Portfolio Risk(Return+Measure)衡量投资组合风险与回报率
2018 CFA level 1 知识点——Portfolio Management
Portfolio ManagementPortfolio Management: An OverviewDescribe the portfolio approach to investing1.The portfolio perspective refers to evaluating individual investments by theircontribution on the risk and return of an investor’s portfolio.投资组合视角指的是通过投资组合对风险和回报的贡献来评估个人投资。
2.把所有钱用于买一只股票并不是一种portfolio perspective，把钱分散在多只证券中才能降低风险，增加收益。
3.One measure of the benefits of diversification is the diversification ratio. It iscalculated as the ratio of the risk of an equally weighted portfolio of n securities to the risk of a single security selected at random from the n securities.衡量多样化的好处之一是多样化比率。
它计算的是n证券等加权组合的风险与随机从n证券中选择的单一证券的风险之比。
4.If the average standard deviation of returns for the n stocks is 25%, and thestandard deviation of returns for an equally weighted portfolio of the n stocks is 18%, the diversification ratio is 18/25=0.72.Describe types of investors and distinctive characteristics and needs of each1.Individual investor个人投资者就是个人为了满足生活目标而进行理财的投资者，是牺牲当前消费以期获得未来更高水平消费的个人。
财务管理专业英语unit6
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12.Allocationally efficient markets 配置有效市场
operationally efficient markets 运营有效市场
informationally efficient markets 信息有效市场
When prices are determined in a way that equates the marginal rates of return (adjusted for risk) for all producers and savers, the market is said to be allocationally efficient.
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14.Anomaly 异常 15.Underpricing 价格低估 16.Monday effect 星期一效应 January effect 元月效应
On average, stocks have lower (negative) returns on Monday, compared to (positive) returns on other days of the week.
place, nor is my whole estate upon the fortune of this present years; Therefore, my merchandise makes me not sad.
——Shakespear, Merchant of Venice
我的买卖的成败并不完全寄托在一艘船上，更不是倚赖着一处地方；我 的全部财产，也不会因为这一年的盈亏而受到影响，所以我的货物并不 能使我忧愁。
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投资组合
狭义的现代资产组合理论——马克威茨 提出的 资产组合理论
广义的现代资产组合理论——资产组合理论、 资本资产定价模型、套购定价理论等。
研究结果表明，在相关系数ρ≤0时会产生向后弯曲的 情况，当ρ＞0时，向后弯曲则可能出现也可能不会出 现。当然，曲线中只有一小段向后弯曲，如果增加证 券A在证券投资组合中的比例，则该证券高的标准差将 使证券组合的标准差值上升。
④没有一位投资者愿意将其所持有的证券组合期望收 益率低于具有最小方差值的证券组合期望收益率。
sp = (0.0125)(1/2) = 0.1118
收益
E[Rp]
投资组合曲线
*A
0
MV* *B
sp 风险
投资组合曲线
结论
①只要两种证券之间的相关系数小于1，则组合风险就 会降低。
②点MV代表证券投资组合的方差最小值。这是证券投 资组合所拥有的最小标准差。
③曲线在B点和MV之间有一段向后弯曲，这表明在某 种比例的证券组合下，当期望收益率增加时，标准差 会减少。
五、组合投资风险分析
1952年，哈里·马克威茨 (H.M.Markowitz) 在 《金融月刊》上发表了“资产选择：投资的有 效分散化”(Portfolio Selection efficient diversi-fication of investments)一文，最早同时 采用风险资产的期望收益率和标准差代表的风 险来研究资产的选择和组合问题。
E(Rp) = XAE(R)A + XB E(R)B
金融工程讲义第三讲投资组合(portfolio)理论基础
第三讲 投资组合(portfolio)理论基础一．单个资产的收益和风险 1．期望收益(expected return)数学期望(mathematical expectation)的定义：若离散型随机变量X 的可能值为),2,1( i x i ，其概率分布为i i p x X P ， ,2,1 i则当：i i ip x1时，称X 的数学期望存在，并且其数学期望记作EX ，定义为：i i i p x EX1对于风险资产而言，其未来的收益是一个随机变量。
在不同的经济条件下，这个随机变量将取不同的值，而每一种经济条件的出现都有其概率。
把资产收益的不同取值乘以不同经济条件出现的概率，就能够对该资产未来的收益做出估计。
用公式表示为：i ni i i i r p p p r E111)( 式中，i r 为该资产收益的第i 状态的取值；i p 为资产收益取值i r 的概率；)(r E 为该资产的期望收益。
例题：已知某种证券在市场状况较好的情况下的投资收益率为45%，在市场状况较差的情况下的投资收益率为-15%，又已知未来市场状况转好的可能性为60%，市场状况转坏的可能性为40%，则该证券的期望收益为多少？%2121.006.027.0%)40%15(%60%45)r (E练习题：假设某种证券资产在A 情况下的收益率为35%，在B 情况下的投资收益率为15%，在C 情况下的投资收益率为-20%。
A 、B 、C 三种情况发生的概率分别为20%，50%和30%，求这种证券资产的预期收益。
2．收益的方差(Variance)方差(variance)和标准差(standard deviation)的定义：设X 为一个随机变量(random variable)，其数学期望EX 存在，则称EX X 为X 的离差(deviation)，进一步，如果2)(EX X E 也存在，则称2)(EX X E 为随机变量X 的方差，记作DX 或VarX ，并称DX 为X 的标准差。
做交易必看：诺奖得主马科维茨,教你如何分配仓位
做交易必看：诺奖得主马科维茨，教你如何分配仓位马科维茨于1990年获得了诺贝尔经济学奖，奖励他在投资组合理论上做出的贡献。
“马科维茨的工作确实不是经济学，不是数学，也不是商学。
它是一个完全不同的学科，就是金融学。
”今天，我们通常认为马科维茨的工作是现代金融学的开端。
本文作者：又一斋主，来自预测者网马科维茨与投资组合理论我多谢我的幸运，我的买卖并没有寄托在一只船上，也并非是到一个地方去的;我的全部财产也并不完全靠今年的命运;所以，我的货物并不足使我忧愁。
梁实秋译《威尼斯商人》第一幕第一景这是《威尼斯商人》中安东尼奥的一段话，而他就是剧中那个差点被高利贷商人夏洛克割了一磅肉的、正直的、而又过于自信的威尼斯商人。
从这段话中，我们可以看出安东尼奥(或者说是莎士比亚)已经理解了投资中的一个重要原则：分散投资原则，也就是“不要把鸡蛋放在一个篮子里”。
尽管这个原则尽人皆知，然而在1950年代初，却没有任何经济学理论可以解释为什么投资者应该分散投资。
当时，投资学的经典文献是John Burr Williams在1938年出版的《Theory of Investment Value》。
在书中，Williams指出，股票的价值是未来股息净现值的均值(即期望值)，也即是：其中R是贴现率，Dt是第t年的股息。
根据此理论，如果投资者只关心均值，那么他们应该将所有资本投资在收益净现值均值最大的一只股票上，也就是把所有鸡蛋放在同一个篮子里。
但这显然与分散投资原则相悖。
马科维茨(1952)就是想要解决这个问题，即解释“为什么投资者会选择分散投资?”1950年，马科维茨只有23岁，是芝加哥大学的一名博士生，师从后来被称为“计量经济学之父”的经济学家Jacob Marschak。
据说1950年的一天，他在Marschak办公室门口碰到了一个股票交易员，他们俩都等着见Marschak，所以就聊了起来。
马科维茨那时正在为博士论文题目发愁，这个交易员就建议他研究股票市场。
金融工程讲义 第三讲 投资组合(portfolio)理论基础
第三讲 投资组合(portfolio)理论基础一．单个资产的收益和风险 1．期望收益(expected return)数学期望(mathematical expectation)的定义：若离散型随机变量X 的可能值为),2,1( =i x i ，其概率分布为{}i i p x X P ==， ,2,1=i则当：∞<∑∞=i i ip x1时，称X 的数学期望存在，并且其数学期望记作EX ，定义为：i i i p x EX ∑∞==1对于风险资产而言，其未来的收益是一个随机变量。
在不同的经济条件下，这个随机变量将取不同的值，而每一种经济条件的出现都有其概率。
把资产收益的不同取值乘以不同经济条件出现的概率，就能够对该资产未来的收益做出估计。
用公式表示为：i ni i i i r p p p r E ∑=---=111)( 式中，i r 为该资产收益的第i 状态的取值；i p 为资产收益取值i r 的概率；)(r E 为该资产的期望收益。
例题：已知某种证券在市场状况较好的情况下的投资收益率为45%，在市场状况较差的情况下的投资收益率为-15%，又已知未来市场状况转好的可能性为60%，市场状况转坏的可能性为40%，则该证券的期望收益为多少？%2121.006.027.0%)40%15(%60%45)r (E ==-=⨯-+⨯=练习题：假设某种证券资产在A 情况下的收益率为35%，在B 情况下的投资收益率为15%，在C 情况下的投资收益率为-20%。
A 、B 、C 三种情况发生的概率分别为20%，50%和30%，求这种证券资产的预期收益。
2．收益的方差(Variance)方差(variance)和标准差(standard deviation)的定义：设X 为一个随机变量(random variable)，其数学期望EX 存在，则称EX X -为X 的离差(deviation)，进一步，如果2)(EX X E -也存在，则称2)(EX X E -为随机变量X 的方差，记作DX 或VarX ，并称DX 为X 的标准差。
投资收益风险度量方法
投资收益风险度量方法投资是一种风险与回报并存的行为。
在进行投资决策时，了解和衡量投资收益的风险是非常重要的。
