金融第十二章-(2)[116页]课件.ppt

1、1Copyright Prentice Hall Inc.2000.Author:Nick Bagley,bdellaSoft,Inc.学习目的学习目的了解资产组合的理论与应用23Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall4 你应该如何更优化的投资你的财富？投资组合选择你的财富组合包含 股票，债券，非公司的业务股份，住房，养老福利，保险政策，所有负债Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall5有一般的原则来指导，但是需要你（

2、或你的配偶）的以下一些因素限制的 年龄，现有的财富，现有的和目标的教育水平，健康，未来的盈利潜力，消费偏好，风险偏好，人生目标，你的孩子的教育需求，对 家里老年人的义务，以及其他因素的主机Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall6投资组合选择研究人应该如何投资自己的财富Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall7你所受的风险取决于你的年龄 考虑两个投资（rho=0.2）证券1有20的波动和12的预期回报 证券2有8的波动和

3、5的预期回报Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall8以下图表显示由回报的二元正态分布产生的两种证券的价格 一个普通股或股票共同基金可能被认为是更危险的证券 债券或债券型基金常被认为是风险较低的安全 Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall9Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall10上，所以，你可以看到的重要特征债券轨迹的风险显然是

4、小于海军股票轨迹和的预期价格在日志格表上呈直线Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall11 总结方格表：波动与投资的长度成正比增加 你开始形成这样的猜想：早期的股价小于价格债券的机会较高Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall12 这只不过是有两种相同资产和两个相同变量及它们之间的关系产生的轨迹的无限数据里的一个，-我没有骗你，这确实是统计数字产生的轨迹-后面的轨迹也没有被重新排序，也未被编辑Copyright 2009

5、 Pearson Education,Inc.Publishing as Prentice Hall13Security Prices101001000100001000000510152025303540YearsValue(Log)StockBondStock_MuBond_MuCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall14Security Prices101001000100001000000510152025303540YearsValue(Log)StockBondStock_MuBond_MuCo

6、pyright 2009 Pearson Education,Inc.Publishing as Prentice Hall15Security Prices101001000100001000000510152025303540YearsValue(Log)StockBondStock_MuBond_MuSecurity Prices101001000100001000000510152025303540YearsValue(Log)StockBondStock_MuBond_MuSecurity Prices101001000100001000000510152025303540Years

7、Value(Log)StockBondStock_MuBond_MuSecurity Prices101001000100001000000510152025303540YearsValue(Log)StockBondStock_MuBond_MuCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall16从猜想到假说Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall17 我答应在在建立模拟轨迹的指令时是绝对的坦率和诚实（pfah）Copyrig

8、ht 2009 Pearson Education,Inc.Publishing as Prentice Hall18Security Prices101001000100001000000510152025303540YearsValue(Log)StockBondStock_MuBond_MuCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall19 债券和股票结束了在大约相同的价格，当预期价格有较大的分离的 要么是有一个很好的解释，或者是一个非常高的概率，我并没有那么绝对的坦诚和诚实Copyright 2009 P

9、earson Education,Inc.Publishing as Prentice Hall20一个小的数学计算后，我们就能够得出未来2，5，10甚至40年的发行的股票和债券的价格 Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall21Probability of Future Price0.0000.0050.0100.0150.0200.0250.0300.035050100150200250300ValueProbability DensityProb_Stock_2Prob_Bond_2Prob_Stoc

10、k_5Prob_Bond_5Prob_Stock_10Prob_Bond_10Prob_Stock_40Prob_Bond_40Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall22 在这里有很多东西在改变着，所以我们将进一步限制我们的观点 先来看看超过10年期的股票价格 价格分布是根据对数正态分布的Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall23Probabilistic Stock Price Changes Over Time0

11、.0000.0020.0040.0060.0080.0100.0120.0140.0160.0180.0200200400600800PriceProbability DensityStock_Year_1Stock_Year_2Stock_Year_3Stock_Year_4Stock_Year_5Stock_Year_6Stock_Year_7Stock_Year_8Stock_Year_9Stock_Year_10Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall24规模为0元至800元 随着时间的推移价格分布

12、向更高的价格扩散和漂移 扩散在前几年较以后的几年更明显 你可能会看到众数，中位数，平均值正随着时间不断的漂移分离开来Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall25你会记得，如果你投资购买了5年的无违约纯贴现债券，回报将是肯定 为了避免这种情况的影响，假设我们做了短期债券的投资，并在到期之后卖掉Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall26Probabilistic Bond Price Changes over Time0.

