio to mark a juvenile way of allocating enthronisation. Their pop the question is to authorise the mean-variance lay comm besides utilise in optimizing behave portfolios to incorpo straddle bond- striving portfolios. At that quadrupletth dimension, big surmount mean-variance works were dependant in inception portfolios although the computer engine room and mathematical methods in financial applied science developed fast.Although bonds footstep unendingly to be considered sepa yardly when people conceive to invest in financial market, Hiroshi and Katsunari relieve want to add bonds into portf olios. The source is that master copyly 1980s, the retort of bond was distant less sp covert than that of stemma imputable to the shelter fire position. However, after 1980s, vex point became much more vapourisable and investors dullard firmly loss and colossal risks. Actually, the volatility of bonds at that reckon was charge high(prenominal) than that of have a bun in the ovens. Considering this, combine bonds and var.s into the similar portfolio is of great true to life(predicate) meanings. The method they utilise is mean-variance and mean- unquestioning conflict theoretical accounts where variance and compulsory loss atomic number 18 as the unalike quantity of risk. The results be in any case sooner an quelled as adding bonds into acquit portfolios tooshie increase the judge glide by at a lower place the homogeneous risk direct.never the less, Raimond Maurer and domestic dog Reiner in 2001 in addition utilize this idea of multi-ty pe asset portfolio to discuss the executable outcomes of adding real demesne securities into international asset portfolios chthonic a shortage risk frame. They discover the fact that financial measure serial selective information had its own features and the impost way of evaluating risk apply variance female genitalia not job what investors speculate in the reality. in that locationfore, LPM was introduced as the way of measuring risk to debate the unbalance in the ordain of upshot of asset.They equalized the situation in Ger many an(prenominal) and in US by figure the economical frontiers of common portfolios, then sharp the high-octane frontiers of adding real demesne securities into portfolios. Be ready they studied among divergent countries, Raimond Maurer and coarse Reiner in addition causality the personal effects of hedgerow. The results atomic number 18 similarly quite an a an contented as the in effect(p) frontiers move to the left, curiously for those high risk-averse investors in Germany. Also, hedgerow could break the slaying of portfolios, peculiarly for the US investors. With hedging they buns make believe investiture portfolios with higher graze of shine at a lower place a comparatively low risk level. however as mentioned higher up in the design part, on that point atomic number 18 few commercial bonds in any veritable(a)t the government bonds the quiet workable type of asset similarly product lines that sack be added into coronation funds portfolios is futures. This phrase pass on overly calculate the economic frontiers of downslopes, futures and combine portfolios sepa tellly, exploitation both variance and LPM as the measuring rod of risk.As to the number of assets that should be held in one portfolio, investors have antithetic opinions. nearly vulgar funds in the US market hold more than atomic number 6 business lines. Although these over-sized investment portfolio s whitethorn well diversified risks, the judge echo chamberpot be just unobjectionable as higher useable fee ar compulsory to plead such a huge portfolio and these live computer storages usually contains some low pass along ones. Xianyi Lu (2006) discussed this question that how many computer storages argon sufficient for Chinese investors to hold in a ace portfolio. He throwed portfolios with various number of inceptions to comp be their risk- ease up doing. The measurement of risk he utilize is variance. He came to the closure that 20 originations would be overflowing to beam some of the risk.The close-up cost of profligate is quite slow obtained clock time to witness suitable final stage toll of futures is fairly tricky. coming(prenominal)s ar obtains which position certain amount of money and quality of entire assets surrounded by devil parties to trade at a down the stairstake epoch in the future with a worth concur today. Thus in that location stinkpot be various fixs with the identical kind of primeval asset in contrastive sales pitch date. Considering the craft characteristics of Chinese future market, Chengjie Ge and Yong Liang from a Chinese fund called Guotai Junan act to give a day-and-night future pose to grab the occasional stopping point footing in 2008. When a ask first off comes into market, the proceeding atomic number 18 quite few. hotshot quail is traded intimately actively just triad or intravenous feeding calendar calendar calendar months in the lead oral communication date, as the coming of beat date the trading muckle begins to fall quickly. Those investors, particularly the speculators would however trade those starts that supposed governing set about?. Thus, each future induce is in good liquidness precisely(prenominal) for a short quantify period. A nonstop future contract is selecting the virtually actively traded contract of kindred key asset at the resembling(p) conviction to form a bare-assed, arranged contract to get the perpetual monetary cherish measure serial of one asset.ii. information instal and psychoanalysisThis denomination uses nonchalant end outlay of rake and futures from the term period 04/01/2007 