Macquarie University Applied Finance Centre AFCL801 Portfolio Management and Valuation Ellipse Investment Management project 2017

麦考瑞大学 应用金融中心

AFCL801 资产组合管理及评估

Ellipse 投资管理

2017 年


project Submission: Your project assessment piece will be submitted via iLearn. Please refer to the project section on your unit’s iLearn site for instructions. The cover sheet to include in your project submission is also located there.

提交：你要通过 iLearn 提交，提交方法请参考 iLearn 网站上页面中的说明。提交时要附上的封面页，封面页也可在该页面中找到。

Penalty for Late Submission: If you have extenuating circumstances that prevent you from submitting your project by the due date please make arrangements with your lecturer prior to the due date. Unless prior arrangements have been made, any late submission of projects will automatically be penalised. In the absence of special circumstances, a zero mark will apply.

迟交处罚：如果你有特殊情况无法按时提交，请在截止日期前与你的讲师联系做出相应的安排。除非提前与讲师安排，否则任何的延迟提交都将会自动受到处罚。如无特殊情况，未按时提交的将被判零分。

Format: A written submission (eg a word document) is required from each student showing any important formulae used. Do not submit spreadsheet files or print outs of spreadsheets with your project answer.

格式：每一位学生都需要提交一份书面形式的材料（例如一份 Word 格式的文档）用来展示所有使用的重要公式。请勿提交电子表格文件或电子表格打印件。

Nature: Teamwork is encouraged in carrying out data analysis. However, all explanations, interpretations and recommendations must represent your own work and not that of another person. You must clearly and accurately acknowledge the source of any reference material you use. If you infringe these rules or encourage or assist another person to infringe them, penalties will apply (refer to the University’s Academic Honesty Policy ).

性质：鼓励学生在分析数据时展开团队合作，但是所有的解释、说明和建议都必须独立完成，而不能是别人的成果。学生须清楚和准确地注明参考资料的来源。若学生违反上述规定或鼓励、协助他人违反上述规定，将受到相应处罚。具体细节请参考学校网站上的“Academic Honesty Policy（学术诚信政策）”。






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Copies: Students should retain a back-up copy of their project submission on paper. 备份留底：每位学生均应保留一份纸质的备份副本。




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Ellipse Investment Management

Ellipse 投资管理


Ellipse Investment Management has been running equity portfolios for ten years and has attracted an impressive collection of institutional clients. They have been attracted by Ellipse’s thorough fundamental analysis. This analysis drives the security selection in the Ellipse equity fund and has led to the timely selection of many stocks which delivered substantial returns. However, the clients have recently raised concerns that the fund’s total performance has not typically reflected that of the wider stock market’s performance. This worry have been fuelled by the way the clients typically model asset allocation. They use market indices to represent the various asset classes and then select active managers to implement each of these components of their portfolios.

Ellipse 投资管理已管理了十年的股权投资组合，并且吸引到了一些令人瞩目的机构投资者客户，这些机构投资者是被 Ellipse 透彻的基本面分析所吸引。这种分析推动 Ellipse 股票基金的选股，让基金及时地挑选了很多股票并从中获得了实质的回报。但是，最近客户开始担忧这只基金的总业绩没有具代表性地反映出更广泛的股票市场表现。引发这种担忧的原因，源自于客户常用的资产配置建模方式。他们为不同的资产类别选取相应的市场指数作为代表，并为各个资产类别挑选主动型基金经理，这些基金经理通过管理相应的市场指数对每个资产类别进行主动型管理。


Equity Portfolio Construction

创建股权投资组合


Zac Adams has been working at Ellipse as a portfolio analyst for the last few years. He has been given the task of designing a way to manage these client concerns while continuing to capitalise on Ellipse’s recognised skill in security selection. He plans to use a single index model based on the S&P ASX 200 index and begins his analysis with the seven stocks which the firm’s security analysts have ranked as their equally preferred top stocks. From this analysis he obtains coefficients for each of the stocks which he uses to construct a variety of potential stock portfolios with alternative portfolio performance objectives.

Zac Adams 作为投资组合分析师已经在 Ellipse 工作了好多年，现在他被分配到了一项

任务，即设计一个方法管理这些客户关切的问题，同时继续利用 Ellipse 公认的选股技术。他计划采用基于标准普尔澳大利亚证券交易所 200 指数（标普澳证 200，S&P ASX

200）的单一指数模型，并从七只股票开始他的分析。这些股票是由公司的证券分析师们列出的公认顶级股票。通过分析，他获取每只股票的系数用来创建各种可能的股票投资组合，而这些组合有不同的投资组合业绩目标。

As Zac carries out this analysis he becomes concerned about the overall validity of the single index model and its resulting coefficients. As an example of his concerns, he is worried about whether high betas actually reflect high risk premia. He therefore conducts a second pass regression test of the single index model (including relevant data on additional stocks that had been previously collated) to evaluate this approach. Further to this concern he ponders whether additional factors would improve upon the single index model. He therefore trials a





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three factor model employing a Consumer Sentiment Index and the Fama-French “High Minus Low” Index alongside the equity index.