本文将介绍几种常见的投资收益风险度量方法，帮助投资者更好地评估投资的风险。
一、标准差法标准差是一种常见的风险度量方法。
它衡量了投资收益的波动性，即收益的离散程度。
标准差越大，投资收益的波动性越高，风险越大。
通过计算历史数据的标准差，投资者可以了解投资的风险水平，并与其他投资进行比较。
然而，标准差法有其局限性。
它假设收益率服从正态分布，但实际上市场收益率往往并不服从正态分布。
此外，标准差法只考虑了收益的波动性，忽略了其他因素对投资收益的影响。
二、价值-at-风险法价值-at-风险法是一种综合考虑风险和回报的度量方法。
它将投资的价值与投资的风险相结合，计算出每单位风险所对应的投资回报。
这种方法更加全面地反映了投资的风险和回报的关系。
价值-at-风险法的核心思想是，投资者应该根据自己的风险承受能力来选择投资组合。
对于风险厌恶型的投资者来说，他们更倾向于选择风险较小的投资组合，而对于风险偏好型的投资者来说，他们更倾向于选择风险较大的投资组合。
通过计算不同投资组合的价值-at-风险比率，投资者可以找到最适合自己的投资组合。
然而，价值-at-风险法也有一些限制。
它需要投资者对自己的风险承受能力有清晰的认识，而这对于一些新手投资者来说可能是困难的。
此外，该方法需要大量的数据和计算，对于一些小规模投资者来说可能不太实用。
三、价值-at-风险法的改进为了克服价值-at-风险法的局限性，一些学者提出了一些改进方法。
例如，风险调整收益率方法（RAROC）是一种将风险和回报结合起来的度量方法。
它通过计算投资的风险调整收益率，来评估投资的风险水平。
风险调整收益率越高，投资的风险越小，回报越高。
此外，还有一些其他的风险度量方法，如半方差法、下行风险法等。
这些方法都有其独特的优缺点，投资者可以根据自己的需求和情况选择合适的方法。
证券投资基金投资组合的风险量化分析
证券投资基金投资组合的风险量化分析证券投资基金（以下简称基金）投资组合的风险量化分析是评估一个基金在市场中所面临的风险程度，并以数值化的方式来进行度量和分析。
通过风险量化分析，投资者可以更好地了解基金的风险特征，并做出相应的投资决策。
风险量化分析需要对基金投资组合的风险源进行识别。
风险源可以包括市场风险、信用风险、流动性风险等。
市场风险是指由于整体市场的波动而导致的风险，信用风险是指由于债券发行者的违约而造成的损失，流动性风险是指由于基金投资组合中的资产无法及时变现而导致的损失。
风险量化分析需要选择合适的指标来度量风险。
常用的风险指标包括标准差、VaR （Value at Risk）、CVaR（Conditional Value at Risk）等。
标准差是最常用的风险指标之一，它衡量了基金投资组合收益的波动性。
VaR是在一定置信水平下，基金投资组合在未来一段时间内可能出现的最大亏损金额。
CVaR是在VaR的基础上，对超过VaR的亏损金额进行平均。
然后，风险量化分析需要根据选定的风险指标，计算出基金投资组合的风险值。
计算风险值的过程中，需要对基金投资组合的历史数据进行分析和处理，包括收益率序列的计算、收益率序列的正态性检验等。
通过计算风险值，可以得到基金投资组合在不同时间段、不同风险指标下的风险水平。
风险量化分析还需要对基金投资组合的风险进行解释和评估。
投资者可以根据风险值的大小，对基金投资组合的风险特征进行比较和评估。
还可以将基金投资组合的风险与其预期收益进行比较，从而对基金的风险收益特征进行评估。
需要注意的是，风险量化分析只是对基金投资组合风险的一种度量和分析方式，并不能完全预测基金的未来风险。
投资者在进行风险量化分析的还需要考虑其他风险因素的影响，如经济周期、政策环境、行业竞争等。
并且，风险量化分析的结果只是一种参考，投资者还需要根据自身的风险承受能力和投资目标，做出适当的投资决策。
衡量企业投资风险的指标
衡量企业投资风险的指标
企业投资风险是指企业采取某种投资行动以后可能面临的风险。
企业投资风险的大小
和实现的概率与所采取的投资行动的性质、环境以及投资者自身的条件和能力等有关。
下
面介绍几个衡量企业投资风险的指标。
一、CAPM 模型
资本资产定价模型（CAPM）是一种衡量投资风险的经济学模型。
它通过收益率的预测
和风险水平的估计来决定资产的价格。
这个模型假设投资者会对收益和风险进行权衡决策，并把资产的预期收益率与无风险资产的收益率之间的差异，与风险的大小相关联。
二、内部收益率（IRR）
内部收益率（IRR）是企业投资风险的另一个常用的指标。
它是一个衡量项目的盈利能力的指标，它表示一个投资项目的实际年收益率，并且是可以与市场的收益率进行比较的。
IRR越高，投资项目的风险越低。
三、财务杠杆
财务杠杆（FL）是企业财务结构的一个重要指标，它是企业固定费用和负债之间的比率。
财务杠杆越高，企业的盈利能力就越高，但其风险也会增加，因为如果企业无法在规
定时间内偿还借款，则可能面临破产的风险。
四、成本效益（C/B）比率
成本效益（C/B）比率是金融分析中一个常用的指标，它是指在一个计划或项目的成本与预期收益之间的比率。
如果C/B比率大于1，那么该计划或项目是值得投资的，否则就
不值得投资。
金融英语词汇
金融英语词汇AAbnormal Return 超常收益比基于风险的证券预期收益更高的那部分实际收益Active Management Strategy 主动型管理战略通过交易活动获得额外收益的策略Advance-Decline Line 腾落线描述价格上涨的股票总数相对于价格下跌的股票总数的技术分析指标American Depository Receipts (ADR) 美国存托凭证代表对外国公司股票的所有权的证券Arbitrage Pricing Theory (APT) 套利定价理论关于较少涉及投资者偏好假设的证券预期收益的均衡理论Arbitrageurs 套利者寻求证券价格差异以获取无风险收益的投资者Ask Quote 卖方报价交易方愿意出售股份的价格Asset Allocation Decision 资产分配决定将资产组合基金分配成不同资产种类，如现金等价物、债券和股票等Asset-backed Securities (ABS) 资产抵押证券由某些与资产相关的债权，如应收信用卡账款或抵押物为担保而发行的证券Asset Management Account 资产管理账户经纪为投资者提供各种服务的账户，如现金余额的投资与支票开立权Average Annual Total Return 平均年度总收益率共同基金所使用的假定收益率，若当年实现了该收益率且在整个期间绩效表现稳定，该收益率将能产生同样的累计总收益BBar Chart 条形图每日股价随时间波动的图形Basis 基差某物品期货价格与现货价格的差异Basis Points 基点 100个基点相当于一个百分点Bear Market 熊市股市的下跌趋势Behavioral Finance (BF) 行为金融学基于投资者并非一直理性的投资行为的研究Benchmark Portfolio 标准组合用于衡量某组合绩效表现的组合Bid Quote 买方报价交易方愿意购买股份的价格Black-Scholes Model 布莱克-斯科尔斯模型广泛使用的期权定价模型Blocks 大宗交易涉及1万股以上的交易Blue Chip Stocks 蓝筹股由知名、稳健、成熟的公司发行的具有长期盈利和分红记录的股票Bond-Equivalent Yield 债券等值收益将每半年的收益加倍所得的年度收益Bond Ratings 债券评级评级机构发布对债券发行人违约可能性的评估 Bonds 债券代表发行人合同义务的长期债务工具Book value 账面价值资产负债表上所示的权益的会计价值Broker 经纪人在债券交易中代表买卖双方并授予一定佣金的中介Bubble 泡沫投机所导致的资产价格的急剧上升Bull Market 牛市股市的上升趋势Business Cycle 商业周期经济扩张、繁荣、收缩和萧条的重复发生Buy-Side Analysts 买方分析师货币管理公司雇佣的用于寻找股权投资机会的分析师CCall 买入期权以特定的价格在特定的时间内购买特定数量相关股份的期权合约Call Provision 赎回条款发行人发行文件上的条款，授予发行人在证券到期之前，赎回相关证券的权利Capital Asset Pricing Model (CAPM) 资本资产定价模型用以说明证券风险与该证券预期回报之间关系的模型，证券风险用.表示Capital Gain (Loss) 资本收益(损失)证券价格在某段时间内的变化Capital Market 资本市场债券和股票等长期证券进行交易的市场Capital Market Line (CML) 资本市场线效率投资组合的预期收益与其风险的比较关系Cash Account 现金账户最常见的经纪账户，在该账户中，客户只进行现金交易 Cash Flow Statement 现金流量表公司的第三种财务报表，用于跟踪公司的现金流动Characteristic Line 特征线将股票收益与市场收益进行回归用于估计.值的回归等式Chartered Financial Analyst (CFA) 注册金融分析师投资领域相关人员的职业资格认定Closed-End Investment Company 定额投资公司具有固定资本结构且其股份在交易所和场外交易市场进行交易的投资公司Coefficient of Determination 决定系数相关系数的平方，用来衡量因变量中的方差百分比，该百分比由自变量解释Common Stock 普通股代表公司所有者权益的股权证券Composite Economic Indexes 综合经济指数经济活动的领先、同步、滞后指数 Composite (Risk-Adjusted) Measures of Portfolio Performance 投资组合绩效综合衡量指标(风险调整) 结合收益和风险计算的投资组合绩效衡量指标Consensus Estimate 一致估计值分析师们预期的最有可能实现的每股盈利(EPS)Constant (Normal) Growth Rate Case 不变(正常)增长率模型三种股息贴现模型之一，即股票股息预计以大致固定的增长率增长Contrarian Investing 反向投资与多数投资者的交易逆向的交易理论Convexity 债券凸性用于衡量某只债券价格与收益的关系偏离某直线的程度Corporate Bonds 企业债券由企业发行的不同类型的长期债务证券Correlation Coefficient 相关系数衡量两个变量相互联系程度的统计指标Covariance 协方差对两个变量倾向于共变或共同运动程度的绝对量度Covered Call 持保看涨期权投资者出售一手看涨期权同时在其底层资产中拥有一个相等的多头头寸Cumulative Abnormal Return (CAR) 累计超常收益检验期内各个超常收益的总计Cumulative Wealth Index 累计财富指数在给定初始财富及一系列资产收益的情况下，一定时间内形成的累计财富Currrency Risk 外汇风险由于汇率变动而对国外投资收益造成负面影响的风险Current Yield 现时收益率债券的年利息除以现时市价Cyclical Industries 周期性行业易受商业周期影响的行业DData Mining 数据挖掘深度分析数据以从中寻找关于股票收益的明显模式Dealers (Market Makers) 交易商(做市商) 通过向投资者购买和出售股票而促成市场交易的个人(公司)Debenture 信用债券无抵押的由公司的一般信用担保的债券Defensive Industries 防护性行业较少受萧条和经济困境影响的行业Delta(德尔塔) 底层股票价格的每一点数的变化所引起的期权理论值的变化Derivative Securities 衍生证券价值全部或部分取决于某些底层证券的证券Differential Return Measure (Alpha) 差异收益率指标(阿尔法)詹森投资组合绩效指标，计算为投资组合实际收益率与相同系统风险水平下预期收益率的差异 Direct Access Notes (DAN) 直接存取票据面值为1000美元、固定利息率、期限为9个月到30年的债券。
(完整word版)投资学第7版Test Bank答案09