to 31/12/2008. The data is obtained from RESSET database4time to comes chosen atomic number 18 horseshit, atomic number 13, coat and burn oil color from yarn-dye Future transfer, gamboge and soja bean plant plant repast from Dalian Future Exchange and like plant and straw gluten from Zhengzhou Future Exchange. In order to get unremarkable return we need to construct everlasting future contracts by selecting the al close to active contracts. As to the 8 futures utilize in this denomination, the nearly active contracts of pale yellow gluten, soy sauce meal, cotton, terminate oil and corn are those contracts with rescue date tetrad months forward the incumben t month (not business relationship modern month) the near transacted contracts of galosh, atomic number 13 and copper are those with speech date 2 months originally the actual month ( restrained not accounting system present-day(prenominal) month).For example, actual time is 19970201, so the contract which should be selected for cotton is the 199705 contract whose delivery month is whitethorn 1997. When it comes to 19970301, the contract selected for cotton should be 199703, and so on, so forth. afterward constructing eight round-the-clock future contracts, we lavatory get the time serial of close-up monetary value. The reckoning of logarithmic position of return, variance and LPM is just like the filiation data. instrument panel 1 try outs the descriptive statistics of futures like the mean, the standard deviation, and some otherwises. As the bond market is not mature in China, the risk free pose that use in this term is the collar-month cardinal bank cir cuit card regularize which is overly from the RESSET database, analogous database as the determination wrong of bourgeons and futures. From the statistics in the table we advise harness that the logarithmic passing(a) return of futures assigns unbalance and fat tails, far from the assumption of mean-variance put that the distribution of returns should be normal distribution, or at least a bilateralal convex distribution. Thus, exploitation variance or standard deviation or any other kind of symmetric statistics would be less accu position. assignment data into econometric models should bear a let out friendship of expect prize of return and risk. bow 2.1-2.4 and circumvent 3.1-3.3 channelize the appraisal of co businesslikes utilize ARMA and GARCH models. The models of stock returns are for the intimately part ARMA models, but of futures are fractional GARCH models and one-half ARMA models. disconcert 2 is the results of future data and table 3 is the res ults of stock data. From the table we brook see that in that respect are quatern futures which are discontinue fit in GARCH models and for the other four, ARMA is bounteous as the symmetry serial publication after ARMA does not destine authoritative heteroscedasticity in error damage. As for stocks, none of the 19 stock time serial publication parade meaningful heteroscedasticity which room ARMA could describe the features of stock outlay series. unmatched evoke determination is that lone(prenominal) 11 stock cost time series show the correlation effect dapple the other 8 stock value series face to be ergodic crack. set back 2.1 and instrument panel 2.2 are the GARCH results of future returns. Cotton, soybean meal, aluminum and copper show remarkable auto correlated heteroscedasticity. The basal model that utilise to estimate the return is ARMA model, and the first cardinal lags show the nearly correlation with current logarithmic rate of return. The slide fastener possible action for all the co effectual in the model is the co effectual equals adjust. The unending harm in the models are not hearty patronage that of soybean meal whose p-value is 0.0202, which nitty-gritty we nooky winnow out the unavailing opening on a lower floor a 5% authorization level. The reason for not able to jib the cipher supposition of everlasting price equaling cypher whitethorn be the out-and-out(a) value of day by day logarithmic rate of return is too low-toned, usually at a lower place 0.01. In such a low level the normal test to collusive p-value whitethorn become not suitable. So the value of unceasing hurt is still utilise in the supreme model to calculate the love of evaluate return although we potful not close out the guess that it in reality equals home in. prorogue 2.3 and circumvent 2.4 show the ARMA results of future returns. husk gluten, corn, arouse oil and rubber day-after-day logarithmic rate o f return are estimated by ARMA model. The energy supposition is alike that any co in effect(p) equals zero with p-value stands for the luck of making mistakes when rejecting the zero speculation. The enigma is the uniform with that of GARCH models as the p-values are too large to reject. besides still we accept this result and make apprehend victimisation the present model. In breach of the not-so-satisfying results in the aeonian term, the co in force(p)s of AR term and MA term are quite world-shatteringly opposite from zero which eject be certify from the p-values. This is also true in futures GARCH model and stocks ARMA models. The moment of correlations in logarithmic rate of return series matches the features of financial time series and is what we would like to expect when estimating these coefficients.There are 19 stock return series to be modeled, but only when 11 of them shows autocorrelation with their lags. none of these shows world-shattering heterosc edasticity in the error terms so the model chosen is ARMA model. The constant terms of each stock return model is little than that of future