在 Zac 进行分析的同时，他也开始担心单一指数模型和其结果系数的总体有效性。比如，他担心高 Beta 值是不是实际上反映了高风险溢价。因此，为了评估这种方法的有效性，他对单一指数模型（包括先前配置的额外股票的相关数据）进行了二次回归分

析。此外，他还在考虑是否额外的因子会改善单一指数模型，所以他尝试了三因子模

型，模型中除了股票指数因子之外，还包含了消费者信心指数、和法马-佛伦奇三因子模型中的账面市值比（高账面市值比 – 低账面市值比）因子。

He is also wondering whether there are better approaches to estimating betas to the equity index which may already be available in the industry.

他也想知道是否有更好的估计股票指数 Beta 值的方法。可能某些方法已经在行业中使用了。


Asset Allocation Construction

资产配置的构建


The Ellipse management is also considering the prospect of expanding their product range to include asset allocation advice. At the very least the exercise should inform them on how large clients view the role of the Ellipse equity fund in the context of the clients’ broader diversified portfolios. Zac has leapt at the opportunity to broaden his involvement and has offered to investigate what asset allocation might potentially look like by combining a stock index with a bond index. The Ellipse management is particularly interested in how a suite of asset allocation choices might be constructed to reflect a range of client risk profiles.

Ellipse 的管理层也在考虑扩大服务产品范围的前景，比如提供资产配置的咨询服务。这项业务至少能够让他们知道，在客户广泛分散投资组合中， Ellipse 股票基金在大客户心里起到的是怎样的作用。Zac 利用这个机会扩大参与度，并提出提供调查研究，以了解：如果将股票指数和债券指数相结合，可能会有怎样的资产配置。Ellipse 管理层特别感兴趣的是如何构建一套资产配置选项，来反映客户一系列的风险状况 。


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Zac has decided to base the asset allocation inputs on the historic risk patterns of stocks and bonds and on the asset allocation return expectations published by BlackRock. This chart shows the return and risk forecast by BlackRock across a wide range of asset classes.

Zac 已决定将资产配置的输入数据基于：股票和债券的历史风险规律、以及贝莱德集团（BlackRock）发布的资产配置预期收益。下图显示了贝莱德预测的不同资产类别的风险和收益。


图中文字翻译：

Expected annualised nominal return 预期年化名义收益

Expected annualised volatility 预期年化波动性

Cash 现金
Credit 信用（债券）
Global corporate 全球企业（债券）
Linkers 联系（债券）
Hedge funds (Global) 对冲基金（全球）
Long gov. bonds 长期政府债券
Local EM debt 本地新兴市场负债
Global high yield 全球高收益（债券）
US bank loans 美国银行贷款
Large cap 高市值股票
Ex-Australia large cap 非澳大利亚高市值股票
Infrastructure equity 基础建设股权
Private equity 私募股权


The actual expected returns can be found on the BlackRock website at 在贝莱德的网站上可以找到真实的预期收益：

https://www.blackrock.com/institutions/en-us/insights/portfolio-design/capital-market-assumptions





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To get an appreciation of how risk aversion is gauged, Zac will locate examples of risk aversion surveys used in the industry and evaluate them in the context of this asset allocation exercise.

为了了解如何衡量风险厌恶，Zac 会找出行业中有关风险厌恶调查问卷的例子，并以资产配置为背景进行评估。


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Questions (marks are equally weighted across the Questions)

问题（每一道问题的分数都相同）

Question 1.

第一题。

(a) Calculate average monthly excess returns for the seven shares and the equity index in the spreadsheet. Report each share’s arithmetic average monthly excess return and standard deviation of excess return (using the population version of the standard deviation equation).

在电子表格中，计算七只股票和股票指数的平均月度超额收益。报告每一只股票的算术平均月度超额收益和超额收益的标准差（采用总体平均的标准差公式）。

(b) Regress the monthly excess returns for each share on the monthly excess returns of the equity index and report each share’s: alpha; beta; t-statistics; and R squared. Also calculate and report each share’s tracking error – as implied by the betas and standard deviations of excess returns – ie from part (a).

使用股票指数的月度超额收益作为自变量，对每一只股票的月度超额收益进行回归分析，然后报告股票的 Alpha，Beta，t 统计值和决定系数（R2），同时计算和报告每一只股票的跟踪误差，由 Beta 和超额收益的标准差体现（也就是 a 题中所得的数据）。

(c) Run a second pass regression by regressing the average excess returns for the shares from part (a) on their betas and tracking errors (in variance form) from part (b) combined with the data for the additional shares provided in the spreadsheet (refer to BKM section 13.1). Report the gamma 0, gamma 1, gamma 2, standard errors, relevant t-statistics and adjusted R squared.