Multiple Choice Questions1. In the context of the Capital Asset Pricing Model (CAPM) the relevant measure of riskisA) unique risk.B) beta.C) standard deviation of returns.D) variance of returns.E) none of the above.Answer: B Difficulty: EasyRationale: Once, a portfolio is diversified, the only risk remaining is systematic risk,which is measured by beta.2. According to the Capital Asset Pricing Model (CAPM) a well diversified portfolio's rateof return is a function ofA) market riskB) unsystematic riskC) unique risk.D) reinvestment risk.E) none of the above.Answer: A Difficulty: EasyRationale: With a diversified portfolio, the only risk remaining is market, or systematic, risk. This is the only risk that influences return according to the CAPM.3. The market portfolio has a beta ofA) 0.B) 1.C) -1.D) 0.5.E) none of the aboveAnswer: B Difficulty: EasyRationale: By definition, the beta of the market portfolio is 1.4. The risk-free rate and the expected market rate of return are 0.06 and 0.12, respectively.According to the capital asset pricing model (CAPM), the expected rate of return on security X with a beta of 1.2 is equal toA) 0.06.B) 0.144.C) 0.12.D) 0.132E) 0.18Answer: D Difficulty: EasyRationale: E(R) = 6% + 1.2(12 - 6) = 13.2%.5. The risk-free rate and the expected market rate of return are 0.056 and 0.125,respectively. According to the capital asset pricing model (CAPM), the expected rate of return on a security with a beta of 1.25 is equal toA) 0.1225B) 0.144.C) 0.153.D) 0.134E) 0.117Answer: A Difficulty: EasyRationale: E(R) = 5.6% + 1.25(12.5 - 5.6) = 14.225%.6. Which statement is not true regarding the market portfolio?A) It includes all publicly traded financial assets.B) It lies on the efficient frontier.C) All securities in the market portfolio are held in proportion to their market values.D) It is the tangency point between the capital market line and the indifference curve.E) All of the above are true.Answer: D Difficulty: ModerateRationale: The tangency point between the capital market line and the indifference curve is the optimal portfolio for a particular investor.7. Which statement is not true regarding the Capital Market Line (CML)?A) The CML is the line from the risk-free rate through the market portfolio.B) The CML is the best attainable capital allocation line.C) The CML is also called the security market line.D) The CML always has a positive slope.E) The risk measure for the CML is standard deviation.Answer: C Difficulty: ModerateRationale: Both the Capital Market Line and the Security Market Line depict risk/return relationships. However, the risk measure for the CML is standard deviation and the risk measure for the SML is beta (thus C is not true; the other statements are true).8. The market risk, beta, of a security is equal toA) the covariance between the security's return and the market return divided by thevariance of the market's returns.B) the covariance between the security and market returns divided by the standarddeviation of the market's returns.C) the variance of the security's returns divided by the covariance between the securityand market returns.D) the variance of the security's returns divided by the variance of the market's returns.E) none of the above.Answer: A Difficulty: ModerateRationale: Beta is a measure of how a security's return covaries with the market returns, normalized by the market variance.9. According to the Capital Asset Pricing Model (CAPM), the expected rate of return onany security is equal toA) R f+ β [E(R M)].B) R f + β [E(R M) - R f].C) β [E(R M) - R f].D) E(R M) + R f.E) none of the above.Answer: B Difficulty: ModerateRationale: The expected rate of return on any security is equal to the risk free rate plus the systematic risk of the security (beta) times the market risk premium, E(R M - R f).10. The Security Market Line (SML) isA) the line that describes the expected return-beta relationship for well-diversifiedportfolios only.B) also called the Capital Allocation Line.C) the line that is tangent to the efficient frontier of all risky assets.D) the line that represents the expected return-beta relationship.E) the line that represents the relationship between an individual security's return andthe market's return.Answer: D Difficulty: ModerateRationale: The SML is a measure of expected return per unit of risk, where risk isdefined as beta (systematic risk).11. According to the Capital Asset Pricing Model (CAPM), fairly priced securitiesA) have positive betas.B) have zero alphas.C) have negative betas.D) have positive alphas.E) none of the above.Answer: B Difficulty: ModerateRationale: A zero alpha results when the security is in equilibrium (fairly priced for the level of risk).12. According to the Capital Asset Pricing Model (CAPM), under priced securitiesA) have positive betas.B) have zero alphas.C) have negative betas.D) have positive alphas.E) none of the above.Answer: D Difficulty: Moderate13. According to the Capital Asset Pricing Model (CAPM), over priced securitiesA) have positive betas.B) have zero alphas.C) have negative betas.D) have positive alphas.E) none of the above.Answer: C Difficulty: ModerateRationale: A zero alpha results when the security is in equilibrium (fairly priced for the level of risk).14. According to the Capital Asset