13、0000.0050.0100.0150.0200.0250.0300.0350.0400.0450100200300400PriceProbability DensityBond_Year_1Bond_Year_2Bond_Year_3Bond_Year_4Bond_Year_5Bond_Year_6Bond_Year_7Bond_Year_8Bond_Year_9Bond_Year_10Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall27 现在的规模是$0至$400（而不是在股票里面提到的0美元到800美元）我们

14、观察到了同类的扩散和漂移的行为，但程度要弱（记得规模调整）Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall28价格分布和轨迹，是由相同的分布产生的。但 他们似乎并不不同意分布显示产生了比运动轨迹比更低的平均值（预期收益）Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall29 结论是分布图有比你的直觉所允许的更肥的尾巴，促使中位数和平均值与众数之间随着时间而越来越远 左尾显示已经远离到无意义的那个区域对平均值有一个比较大的影响Copyrig

15、ht 2009 Pearson Education,Inc.Publishing as Prentice Hall30 下面的一系列的幻灯片对比了证券和债券在未来1、2、5、10和40年的的价格分布 有一些幻灯片显示不同的中央趋势量数 注意这些数据随着时间的增长而发生的变化Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall311-Year Out0.00000.00500.01000.01500.02000.02500.03000.03500.04000.0450020406080100120140160180200

16、PriceDensityStock_1_YearBond_1_YearMode=104Mode=106Median=104Mean=104Median=111Mean=113Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall32Two Years Out0.0000.0050.0100.0150.0200.0250.0300.035020406080100120140160180200PriceDensityStock_2_YearBond_2_YearCopyright 2009 Pearson Education

17、,Inc.Publishing as Prentice Hall335-Years Out0.0000.0020.0040.0060.0080.0100.0120.0140.0160.0180.0200100200300400500PriceDensityStock_5_YearBond_5_YearMode=122 Mode=135 Median=126Mean=128Median=165Mean=182Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall3410-Years Out0.0000.0020.0040.

18、0060.0080.0100.01202004006008001,000ValueDensityStock_10_YearBond_10_YearCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall3540 Years Out0.0000.0000.0000.0010.0010.0010.0010.0010.00205,00010,00015,00020,00025,00030,000ValueDensityStock_40_YearBond_40_YearMode=503 Mode=1,102 Median=650M

19、ean=739Median=5,460Mean=12,151Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall36 下表总结了中央趋势量数的动势 请注意，平均值的确是与轨迹回接了 最后一个轨迹（异常？）并不是一种罕见的状况，我对你是绝对坦诚和诚实的Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall37Value of Central Tendency Statistics for the LogNormal1_Year2_Years5_Ye

20、ars10_Years 40_YearsAssume:Sig=0.20,Mu=0.12mode$106.18$112.75$134.99$182.21$1,102.32median$110.52$122.14$164.87$271.83$5,459.82mean$112.75$127.12$182.21$332.01$12,151.04Assume:Sig=0.08,Mu=0.05mode$104.12$108.42$122.38$149.78$503.29median$104.79$109.81$126.36$159.68$650.13mean$105.13$110.52$128.40$16

21、4.87$738.91modeThe most probable pricemedian50%of prices are equal or lower that thismeanThe expected or average priceCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall38如果你年纪大了，投资的平均剩余寿命是比较短，那么你的风险证券投资有较大的概率是以亏损为结果的，如果你还有大量的资产，你能负担得起去冒这个险，并享有较高的预期回报的话，这些问题当然就不是问题了Copyright 2009 Pearso