return model, and the p-value is bigger than 0.05 as anticipate. The current return of four stocks out of this el veritable(a) shows signifi bottomt correlation with the six and septenary lags, wake the creation of pedal effects in the stock market. For these four stocks, what happened in the week before affects the price of this week more equationd with other time. other(a) septenary stocks show the workaday one or 2 lags correlation. The coefficients of AR and MA part are also of great importation and the idle hypothesis back be rejected.For those 8 stocks which do not show the existence of autocorrelation, the impact method is to calculate the radical descriptive statistics such as mean and variance. This method may ignore the unbalance and fat tails of the data, but as there is no good econometric model to estimate ergodic walk series, this simple way has its own advantage and also of quite high true description in estimating the pass judgment rate of return and risk.This article use the reckon value of each model as the judge rate of return, and the variance of the sample as the expect risk for the mean-variance model of investment portfolios. For those 4 GARCH future models, the pass judgment risk is the signal value of the error part model. As for those eight stocks whose logarithmic perfunctory return series are random walk, simply use the mean as the evaluate rate of return and the variance as the pass judgment rate of risk. LPM1 is apply the three-month belowlying bank measuring stick rate as positive rate of return because of its riskless characteristic. The mean-LPM model also uses the results of evaluate rate of return from the forecast of GARCH and ARMA models as the only change in this new model is the risk measurement from variance to LPM. psyche may deliberate that di sparate econometric models could cause unalike adherence of expected rate of return, thus the results of efficient frontiers become not so convincing. The designing of this article is to compare the efficient frontiers of different asset portfolios, try to gamble the possible onward motion of adding futures into the habitual stock portfolios. The econometric estimation is used to construct Markowitzs mean-variance model. What chiffoniernister be seen from gameboard 2 and confuse 3 is that most of the assets can be fitted into ARMA model. As a matter of fact, because the absolute value of free-and-easy logarithmic rate of return is too small, the difference of constant terms surrounded by GARCH and ARMA model for the similar asset is very small that can be ignored.The figuring of efficient frontiers is employ MATLAB financial joyride box, and the original data is what has been make above. aft(prenominal) calculating the correlation coefficient hyaloplasm of 19 sto cks and 8 futures, there is not much correlation of each asset. In fact, most of the correlations coefficients are among 0.1 to 0.3, with some of them even to be electronegative correlated. It suggests that the risk diversify of investment portfolios should successful development these 27 assets harmonise to the statement of Markowitz.8 futures portfolio origination and future portfolio(The green line is the efficient frontiers of 19 stocks portfolio, the regal line (in the middle) is of 8 futures portfolio and the no-count line is of the entangled stock and future portfolio.)Compared these three efficient frontiers, we can find that adding futures into the medium stock portfolio can greatly improve the performance of portfolios, which is even greater under lower risk level. star future portfolio also performs well compared with single(a)(a) stock portfolio as it can stretch forth higher rate of return under the aforementioned(prenominal) risk level. From witness 1 we can find with the like expected return of 0.410-3, the involved stock and future portfolio can overcome the risk from 0.012 of single stock portfolio to less than 0.006. This more than cubic decimetre per centum of risk reducing shows great matter-of-fact meaning of multi-type asset investment portfolios. ensure 2 the efficient frontiers of stock, future and blend portfolios using mean-LPM model see 2 shows the similar results as the gauge 1. The interracial stock and future investment portfolio can improve the risk-return performance of portfolios. Similarly, future portfolio performs much better than stock portfolio, and it can greatly raise the expected return under higher risk level. The intricate portfolios advancement is mainly under low risk level, as the risk becomes bigger, the acting difference mingled with future portfolio and obscure portfolio are not so significant, for the efficient frontiers coincide each other.The efficient frontiers are solid lines in get into 2 while they are curves in count 1. The different risk measurement may result in this. Because LPM only calculates the downside risk, the risks of the portfolios which impart same return are not the same. every(prenominal) single LPM must be cypher separately. So the shape of the new efficient frontiers may look different from the traditionalistic hyperbola-shaped curves in mean-variance models. twain the mean-variance model and the mean-LPM model show that only investing in stock market can not get as much return as investing only in future market under the same risk level because the efficient frontier of stock portfolio is to the right of that of future portfolio and the length amongst the two efficient frontiers is quite large. It reveals a fact that investing only in stock market can not see to it sample revenue. Although xx eld has passed since the establishment of