Pricing Model (CAPM),A) a security with a positive alpha is considered overpriced.B) a security with a zero alpha is considered to be a good buy.C) a security with a negative alpha is considered to be a good buy.D) a security with a positive alpha is considered to be underpriced.E) none of the above.Answer: D Difficulty: ModerateRationale: A security with a positive alpha is one that is expected to yield an abnormal positive rate of return, based on the perceived risk of the security, and thus isunderpriced.15. According to the Capital Asset Pricing Model (CAPM), which one of the followingstatements is false?A) The expected rate of return on a security decreases in direct proportion to a decreasein the risk-free rate.B) The expected rate of return on a security increases as its beta increases.C) A fairly priced security has an alpha of zero.D) In equilibrium, all securities lie on the security market line.E) All of the above statements are true.Answer: A Difficulty: ModerateRationale: Statements B, C, and D are true, but statement A is false.16. In a well diversified portfolioA) market risk is negligible.B) systematic risk is negligible.C) unsystematic risk is negligible.D) nondiversifiable risk is negligible.E) none of the above.Answer: C Difficulty: ModerateRationale: Market, or systematic, or nondiversifiable, risk is present in a diversified portfolio; the unsystematic risk has been eliminated.17. Empirical results regarding betas estimated from historical data indicate thatA) betas are constant over time.B) betas of all securities are always greater than one.C) betas are always near zero.D) betas appear to regress toward one over time.E) betas are always positive.Answer: D Difficulty: ModerateRationale: Betas vary over time, betas may be negative or less than one, betas are not always near zero; however, betas do appear to regress toward one over time.18. Your personal opinion is that a security has an expected rate of return of 0.11. It has abeta of 1.5. The risk-free rate is 0.05 and the market expected rate of return is 0.09.According to the Capital Asset Pricing Model, this security isA) underpriced.B) overpriced.C) fairly priced.D) cannot be determined from data provided.E) none of the above.Answer: C Difficulty: ModerateRationale: 11% = 5% + 1.5(9% - 5%) = 11.0%; therefore, the security is fairly priced.19. The risk-free rate is 7 percent. The expected market rate of return is 15 percent. If youexpect a stock with a beta of 1.3 to offer a rate of return of 12 percent, you shouldA) buy the stock because it is overpriced.B) sell short the stock because it is overpriced.C) sell the stock short because it is underpriced.D) buy the stock because it is underpriced.E) none of the above, as the stock is fairly priced.Answer: B Difficulty: ModerateRationale: 12% < 7% + 1.3(15% - 7%) = 17.40%; therefore, stock is overpriced and should be shorted.20. You invest $600 in a security with a beta of 1.2 and $400 in another security with a betaof 0.90. The beta of the resulting portfolio isA) 1.40B) 1.00C) 0.36D) 1.08E) 0.80Answer: D Difficulty: ModerateRationale: 0.6(1.2) + 0.4(0.90) = 1.08.21. A security has an expected rate of return of 0.10 and a beta of 1.1. The market expectedrate of return is 0.08 and the risk-free rate is 0.05. The alpha of the stock isA) 1.7%.B) -1.7%.C) 8.3%.D) 5.5%.E) none of the above.Answer: A Difficulty: ModerateRationale: 10% - [5% +1.1(8% - 5%)] = 1.7%.22. Your opinion is that CSCO has an expected rate of return of 0.13. It has a beta of 1.3.The risk-free rate is 0.04 and the market expected rate of return is 0.115. According to the Capital Asset Pricing Model, this security isA) underpriced.B) overpriced.C) fairly priced.D) cannot be determined from data provided.E) none of the above.Answer: B Difficulty: ModerateRationale: 11.5% - 4% + 1.3(11.5% - 4%) = -2.25%; therefore, the security isoverpriced.23. Your opinion is that CSCO has an expected rate of return of 0.1375. It has a beta of 1.3.The risk-free rate is 0.04 and the market expected rate of return is 0.115. According to the Capital Asset Pricing Model, this security isA) underpriced.B) overpriced.C) fairly priced.D) cannot be determined from data provided.E) none of the above.Answer: C Difficulty: ModerateRationale: 13.75% - 4% + 1.3(11.5% - 4%) = 0.0%; therefore, the security is fairlypriced.24. Your opinion is that CSCO has an expected rate of return of 0.15. It has a beta of 1.3.The risk-free rate is 0.04 and the market expected rate of return is 0.115. According to the Capital Asset Pricing Model, this security isA) underpriced.B) overpriced.C) fairly priced.D) cannot be determined from data provided.E) none of the above.Answer: A Difficulty: ModerateRationale: 15% - 4% + 1.3(11.5% - 4%) = 1.25%; therefore, the security is under priced.25. Your opinion is that Boeing has an expected rate of return of 0.112. It has a beta of 0.92.The risk-free rate is 0.04 and the market expected rate of return is 0.10. According to the Capital Asset Pricing Model, this security isA) underpriced.B) overpriced.C) fairly priced.D) cannot be determined from data provided.E) none of the above.Answer: A Difficulty: ModerateRationale: 11.2% - 4% + 0.92(10% - 4%) = 1.68%; therefore, the security is underpriced.26. Your opinion is