風(fēng)險(xiǎn)價(jià)值計(jì)算題附答案

1、考慮一個(gè)兩股票的組合，投資金額分別為60萬(wàn)和40萬(wàn)。I一、下一個(gè)交易日，該組合在99%置信水平下的VaR是多少？二、該組合的邊際VaR、成分VaR是多少？三、如追加50萬(wàn)元的投資，該投資組合中的那只股票？組合的風(fēng)險(xiǎn)如何變化?要求：100萬(wàn)元投資股票深發(fā)展（000001）,求99%置信水平下1天的VaR=?解：1、 歷史模擬法樣本數(shù)據(jù)選擇2004年至2005年每個(gè)交易日收盤(pán)價(jià)（共468個(gè)數(shù)據(jù)）,禾用EXCEL:獲取股票每日交易數(shù)據(jù)，首先計(jì)算其每日簡(jiǎn)單收益率，公式為：簡(jiǎn)單收益率=（Pt-Pt-i）/Pt-i,生成新序列，然后將序列中的數(shù)據(jù)按升序排列，找到對(duì)應(yīng)的第468X1%=4.68t數(shù)據(jù)（謹(jǐn)慎起

2、見(jiàn)，我們用第4個(gè)），即-5.45%。于是可得，VaR=100X5.45%=5.45萬(wàn)。如圖：MicrosoftExce101F密文件（E）編輯場(chǎng)視圖插入格式工具數(shù)據(jù)窗口色）郭助出）frticrQsoftOffice是非正版橙校版本.點(diǎn)擊此處，立即行動(dòng)。遠(yuǎn)離潛在風(fēng)險(xiǎn)、享受正版卓越體臉.D3於=(B3-B2)/B2ACDEFG1日期價(jià)格P簡(jiǎn)單收益率YY由低至圖排序結(jié)果22004-01-028,6432004-01-058.920.03240740”-0.09803921642004-01-069.330.045964126-0.08246073352004-01-079.390.006430868

3、06734006762004-01-089.410.002129925-0.054s4545572004-01-099.03-0.040382572-0.05186020382004-01-129.190.0177187150.04662379492004-01-139.18-0.001088139-0.043227666102004-01-149.03-0.016339869-0.042881647112004-01-159.10.007751938-0.041731066122004-01-169.280.01978022-0.041025641132004-01-299.530.0269

4、39655-0.040697674142004-01-309.28-0.026232949040382572152004-02-029.670.042025862-0.040257649162004-02-039.830.016546019-0.038580247172004-02-0410.010.018311292-0.038461538132004-02-0510.060.004995005-0.038073908192004-02-0610.510.04473161-0.037735849202004-02-0910.590.007611798-0.036964981212004-02

5、-1010.740.014164306036020583222004-02-1110,62-0.011173184-0.035335689232004-02-1210.51-0.0103578150.0352622062、 蒙特卡羅模擬法(1)利用EVIEWS軟件中的單位根檢驗(yàn)(ADF檢驗(yàn))來(lái)判斷股票價(jià)格序列的平穩(wěn)性，結(jié)果如下：NullHypothesis:SFZhasaunitrootExogenous:ConstantLagLength:0(AutomaticbasedonSIC,MAXLAG=0)t-StatisticProb.*AugmentedDickey-Fullerteststa

6、tistic-1.0382260.7407Testcriticalvalues:1%level-3.4441285%level-2.86750910%level-2.570012*MacKinnon(1996)one-sidedp-values.由于DF=-1.038226,大于顯著性水平是10%的臨界值-2.570012,因此可知該序列是非平穩(wěn)的。(2)利用EVIEWS軟件中的相關(guān)性檢驗(yàn)來(lái)判斷序列的自相關(guān)性。選擇價(jià)格序列的一階差分(P=R-Pt-1)和30天滯后期。結(jié)果如下：Date:10/20/09Time:17:03Sample:1/02/200412/30/2005Includedob

7、servations:467AutocorrelationPartialCorrelationACPACQ-StatProb.|.|.|.|1-0.012-0.0120.06600.797.|.|.|.|2-0.020-0.0200.24620.884.|.|.|.|30.0060.0060.26370.967.|.|.|.|40.0440.0441.17280.883*|.|*|.|5-0.083-0.0824.44530.487*|.|*|.|6-0.070-0.0716.78800.341.|.|.|.|7-0.004-0.0096.79480.451.|*|.|*|80.0780.07