22、n Education,Inc.Publishing as Prentice Hall39如果你年轻，退休投资的平均剩余寿命有更长的时间，那么风险证券投资基本上都会比安全的那个获利多 在风险较低的证券投资往往导致在退休后的收入明显较小Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall40 在一个典型的生命周期相对比较早期的时候，有可能需要清算一些投资基金，或许为了购房保证金，孩子的教育，或非投保医疗急用 提前清算的投资的情况可能会损害长远的目标，应该在低风险的证券投资一些做预防用的资金Copyright 2009 P

23、earson Education,Inc.Publishing as Prentice Hall41 规划时间跨度 调整投资组合决策间隔的时间长度 投资者可以修改其投资组合 的可能是最短的时间间隔Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall42 死亡率表可以被归纳为三列：精算师计算出的年龄，每前人死亡人数/每年，以及预期寿命。注意：如果你能从60活到65岁，例如，预计死亡提前了3至4年 年轻妇女预期寿命比男性高，但随着年龄的增长这种优势将会失去Copyright 2009 Pearson Education,I

24、nc.Publishing as Prentice Hall43 精算学会建设了一个网站，提供详细的死亡率表，交互式的计算机模型，抵押贷款的经验，职业信息，目前的研究论文Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall44Mortality Table Male FemaleAge MDePm MExLife FDePmFExLife6016.0817.519.4721.256117.5416.7910.1320.446525.4214.0414.5917.327039.5110.9622.1113.677564.

25、198.3138.2410.328098.846.1865.997.4885152.954.46116.15.1890221.773.18190.753.4595329.961.87317.321.91Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall45Deaths Per Thousand M&F0501001502002503003506065707580859095AgeDeaths/1000MDePmFDePmCopyright 2009 Pearson Education,Inc.Publishing a

26、s Prentice Hall46Life Expectancy05101520256065707580859095AgeRemaining Expected LifeMExLifeFExLifeCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall47 你对风险的耐受力是投资组合选择的主要因素 这是风险厌恶的镜像 无论其原因是什么，我们不区分城带风险的能力和对风险的态度Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall48 大多数人都没有时间

27、也没有必要的技能，去实现资产组合的最优化 专业的基金经理提供这种服务 单独设计满足顾客的确切需要的解决方案（$）一系列的金融产品，这可能会用来满足大多数客户的目标（$）Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall49假设一个世界只有一种单一的风险资产和一个单一的无风险资产 风险资产，在现实世界中，是一个风险资产的投资组合 无风险资产是一个具有到期日与投资者的决策时间跨度相同的无违约债券 Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hal

28、l50 这种只有有风险和无风险的证券的假设简化了分析Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall51Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall52 假设你投资了财富的W1比例购买第一种证券和W2比例的财富购买第二种证券。你的投资必须在1或2中，所以 W1+W2=1 让2作无风险资产，1为风险资产（组合）Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hal

29、l53 您的数据统计资料告诉你如何确定预期收益和任何两种证券组合的波动性 1.设有两个给定的随机变量R1和R2，从这两个变量的出的新的变量是投资组合收益RP 545556Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall57 无风险利率风险证券的预期收益率 58Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall59 考虑所有投资组合（长期或短期）的集合，都可以通过投资以下的几种形成 20的波动和15的预期回报 的风险证券 0的波动和已知的5

30、的收益 无风险证券Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall60A Portfolio of a Risky and a Riskless Security-0.20-0.15-0.10-0.050.000.050.100.150.200.250.300.000.100.200.300.400.50VolatilityReturnCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall61风险收益线的较低的部分而言，投资较高的部分是首选（

31、对于正常平民），所以我们当前的目的可能忽略低线 也就是说，我们不会出售短期风险资产而是将收益投资到无风险证券 Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall62Capital Market Line0.000.050.100.150.200.250.300.000.050.100.150.200.250.300.350.400.450.50VolatilityReturn Long risky and short risk-free Long both risky and risk-free 100%Risky