that Boeing has an expected rate of return of 0.0952. It has a beta of0.92. The risk-free rate is 0.04 and the market expected rate of return is 0.10.According to the Capital Asset Pricing Model, this security isA) underpriced.B) overpriced.C) fairly priced.D) cannot be determined from data provided.E) none of the above.Answer: C Difficulty: ModerateRationale: 9.52% - 4% + 0.92(10% - 4%) = 0.0%; therefore, the security is fairly priced.27. Your opinion is that Boeing has an expected rate of return of 0.08. It has a beta of 0.92.The risk-free rate is 0.04 and the market expected rate of return is 0.10. According to the Capital Asset Pricing Model, this security isA) underpriced.B) overpriced.C) fairly priced.D) cannot be determined from data provided.E) none of the above.Answer: C Difficulty: ModerateRationale: 8.0% - 4% + 0.92(10% - 4%) = -1.52%; therefore, the security is overpriced.28. The risk-free rate is 4 percent. The expected market rate of return is 11 percent. If youexpect CAT with a beta of 1.0 to offer a rate of return of 10 percent, you shouldA) buy stock X because it is overpriced.B) sell short stock X because it is overpriced.C) sell stock short X because it is underpriced.D) buy stock X because it is underpriced.E) none of the above, as the stock is fairly priced.Answer: B Difficulty: ModerateRationale: 10% < 4% + 1.0(11% - 4%) = 11.0%; therefore, stock is overpriced andshould be shorted.29. The risk-free rate is 4 percent. The expected market rate of return is 11 percent. If youexpect CAT with a beta of 1.0 to offer a rate of return of 11 percent, you shouldA) buy stock X because it is overpriced.B) sell short stock X because it is overpriced.C) sell stock short X because it is underpriced.D) buy stock X because it is underpriced.E) none of the above, as the stock is fairly priced.Answer: E Difficulty: ModerateRationale: 11% = 4% + 1.0(11% - 4%) = 11.0%; therefore, stock is fairly priced. 30. The risk-free rate is 4 percent. The expected market rate of return is 11 percent. If youexpect CAT with a beta of 1.0 to offer a rate of return of 13 percent, you shouldA) buy stock X because it is overpriced.B) sell short stock X because it is overpriced.C) sell stock short X because it is underpriced.D) buy stock X because it is underpriced.E) none of the above, as the stock is fairly priced.Answer: D Difficulty: ModerateRationale: 13% > 4% + 1.0(11% - 4%) = 11.0%; therefore, stock is under priced. 31. You invest 55% of your money in security A with a beta of 1.4 and the rest of yourmoney in security B with a beta of 0.9. The beta of the resulting portfolio isA) 1.466B) 1.157C) 0.968D) 1.082E) 1.175Answer: E Difficulty: ModerateRationale: 0.55(1.4) + 0.45(0.90) = 1.175.32. Given the following two stocks A and BIf the expected market rate of return is 0.09 and the risk-free rate is 0.05, which security would be considered the better buy and why?A) A because it offers an expected excess return of 1.2%.B) B because it offers an expected excess return of 1.8%.C) A because it offers an expected excess return of 2.2%.D) B because it offers an expected return of 14%.E) B because it has a higher beta.Answer: C Difficulty: ModerateRationale: A's excess return is expected to be 12% - [5% + 1.2(9% - 5%)] = 2.2%. B's excess return is expected to be 14% - [5% + 1.8(9% - 5%)] = 1.8%.33. Capital Asset Pricing Theory asserts that portfolio returns are best explained by:A) economic factors.B) specific risk.C) systematic risk.D) diversification.E) none of the above.Answer: C Difficulty: EasyRationale: The risk remaining in diversified portfolios is systematic risk; thus, portfolio returns are commensurate with systematic risk.34. According to the CAPM, the risk premium an investor expects to receive on any stockor portfolio increases:A) directly with alpha.B) inversely with alpha.C) directly with beta.D) inversely with beta.E) in proportion to its standard deviation.Answer: C Difficulty: EasyRationale: The market rewards systematic risk, which is measured by beta, and thus, the risk premium on a stock or portfolio varies directly with beta.35. What is the expected return of a zero-beta security?A) The market rate of return.B) Zero rate of return.C) A negative rate of return.D) The risk-free rate.E) None of the above.Answer: D Difficulty: ModerateRationale: E(R S) = r f + 0(R M - r f) = r f.36. Standard deviation and beta both measure risk, but they are different in thatA) beta measures both systematic and unsystematic risk.B) beta measures only systematic risk while standard deviation is a measure of totalrisk.C) beta measures only unsystematic risk while standard deviation is a measure of totalrisk.D) beta measures both systematic and unsystematic risk while standard deviationmeasures only systematic risk.E) beta measures total risk while standard deviation measures only nonsystematic risk.Answer: B Difficulty: EasyRationale: B is the only true statement.37. The expected return-beta relationshipA) is the most familiar expression of the CAPM to practitioners.B) refers to the way in which the covariance between the returns on a stock and returnson the market measures the contribution of the stock to the variance of the marketportfolio, which is beta.C) assumes that investors hold well-diversified portfolios.D) all