8、59.67260.289.|.|.|.|90.0040.0149.67870.377.|.|.|.|10-0.023-0.0229.93030.447可知股票價(jià)格的一階差分序列P滯后4期以?xún)?nèi)都不具有相關(guān)性，即其分布具有獨(dú)立性(3)通過(guò)上述檢驗(yàn)，我們可以得出結(jié)論，深發(fā)展股票價(jià)格服從隨機(jī)游走，即：Pt=Pt-1+et。下面，我們利用EXCEL軟件做蒙特卡羅模擬，模擬次數(shù)為10000次：首先產(chǎn)生10000個(gè)隨機(jī)整數(shù)，考慮到股市漲跌停板限制，以樣本期最后一天的股價(jià)(6.14)為起點(diǎn)，即股價(jià)在下一天的波動(dòng)范圍為(-0.614,0.614)。故隨機(jī)數(shù)的函數(shù)式為：RANDBETWEEN(-614,614)用

9、生成的隨機(jī)數(shù)各除以1000,就是我們需要的股價(jià)隨機(jī)變動(dòng)數(shù)£to然后計(jì)算模擬價(jià)格序列：模擬彳/T格=P0+隨機(jī)數(shù)+1000再將模擬后的價(jià)格按升序重新排列，找出對(duì)應(yīng)99%的分位數(shù)，即10000X1%=100個(gè)交易日對(duì)應(yīng)的數(shù)值：5.539,于是有VaR=100X(5.539-6.14)+6.14=9.79萬(wàn)；HiVU44獨(dú)7孑咄的4,E*Ias整工.RJu-E10L推S.539E：模©價(jià)格的升序排列5.5265.S26UhiJdLVbbZb5.5265.5275.52TAB71初始價(jià)格PO隨機(jī)數(shù)(RANDBETWEE1U614,614)模默價(jià)格=口卜硬機(jī)效，10皿LUU14173

10、6.313j-jt.i?yi26.14-S56S.SB4256.14-5465.5945.529jT&.14308氏4485.5326.14-2226.9195.5366.idTS135.657E.53S區(qū)144906.635.5356.142436.3B35.53SE.H-2795.8615.5366.H293R4325,536bBJ"-fl1*1&tND"Cl6.14696.2095.53T916.14-93S.0475.53T92僅141006.245.537966.143566.496S.E3S976.14366息5065.539986.142636

11、.4035.539996.143086.4435.5391006.14-2565.8S45.5391016.H233瓦37215.5391C26.M6.52855391036.14-4025.T3B5.539104&a14328息4635.539區(qū)3馴三、參數(shù)法(樣本同歷史模擬法)(一)靜態(tài)法：假設(shè)方差和均值都是恒定的簡(jiǎn)單收益率的分布圖：R=(Pt-Pt-i)/Pt-iSeries:SFZ3Sample1/02/200412/30/2005Observations467Mean-0.000490Median-0.001253Maximum0.100694Minimum-0.098039

12、Std.Dev.0.022079Skewness0.621496Kurtosis7.030289Jarque-Bera346.1299Probability0.000000對(duì)數(shù)收益率的分布圖：R=LN(Pt)-LN(Pt-i)120100806040200-0.10-0.05-0.000.050.10Series:SFZ2Sample1/02/200412/30/2005Observations467Mean-0.000731Median-0.001254Maximum0.095941Minimum-0.103184Std.Dev.0.021970Skewness0.436698Kurtosi

13、s6.794598Jarque-Bera295.0232Probability0.000000通過(guò)對(duì)簡(jiǎn)單收益率和對(duì)數(shù)收益率的統(tǒng)計(jì)分析可知，與正態(tài)分布相比，二者均呈現(xiàn)出“尖峰厚尾”的特征。相對(duì)而言，對(duì)數(shù)收益率更接近于正態(tài)分布。因此，采用對(duì)數(shù)收益率的統(tǒng)計(jì)結(jié)果，標(biāo)準(zhǔn)差為0.02197。根據(jù)VaR的計(jì)算公式可得：VaR=2.33X0.02197X100=5.119萬(wàn)(二)動(dòng)態(tài)法：假設(shè)方差和均值隨時(shí)間而變化可以有多種不同的方法，下面簡(jiǎn)單舉例：1、簡(jiǎn)單移動(dòng)平均法：取30天樣本，公式為：一=(2R2)+30,通過(guò)EXCEL處理后結(jié)果為:62=0.000211028,貝U有(t=0.0145VaR=2.33X

14、0.0145X100=3.379萬(wàn)E469，枚=AVERAGE(D440:D469)ABcDEF1日期價(jià)格P簡(jiǎn)單收益率簡(jiǎn)單收益率平方方差預(yù)測(cè)值22004-01-028.6432004-01-058.920.0324074070.0010502452004-01-079.390.0064308684.13561E-05182004-02-0510.060.0049950052.49501E-05202004-02-0910.590.0076117985.79395E-05292004-02-2011.120.0500472140.002504724302004-02-2310.91-0.0188