进行第二次回归分析，用（b）中得到的 Beta 和跟踪误差（方差形式）以及电子表格中额外股票的数据（参考 BKM 第 13.1 小节）对（a）中得到股票平均超额收益回归，并报告 gamma 0、gamma 1、gamma 2、标准误差、相关 t 值和调整后的决定系数

（adjusted R2）。

(d) Run a multi variable regression for each of the seven shares by regressing the share’s monthly excess returns on the monthly excess returns of the equity index and the additional factor data (ie Consumer Sentiment Index and Fama-French HML index. HML = High Minus Low see page 340 for an explanation of this factor) provided in the spreadsheet – refer to page 425 for an example of a multi factor model (NB: we’re only running a first pass regression here). Report each share’s alpha, betas; t-statistics; and adjusted R squared.

对这七只股票进行多元回归分析，用股票月度超额收益对股票指数月度超额收益和电子表格中额外因子的数据（比如，消费者信心指数和法马-佛伦奇的账面市值比指数。账面市值比（HML） 因子= 高账面市值比 – 低账面市值比 ，请参考 340 页上有关该因子的解释），请参考 425 页的多因子模型的示例（注意：我们在这里只进行第一部分的回归）。报告每一只股票的 Alpha，Beta，t 值和调整决定系数。





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Question 2.

第二题。

Two asset pricing models have been tested in Question 1. Use the results from that question to evaluate these asset pricing models in the context of Ellipse’s equity portfolio construction.

在第一题中测试了两种资产定价模型，根据 Ellipse 创建的股票投资组合，评估这些资产定价模型。（字数限制为 450 汉字）。



Question 3.

第三题。

Research two providers of share betas where the betas are estimated differently to the methods used in this project. Explain how they estimate beta and evaluate their approaches in contrast to the methods used in this project.

对股票 Beta 的两家提供机构进行研究，要求这两家机构对 Beta 的估计方法与这份中的方法不同。解释他们估计 Beta 的方法，通过与中采用的方法进行对比，来评估他们的方法。（字数限制为 600 汉字）



Question 4.

第四题。

Use the results from Question 1 parts (a) and (b) to construct the following share portfolios. Only include the original seven shares in the portfolio – ie do not include the equity index or the additional share data used in Question 1 part (c). Assume zero correlation between the shares’ non-systematic returns when calculating portfolio tracking error (ie portfolio non-systematic risk). Calculate total portfolio risk by combining the systematic element and tracking error of the portfolio per equation 8.16 on page 263 of BKM.

第四题。用第一题（a）和（b）中的结果构建如下的股票投资组合。仅纳入最初的七只股票在这个投资组合中，也就是不包含股票指数或第一题（c）中额外的股票数据。在计算投资组合跟踪误差（即投资组合的非系统性风险）的时候，假设股票间非系统性收益的相关系数为零。根据 BKM 中第 263 页的公式 8.16，通过结合投资组合的系统性元素和跟踪误差，计算投资组合的总体风险。

(a) Use solver to find the portfolio weights for a long-only share portfolio with the maximum amount of alpha. State the portfolio weights, alpha, beta, tracking error, information ratio and Sharpe ratio.

用规划求解为一个多头交易股票投资组合寻找投资组合的权重，这个权重要使 Alpha 的数值最大化。写出投资组合的权重、Alpha、Beta、跟踪误差、信息比率和夏普比率。








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(b) Use solver to find the portfolio weights for a long-only share portfolio with the minimum amount of tracking error. State the portfolio weights, alpha, beta, tracking error, information ratio and Sharpe ratio.

用规划求解为一个多头交易股票投资组合寻找投资组合的权重，这个权重要使跟踪误差最小化。写出投资组合的权重、Alpha、Beta、跟踪误差、信息比率和夏普比率。

(c) Use solver to find the portfolio weights for a long-only share portfolio with the maximum amount of information ratio plus a beta constrained to a value of one. State the portfolio weights, alpha, beta, tracking error, information ratio and Sharpe ratio.

用规划求解为一个多头交易股票投资组合寻找投资组合的权重，这个权重要使信息比率最大化以及限制 Beta 的值为 1。写出投资组合的权重、Alpha、Beta、跟踪误差、信息比率和夏普比率

(d) Use solver to find the portfolio weights for a long-only share portfolio with the maximum amount of Sharpe ratio. State the portfolio weights, alpha, beta, tracking error, information ratio and Sharpe ratio.