of the above are true.E) none of the above is true.Answer: D Difficulty: ModerateRationale: Statements A, B and C all describe the expected return-beta relationship.38. The security market line (SML)A) can be portrayed graphically as the expected return-beta relationship.B) can be portrayed graphically as the expected return-standard deviation of marketreturns relationship.C) provides a benchmark for evaluation of investment performance.D) A and C.E) B and C.Answer: D Difficulty: ModerateRationale: The SML is a measure of expected return-beta (the CML is a measure of expected return-standard deviation of market returns). The SML provides the expected return-beta relationship for "fairly priced" securities; thus if a portfolio manager selects securities that are underpriced and produces a portfolio with a positive alpha, thisportfolio manager would receive a positive evaluation.39. Research by Jeremy Stein of MIT resolves the dispute over whether beta is a sufficientpricing factor by suggesting that managers should use beta to estimateA) long-term returns but not short-term returns.B) short-term returns but not long-term returns.C) both long- and short-term returns.D) book-to-market ratios.E) None of the above was suggested by Stein.Answer: A Difficulty: Difficult40. Studies of liquidity spreads in security markets have shown thatA) liquid stocks earn higher returns than illiquid stocks.B) illiquid stocks earn higher returns than liquid stocks.C) both liquid and illiquid stocks earn the same returns.D) illiquid stocks are good investments for frequent, short-term traders.E) None of the above is true.Answer: B Difficulty: Difficult41. An underpriced security will plotA) on the Security Market Line.B) below the Security Market Line.C) above the Security Market Line.D) either above or below the Security Market Line depending on its covariance withthe market.E) either above or below the Security Market Line depending on its standard deviation.Answer: C Difficulty: EasyRationale: An underpriced security will have a higher expected return than the SML would predict; therefore it will plot above the SML.42. The risk premium on the market portfolio will be proportional toA) the average degree of risk aversion of the investor population.B) the risk of the market portfolio as measured by its variance.C) the risk of the market portfolio as measured by its beta.D) both A and B are true.E) both A and C are true.Answer: D Difficulty: ModerateRationale: The risk premium on the market portfolio is proportional to the averagedegree of risk aversion of the investor population and the risk of the market portfolio measured by its variance.43. In equilibrium, the marginal price of risk for a risky security must beA) equal to the marginal price of risk for the market portfolio.B) greater than the marginal price of risk for the market portfolio.C) less than the marginal price of risk for the market portfolio.D) adjusted by its degree of nonsystematic risk.E) none of the above is true.Answer: A Difficulty: ModerateRationale: In equilibrium, the marginal price of risk for a risky security must be equal to the marginal price of risk for the market. If not, investors will buy or sell the security until they are equal.44. The capital asset pricing model assumesA) all investors are price takers.B) all investors have the same holding period.C) investors pay taxes on capital gains.D) both A and B are true.E) A, B and C are all true.Answer: D Difficulty: EasyRationale: The CAPM assumes that investors are price-takers with the same single holding period and that there are no taxes or transaction costs.45. If investors do not know their investment horizons for certainA) the CAPM is no longer valid.B) the CAPM underlying assumptions are not violated.C) the implications of the CAPM are not violated as long as investors' liquidity needsare not priced.D) the implications of the CAPM are no longer useful.E) none of the above is true.Answer: C Difficulty: ModerateRationale: This is discussed in the chapter's section about extensions to the CAPM. It examines what the consequences are when the assumptions are removed.46. The value of the market portfolio equalsA) the sum of the values of all equity securities.B) the sum of the values of all equity and fixed income securities.C) the sum the values of all equity, fixed income, and derivative securities.D) the sum of the values of all equity, fixed income, and derivative securities plus thevalue of all mutual funds.E) the entire wealth of the economy.Answer: E Difficulty: ModerateRationale: The market portfolio includes all assets in existence.47. The amount that an investor allocates to the market portfolio is negatively related toI)the expected return on the market portfolio.II)the investor's risk aversion coefficient.III)the risk-free rate of return.IV)the variance of the market portfolioA) I and IIB) II and IIIC) II and IVD) II, III, and IVE) I, III, and IVAnswer: D Difficulty: ModerateRationale: The optimal proportion is given by y = (E(R M)-r f)/(.01xAσ2M). This amount will decrease as r f, A, and σ2M decrease.48. One of the assumptions of the CAPM is that investors exhibit myopic behavior. Whatdoes this mean?A) They plan for one identical holding period.B) They are price-takers