32、100%Risk-lessCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall63具有低风险承受能力的投资者可能会投资于一个包含小的风险证券和相应 的较高的无风险证券组合，一个高风险承受能力的投资者可能出售他不想要的无风险证券，将收益投资在 风险投资上 他们都会使用两个证券Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall64 该图已有点过早被贴上了“资本市场线”的标签 我们很快就会发现，如果 风险证券是风险证券的市场组合 投资者们有相似的期

33、望和时间跨度所有的投资者将投资市场组合和无风险的证券（长期或者短期）资本市场线加入风险和无风险证券的资本市场Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall65你的老板刚刚读了一个广告，这个广告包括杰纳斯二十基金（科学美国人，1998年9月，第6页）的数据“你击败他们，否则我就换另一个投资组合经理”，她打趣道“用了错误的方式来计算收益吗？”你在奔向门口时冒险问道Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall66YTD1-Yr3-Yrs

34、5-Yrs10-Yrs Life14.81 30.4015.8714.1516.5316.966768Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall69Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall70 它不需要太多技巧去巧用投资组合;股票经纪人将让大多数投资者进行有保证金的交易 评估投资的表现时，你必须对风险和预期收益都进行检查Copyright 2009 Pearson Education,Inc.Publishing as P

35、rentice Hall71共同基金的广告一般不披露的风险量化的措施，而Janus也不例外 从财务角度来看，广告的“二十基金”的收益是完全没有意义 需要更多的信息Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall72你可以利用预期的资金上升或者下降 如果你想要10或20，30，40，50，60的预期回报，你可以得到你想要的（前提是你可以继续在无风险利率借入为）Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall73 现在来回答这个问题还有点早

36、如果风险证券是市场组合，然后给你投资组合的风险，CML线以上的稳定收益会有很大的吸引力Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall74Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall75一个有效的投资组合被定义为在一个特定的风险下投资组合为投资者提供可能的最高预期收益率 我们现在探讨有多个风险资产的投资组合Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall

37、76 我们曾考虑 仅有单一的风险证券和单一的无风险证券的投资 每个证券共享相同的潜在的收益数据统计 的投资 现在，我们将探讨多个 多相的 股票的投资771 with;212211wwrwrwrpCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall78Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall792211wwpCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall

38、80 理想的情况下，我们希望有一个相似的风险结果)错了(2211wwp22222,12121212122wwwwp81Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall82W1*Sig1W2*Sig2W1*Sig11Rho(1,2)W2*Sig2Rho(2,1)12,121212222212122wwwwpCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall83W1*Sig1 W2*Sig2W3*Sig3W1*Sig11Rho(1,2)Rho

39、(1,3)W2*Sig2 Rho(2,1)1Rho(2,3)W3*Sig3 Rho(3,1)Rho(3,2)13,232323,131312,121212323222221212222wwwwwwwwwpCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall84与b的相关性与b和a的相关性是平等的 对于每一个上部三角的元素，都有一个对应的在较低的三角形的元素 所以计算 上三角元素一次之后，只需乘2就行 这推广了预期的方式85Copyright 2009 Pearson Education,Inc.Publishing a

40、s Prentice Hall862-Shares:Is One Better?00.020.040.060.080.10.120.140.1600.050.10.150.20.250.3Standard Deviation Expected Return Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall87 统计数据表明，一个证券似乎可以完全主宰其他的 证券1相对于证券2 具有较低的风险和较高的收益 在一个有效的市场：不是每个人都减少2，而购买1吗？不会提供然后需求，然后引起的相对预期收益“翻转”吗？Copyri

41、ght 2009 Pearson Education,Inc.Publishing as Prentice Hall88 用这种矛盾的形式选择两股的目的是为了说明下面的一个重要的观点 这种关系确实发生在现实世界中Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall89下图显示了根据我们选择的数据统计出来的两个股票价格的轨迹Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall90Share Prices0501001502002503003500