15、84890.00035663931zuuq-uz-zaiu.bi-u.uzrayrriU.UUUi322004-02-2510.3-0.029217720.0008536750.00061609332004-02-2610.340.0038834951.50815E-050.000581585342004-02-2710.360.0019342363.74127E-060.000511286352004-03-0110.370.0009652519.31709E-070.000509939出2004-03-0210.450.0U7Y14561b.9514515-050.UUObllYYl382

16、004-03-0411.060.0424128180.0017988470.000514723392004-03-0510.67-0.035262210.0012434230.0005561314u2U04-0y-0K10.41-0.UZ436Y390.000597()90.00U5(>7024602004-04-0510.59-0.013047530.0001702380.00036012410y.U.uuyI4UZO3也（4fuuuuzo(r£2wumr0一乙ubaaaro=UHUU3mUUJ學(xué)i,r"hrTrir一1=i-rir-學(xué).DUQQU-UQITITW%

17、rBBHTrT5UVUlUlJR音七wuMX±O5MM9口心.3204V。2UU5-UY-U55.Yb-u.U13byMb3U.UUUIXYbbZU.UUUb4iyUK4Ub2uu&-uy-uyVVVXV-Ub.Zb-u.UllUYbybV-VU.UUU122bYTv.vv_i_uu-vuu-vU.UUU2Y4Jy2V.vvvv4632005-12-226.06000.0002059734642005-12-236.130.on55n550.0001334290.0002103134652005-12-266.230.0163132140.0002661210.0002152

18、744662005-12-276.2-0.004815412.31882E-050.000215944672005-12-286.17-0.004838712.34131E-050.0002140734682005-12-296.220.0081037286.56704E-050.0002158464692005-12-306.14-0.012861740.0001654240.000211028.12、指數(shù)移動(dòng)平均法：借鑒RISKMETRICS技術(shù)，令衰減因子入=0.94,在EVIEWS中做二次指數(shù)平滑,結(jié)果如下圖：Date:10/20/09Time:21:50Sample:1/05/200

19、410/18/2005Includedobservations:467Method:DoubleExponentialOriginalSeries:SFZ4ForecastSeries:SFZ4SMParameters:Alpha0.9400SumofSquaredResiduals0.002756RootMeanSquaredError0.002429EndofPeriodLevels:Mean0.000165Trend9.24E-05方差的預(yù)測(cè)值(T2=0.000165,貝U有(t=0.0128VaR=2.33X0.0128X100=2.982萬(wàn)3、GARCH通過(guò)觀察發(fā)現(xiàn)，該股票收益率的波

20、動(dòng)具有明顯的集聚現(xiàn)象，因而考慮其異方差性。對(duì)殘差進(jìn)行ARCH檢驗(yàn)，結(jié)果表明存在著明顯的ARCH效應(yīng)ARCHTest:F-statistic11.76612Probability0.000657Obs*R-squared11.52408Probability0.000687TestEquation:DependentVariable:RESIDA2Method:LeastSquaresDate:10/20/09Time:23:19Sample(adjusted):1/07/200410/18/2005Includedobservations:465afteradjustmentsVariable

21、CoefficientStd.Errort-StatisticProb.C0.0004025.75E-056.9835550.0000RESIDA2(-1)0.1571270.0458073.4301770.0007R-squared0.024783Meandependentvar0.000478AdjustedR-squared0.022677S.D.dependentvar0.001159S.E.ofregression0.001146Akaikeinfocriterion-10.70047Sumsquaredresid0.000608Schwarzcriterion-10.68266Lo

22、glikelihood2489.860F-statistic11.76612Durbin-Watsonstat2.022064Prob(F-statistic)0.000657利用EVIEWS建立GARCH(1,1)模型如下：Rt=-0.051501Rt-i+&t(Tt2=0.0000231+0.084672£t-i+0.8662126t-i2DependentVariable:SFZ2Method:ML-ARCH(Marquardt)-NormaldistributionDate:10/20/09Time:23:13Sample(adjusted):1/06/200410/

23、18/2005Includedobservations:466afteradjustmentsConvergenceachievedafter14iterationsVariancebackcast:ONGARCH=C(2)+C(3)*RESID(-1)A2+C(4)*GARCH(-1)CoefficientStd.Errorz-StatisticProb.SFZ2(-1)-0.0515010.049748-1.0352490.3006VarianceEquationC2.31E-056.45E-063.5737520.0004RESID(-1)A20.0846720.0162455.2121

24、560.0000GARCH(-1)0.8662120.02061342.021720.0000R-squared-0.002784Meandependentvar-0.000801AdjustedR-squared-0.009295S.D.dependentvar0.021941S.E.ofregression0.022043Akaikeinfocriterion-4.895787Sumsquaredresid0.224484Schwarzcriterion-4.860214Loglikelihood1144.718Durbin-Watsonstat1.924864進(jìn)而可根據(jù)上述方程來(lái)預(yù)測(cè)下一期的收益Rt+1和方差口+12,在EVIEWS