who can't affect market prices through their trades.C) They are mean-variance optimizers.D) They have the same economic view of the world.E) They pay no taxes or transactions costs.Answer: A Difficulty: ModerateRationale: Myopic behavior is shortsighted, with no concern for medium-term orlong-term implications.49. The CAPM applies toA) portfolios of securities only.B) individual securities only.C) efficient portfolios of securities only.D) efficient portfolios and efficient individual securities only.E) all portfolios and individual securities.Answer: E Difficulty: ModerateRationale: The CAPM is an equilibrium model for all assets. Each asset's risk premium is a function of its beta coefficient and the risk premium on the market portfolio.50. Which of the following statements about the mutual fund theorem is true?I)It is similar to the separation property.II)It implies that a passive investment strategy can be efficient.III)It implies that efficient portfolios can be formed only through active strategies.IV)It means that professional managers have superior security selection strategies.A) I and IVB) I, II, and IVC) I and IID) III and IVE) II and IVAnswer: C Difficulty: ModerateRationale: The mutual fund theorem is similar to the separation property. The technical task of creating mutual funds can be delegated to professional managers; thenindividuals combine the mutual funds with risk-free assets according to theirpreferences. The passive strategy of investing in a market index fund is efficient.51. The expected return -- beta relationship of the CAPM is graphically represented byA) the security market line.B) the capital market line.C) the capital allocation line.D) the efficient frontier with a risk-free asset.E) the efficient frontier without a risk-free asset.Answer: A Difficulty: EasyRationale: The security market line shows expected return on the vertical axis and beta on the horizontal axis. It has an intercept of r f and a slope of E(R M) - r f.52. A “fairly priced” asset liesA) above the security market line.B) on the security market line.C) on the capital market line.D) above the capital market line.E) below the security market line.Answer: B Difficulty: EasyRationale: Securities that lie on the SML earn exactly the expected return generated by the CAPM. Their prices are proportional to their beta coefficients and they have alphas equal to zero.53. For the CAPM that examines illiquidity premiums, if there is correlation among assetsdue to common systematic risk factors, the illiquidity premium on asset i is a function ofA) the market's volatility.B) asset i's volatility.C) the trading costs of security i.D) the risk-free rate.E) the money supply.Answer: C Difficulty: ModerateRationale: The formula for this extension to the CAPM relaxes the assumption thattrading is costless.54. Your opinion is that security A has an expected rate of return of 0.145. It has a beta of1.5. The risk-free rate is 0.04 and the market expected rate of return is 0.11. Accordingto the Capital Asset Pricing Model, this security isA) underpriced.B) overpriced.C) fairly priced.D) cannot be determined from data provided.E) none of the above.Answer: C Difficulty: ModerateRationale: 14.5% = 4% + 1.5(11% - 4%) = 14.5%; therefore, the security is fairlypriced.55. Your opinion is that security C has an expected rate of return of 0.106. It has a beta of1.1. The risk-free rate is 0.04 and the market expected rate of return is 0.10. Accordingto the Capital Asset Pricing Model, this security isA) underpriced.B) overpriced.C) fairly priced.D) cannot be determined from data provided.E) none of the above.Answer: A Difficulty: ModerateRationale: 4% + 1.1(10% - 4%) = 10.6%; therefore, the security is fairly priced.56. The risk-free rate is 4 percent. The expected market rate of return is 12 percent. If youexpect stock X with a beta of 1.0 to offer a rate of return of 10 percent, you shouldA) buy stock X because it is overpriced.B) sell short stock X because it is overpriced.C) sell stock short X because it is underpriced.D) buy stock X because it is underpriced.E) none of the above, as the stock is fairly priced.Answer: B Difficulty: ModerateRationale: 10% < 4% + 1.0(12% - 4%) = 12.0%; therefore, stock is overpriced and should be shorted.57. The risk-free rate is 5 percent. The expected market rate of return is 11 percent. If youexpect stock X with a beta of 2.1 to offer a rate of return of 15 percent, you shouldA) buy stock X because it is overpriced.B) sell short stock X because it is overpriced.C) sell stock short X because it is underpriced.D) buy stock X because it is underpriced.E) none of the above, as the stock is fairly priced.Answer: B Difficulty: ModerateRationale: 15% < 5% + 2.1(11% - 5%) = 17.6%; therefore, stock is overpriced and should be shorted.58. You invest 50% of your money in security A with a beta of 1.6 and the rest of yourmoney in security B with a beta of 0.7. The beta of the resulting portfolio isA) 1.40B) 1.15C) 0.36D) 1.08E) 0.80Answer: B Difficulty: ModerateRationale: 0.5(1.6) + 0.5(0.70) = 1.15.。
CFA一级组合管理高频错题精选
CFA一级组合管理高频错题精选Portfolio risk and return：这道题是数量与组合两个学科的结合。
首先要注意题干给的信息是geometric return，题目要求的是risk premium for equities。
易错点分析：这道题很多同学没有注意到题干给的信息是geometric return，亦或者看到了，对如何用几何法求收益率不熟悉，所以这个推导过程大家可以记忆一下。