42、12345678910YearsValue(adjusted for Splits)ShareP_1ShareP_2Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall91 如果你从一个轨迹“切下一块”，重新衡量相对价格差异，并滑过其他部分，你会观察这两个轨迹表现出大致相同的过程，但每个人又都有独立的行为 在1至4年的区域，价格已经接近时快速确认Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall92 两股股票高度相关他们密切的跟着彼此，但即使

43、调整为不同的平均回报，他们也有一些个体行为Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall93Portfolio of Two Securities0.000.050.100.150.200.250.150.170.190.210.230.250.270.29Standard Deviation Expected Return Share 1Share 2EfficientSub-optimalMinimumVarianceCopyright 2009 Pearson Education,Inc.Publishin

44、g as Prentice Hall94高风险，低回报的股票，并重新投资在低风险，高回报的股票，创造高效的投资组合 减少80的净财富创造一个波动性为20和收益率为19（证券1的成本是15）的投资组合 减少180得到25的波动性和24的收益率（证券2成本是10）Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall95为了得到一个有着同样的风险，但有较高的收益率投资组合，求出权重最小的组合，方程稍后给出 使用其关系Copyright 2009 Pearson Education,Inc.Publishing as Pren

45、tice Hall96 另一种方式来得到两种证券是找到包含风险和无风险两种债券的投资组合，且满足有效的界限 结果：两个组合是延长风险债券，和削短无风险的证券 缩短投资组合中的一个，并在对其他的进行投资，以得到一种所需的有效组合 重复以得到其他的组合 证明无风险证券变得无关紧要Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall97下面的幻灯片是用于生成图表的计算样本Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall98Data For two

46、 securitiesThis data has been constructed to produce the mean-varience paradoxmu_115.00%mu_210.00%sig_120.00%sig_225.00%rho90.00%w_1w_2Port_SigPort_Mu-2.503.500.4776-0.0250-2.403.400.4674-0.0200-2.303.300.4573-0.0150-2.203.200.4472-0.0100-2.103.100.4372-0.0050-2.003.000.42720.0000-1.902.900.41730.00

47、50-1.802.800.40740.0100-1.702.700.39760.01501.30-0.300.19530.16501.40-0.400.19490.17001.50-0.500.19530.17501.60-0.600.19620.18001.70-0.700.19780.18501.80-0.800.20000.19001.90-0.900.20280.19502.00-1.000.20620.20002.10-1.100.21010.20502.20-1.200.21450.21002.30-1.300.21940.21502.40-1.400.22470.22002.50

48、-1.500.23050.2250-0.301.300.27230.0850-0.201.200.26460.0900-0.101.100.25710.09500.001.000.25000.10000.100.900.24320.10500.200.800.23660.11000.300.700.23050.1150Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall99w_1w_2Port_SigPort_Mu-2.5=1-A14=SQRT(w_12*sig_12+2*w_1*w_2*sig_1*sig_2*rho

49、+w_22*sig_22)=w_1*mu_1+w_2*mu_2=A14+0.1=1-A15=SQRT(w_12*sig_12+2*w_1*w_2*sig_1*sig_2*rho+w_22*sig_22)=w_1*mu_1+w_2*mu_2=A15+0.1=1-A16=SQRT(w_12*sig_12+2*w_1*w_2*sig_1*sig_2*rho+w_22*sig_22)=w_1*mu_1+w_2*mu_2=A16+0.1=1-A17=SQRT(w_12*sig_12+2*w_1*w_2*sig_1*sig_2*rho+w_22*sig_22)=w_1*mu_1+w_2*mu_2=SQRT

50、(w_12*sig_12+2*w_1*w_2*sig_1*sig_2*rho+w_22*sig_22)=w_1*mu_1+w_2*mu_2Copyright 2009 Pearson Education,Inc.Publishing as Prentice Hall100*122212,121212,121*222212,121212,122*1122wwwCopyright 2009 Pearson Education,Inc.Publishing as Prentice Hall101Copyright 2009 Pearson Education,Inc.Publishing as Pr