切记读题目的时候要对一些关键词保持敏感。
Portfolio risk and return:首先要看懂题干的表格，一共有3个资产。
根据题意，一共有三种情况，每种情况发生概率相同，即发生概率都是1/3。
每个资产在不同情况下会产生不同的收益。
比如资产1，在第一种情况下，产生的收益率为12%；资产2，在第一种情况下，产生的收益率也是12%；资产3，在第一种情况下，产生的收益率是0%。
观察表格发现，三种资产产生的收益率不外乎12%，6%，0%，这正是题目巧妙的地方，所以正如表格最后一列所示，这三种资产的预期收益率都是6%（=1/3*12%+1/3*6%+1/3*0%）。
题目问的是哪对资产是完全负相关，即要找哪两对资产收益率的相关性系数= -1。
解答这道题有两种方法：一是定性分析。
相关性系数反映的是两组数据变化的同步性。
如果一组数据逐渐变大，同时另一组数据逐渐变小，那么这两组数据相关性就是负的。
观察表格中的数字，比较明显可以看出的是资产2和资产3的收益率是完全负相关的。
outcome 1→outcome 2→outcome 3时，资产2的收益率12%→6%→0，逐渐变小；outcome 1→outcome 2→outcome 3时，资产3的收益率0→6%→12%，逐渐变大。
二是利用计算器求两组资产之间的相关系数。
以A选项资产1 &资产2的收益率相关性系数计算为例，打开金融计算器：【2nd】【7】进入data模式，首先清除历史记录【2nd】【CLR WORK】依次输入两组数据：X01=12【↓】Y01=12【↓】X02=0【↓】Y02=6【↓】X03=6【↓】Y03=0【↓】；然后[2nd][8]进入STAT模式，一直按向下的箭头，直到出现r，r=0.5。
马科维茨投资组合理论
马科维茨投资组合理论马科维茨(Harry M 。
Markowitz,）1990年因其在1952年提出的投资组合选择（Portfolio Selection)理论获得诺贝尔经济学奖。
主要贡献：发展了一个在不确定条件下严格陈述的可操作的选择资产组合理论：均值方差方法 Mean-Variance methodology.主要思想:Markowitz 把投资组合的价格变化视为随机变量，以它的均值来衡量收益，以它的方差来衡量风险（因此Markowitz 理论又称为均值－方差分析）；把投资组合中各种证券之间的比例作为变量，那么求收益一定的风险最小的投资组合问题就被归结为一个线性约束下的二次规划问题.再根据投资者的偏好，由此就可以进行投资决策。
基本假设:H1. 所有投资都是完全可分的。
每一个人可以根据自己的意愿（和支出能力）选择尽可能多的或尽可能少的投资。
H2。
一个投资者愿意仅在收益率的期望值和方差(标准差)这两个测度指标的基础上选择投资组合。
p E =对一个投资组合的预期收益率p σ=对一个投资组合的收益的标准差（不确定性）H3。
投资者事先知道投资收益率的概率分布,并且收益率满足正态分布的条件。
H4。
一个投资者如何在不同的投资组合中选择遵循以下规则:一,如果两个投资组合有相同的收益的标准差和不同的预期收益，高的预期收益的投资组合会更为可取； 二，如果两个投资组合有相同的收益的预期收益和不同的标准差，小的标准差的组合更为可取；三,如果一个组合比另外一个有更小的收益标准差和更高的预期收益，它更为可取。
基本概念1．单一证券的收益和风险：对于单一证券而言，特定期限内的投资收益等于收到的红利加上相应的价格变化，因此特定期限内的投资收益为：11P P P t t t r --==价格变化＋现金流(如果有）持有期开始时的价格－＋CF 假定投资者在期初时已经假定或预测了该投资期限内的投资收益的概率分布；将投资收益看成是随机变量。
2018-CFA-level-1-知识点——Portfolio-Management
Portfolio ManagementPortfolio Management: An OverviewDescribe the portfolio approach to investing1.The portfolio perspective refers to evaluating individual investments by theircontribution on the risk and return of an investor’s portfolio.投资组合视角指的是通过投资组合对风险和回报的贡献来评估个人投资。
2.把所有钱用于买一只股票并不是一种portfolio perspective，把钱分散在多只证券中才能降低风险，增加收益。
3.One measure of the benefits of diversification is the diversification ratio. It iscalculated as the ratio of the risk of an equally weighted portfolio of n securities to the risk of a single security selected at random from the n securities.衡量多样化的好处之一是多样化比率。
它计算的是n证券等加权组合的风险与随机从n证券中选择的单一证券的风险之比。
4.If the average standard deviation of returns for the n stocks is 25%, and thestandard deviation of returns for an equally weighted portfolio of the n stocks is 18%, the diversification ratio is 18/25=0.72.Describe types of investors and distinctive characteristics and needs of each1.Individual investor个人投资者就是个人为了满足生活目标而进行理财的投资者，是牺牲当前消费以期获得未来更高水平消费的个人。
金融资产收益与风险的衡量
单一资产收益与风险的衡量1、历史的收益与风险2、预期的收益与风险 收益率：11n i it t r r n ==∑ 1()n i is s s E r r π==∑ 方差：2211()1n i it i t r r n σ==--∑ []21()n is i s s r E r π=-∑标准差：i σ=i σ=资产组合（Portfolio ）收益与风险的衡量1、历史的收益与风险收益率：1npt it it i r r w ==∑ 方差：2*22111cov 2cov ,*2n n n p ij i j i ij i j i j i n n w w w w σσ===-==+=∑∑∑∑（协方差的项数） 资产间的协方差：()()11cov 1n ij it i jt j t r r r r n ==---∑ 相关系数：cov ijij i j ρσσ=2、预期的收益与风险收益率：1()()np i i i E r E r w ==∑ 方差：2*22111cov 2cov ,*2n n n p ij i j i ij i j i j i n n w w w w σσ===-==+=∑∑∑∑（协方差的项数） 资产间的协方差：[]1cov ()()nij i i j j s s r E r r E r π=⎡⎤=--⎣⎦∑ 相关系数：cov ijij i j ρσσ=（一）资产组合的数学基础1、方差和标准方差(1)单个资产收益率的方差是一种衡量资产的各种可能收益率相对于期望收益率的分散程度的指标，人们常用收益率的方差来衡量资产风险的大小。
方差通常用σ 2 来表示。
其中：i P代表收益率i R 发生的概率，i R 代表资产在第i 中状态下产生的收益率，m 表示资产有可能产生m 种不同的收益率，E(R)代表资产的期望收益率。
可见，将概率乘以相应利差的平方，然后再加总，即可得到方差（方差也被称为均方差）。
注意，如果收益率用百分率来表示，那么方差的单位则是“百分率的平方”；如果收益率用人民币来表示，那么方差的单位则为“人民币的平方”。
资产管理的投资组合风险和回报评估
资产管理的投资组合风险和回报评估在资产管理的领域中，投资组合风险和回报评估是非常重要的方面。
通过评估投资组合的风险和回报，资产管理者可以更好地了解投资组合的潜在风险，并作出相应的决策来实现投资目标。
本文将介绍资产管理中投资组合风险和回报评估的方法和重要性。
1. 投资组合风险评估投资组合风险评估是指对投资组合中的不同资产进行风险测量和分析的过程。
常用的方法包括标准差、协方差矩阵、Value-at-Risk（VaR）等。
标准差是一种衡量投资组合风险的常用指标，它反映了投资组合收益的波动程度。
协方差矩阵则可以帮助投资者了解不同资产之间的相关性，进一步衡量投资组合的系统风险。
另外，Value-at-Risk（VaR）是一种度量投资组合风险的方法，它可以提供一个概率值，表示在给定时间区间内投资组合可能的最大损失。
通过对投资组合的VaR进行评估，资产管理者可以更好地了解投资组合的风险暴露，并采取相应的风险管理措施。
2. 投资组合回报评估投资组合的回报评估是指对投资组合中不同资产的预期回报进行分析和估算的过程。
常用的方法包括历史回报率、收益风险比、夏普比率等。
历史回报率是根据过去一段时间的收益数据对投资组合未来回报进行估计的方法，它可以帮助资产管理者了解投资组合的长期收益表现。
收益风险比是将投资组合的预期回报与风险相对比的指标，它可以帮助资产管理者判断投资组合的回报是否合理。
夏普比率则是一种综合考虑了回报和风险的指标，通过计算投资组合预期超额回报和标准差之比，来评估投资组合的表现。
3. 投资组合风险和回报的重要性评估投资组合的风险和回报对资产管理者来说非常重要。
首先，风险评估可以帮助资产管理者了解投资组合的潜在风险，并制定相应的风险管理策略。
通过合理评估投资组合的风险，资产管理者可以平衡风险和回报，降低投资组合的潜在损失。
其次，回报评估可以帮助资产管理者了解投资组合的预期收益，并制定相应的投资策略。
通过对回报进行评估，资产管理者可以选择具有良好回报潜力的资产，进一步增加投资组合的回报水平。
统计学方法如何帮助评估金融市场中的投资组合风险
统计学方法如何帮助评估金融市场中的投资组合风险投资是金融市场中常见的一项活动，投资者希望通过投资获得较高的回报。
然而，投资伴随风险，了解和评估投资组合的风险水平对于投资者来说至关重要。
统计学方法为评估金融市场中的投资组合风险提供了有效的工具和技术。
本文将介绍统计学方法在评估投资组合风险方面的应用，并探讨其重要性。
一、方差与标准差分析统计学中的方差和标准差是衡量数据分散程度的常用指标。
在金融市场中，投资组合的波动性是一个重要的风险指标。
通过计算投资组合中各个资产的方差和标准差，可以评估投资组合的整体波动性。
方差和标准差越大，代表投资组合的风险越高。
投资者可以根据投资目标和风险承受能力，采取相应的风险管理策略。
二、协方差与相关系数分析协方差和相关系数分析是统计学中常用的方法，用于度量不同资产之间的相关性。
在投资组合中，不同资产之间的相关性直接影响整体投资组合的风险水平。
协方差衡量不同资产之间的变动趋势是否一致，相关系数则衡量变动趋势的强度和方向。
通过计算协方差矩阵和相关系数矩阵，投资者可以了解投资组合中各个资产之间的相关性，进而评估整体风险水平。
若资产之间相关性较高，则投资组合的风险相应增加；若资产之间相关性较低，则投资组合的风险可能会降低。
三、VaR（Value at Risk）模型VaR（Value at Risk）是衡量投资风险的重要指标。
统计学方法可以应用于VaR模型中，通过计算概率分布和历史数据，评估投资组合在给定置信水平下面临的最大可能损失。
VaR模型将投资组合的风险量化为一个具体的数值，投资者可以据此制定风险控制策略。
VaR模型有助于投资者了解投资组合可能面临的风险范围，从而更好地进行风险管理和资产配置。
四、蒙特卡洛模拟法蒙特卡洛模拟法是一种基于概率统计的方法，用于模拟和评估不确定性问题。
在金融市场中，蒙特卡洛模拟法可以应用于评估投资组合的风险。
通过随机生成大量可能的投资回报率，并基于这些回报率进行模拟和计算，投资者可以得到投资组合的风险分布情况。