用规划求解为一个多头交易股票投资组合寻找投资组合的权重，这个权重要使夏普比率最大化。写出投资组合的权重、Alpha、Beta、跟踪误差、信息比率和夏普比率



Question 5.

第五题。

(a) Calculate the standard deviation (using the population version of the formula) of annual returns for Australian equities (based on the S&P/ASX 200 Index data in the spreadsheet), Australian bonds (based on the S&P Australian Bond Index data) and Australian cash (based on the Bloomberg Ausbond Bank Bill Index data) and the correlation of returns between these three asset classes. Combine these risk estimates with BlackRock’s expected returns for Australian equities (use the “Australia large cap Equities Long Term Expected Return”) and the Australian bonds (use the “Australian treasuries (all maturities) long term expected return”) to chart the opportunity set comprised of a wide range of possible “risky portfolios”. Your chart should show standard deviation pa on the horizontal axis, and expected return pa on the vertical axis.

计算澳大利亚股票（基于电子表格中的标普澳证 200 指数数据）、澳大利亚债券（基于标普澳大利亚债券指数数据）和澳大利亚现金（基于彭博澳大利亚债券-银行汇票指数数据）年度收益的标准差（采用总体平均的标准差公式），以及这三种资产类别之间收益的相关系数。把这些估计出的风险与贝莱德的澳大利亚股票（采用澳大利亚高市值股票长期预期收益）和澳大利亚债券（采用所有期限澳大利亚国库券的长期预期收益）的预期收益相结合，制作一张机会集的图表，要求这个机会集广泛地包含了可能的“风险投资组合”。你的图表应该在横坐标上显示每年的标准差，并在纵坐标上显示每年的预期收益。

(b) Using the return and risk results from the previous question and BlackRock’s expected returns for Australian cash, find the asset class weights for the optimal risky portfolio






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(assuming cash as a proxy for the risk free asset and using BlackRock’s expected return) and state the portfolio’s weights, expected return, risk and Sharpe ratio.

用前面问题中风险和收益的结果以及贝莱德的澳大利亚现金的预期收益，为最优风险投资组合找到各资产类别的权重（假设现金代表了无风险资产并采用贝莱德的预期收益），得出投资组合的权重、预期收益、风险和夏普比率。

(c) Based on the optimal risk portfolio from part (b), chart the capital allocation line. 基于（b）的最优风险投资组合，画出资本配置线。

(d) Using the capital allocation line from part (c) and potentially the opportunity set from part (a), present asset allocation portfolios for range of risk attitudes (ie three different levels of risk aversion).

用（c）中得到的资本配置线和（a）中得到的机会集， 给出一系列风险取向（即三个不同等级的风险厌恶）的资产配置投资组合。



Question 6.

第六题。

Locate two risk aversion surveys used by fund managers or advisors. Evaluate those surveys in the context of the asset allocation exercise in this project.

找到基金经理或顾问所用的两份风险厌恶调查。根据这份做资产配置，评估这些调查。（字数限制为 600 汉字）



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Appendix A: Notes on data and spreadsheet analysis 附录A：关于数据和电子表格分析的注释


Data

数据


The S&P ASX 200 index data presented in the project excel file is a cap-weighted, total return index of 200 companies listed on the Australian stock exchange. The S&P Australian Bond Index data in the project is a total return index of a diversified portfolio of Australian Bonds. The S&P and Bloomberg Australian Bank Bill Indices are both intended to measure the performance of typical Australian managed cash portfolios. The monthly data for the individual shares are also total return indices. “Returns” can be calculated for both the Consumer Sentiment Index and the Fama French HML Index in the same way as calculating returns for the other indices – however do not deduct cash returns from their returns.

在的电子表格中，标普澳证 200 指数的数据是在澳大利亚股票交易所上市的 200 家公司市值加权平均总收益的指数；标普澳大利亚债券指数数据是一个澳大利亚债券分散投资组合的总收益指数；标准普尔和彭博的澳大利亚银行汇票指数都是为了度量澳大利亚典型的现金管理投资组合的业绩。个股的月度数据也是总收益指数。计算消费者信心指数和法马-佛伦奇账面市值比指数的“收益”，与计算其他指数收益的方法相同，只是不要从收益中减去现金收益。


Calculating Rates of Return

计算收益率

The annual holding period returns can be calculated using the following formula:

Holding Period Return IndexEND IndexBEGIN 1 通过下面的公式可以计算年度持有收益率：持有期收益率 IndexEND IndexBEGIN 1

Spreadsheet Usage

使用电子表格

You will need to use a spreadsheet like Microsoft Excel to complete this project. You may find the built-in statistical functions {eg STDEV.P( ) and CORREL( ) etc} to be useful – in addition to the regression analysis tool. Use the Excel HELP to find out how what specific equations these functions are applying.

你需要使用像微软 Excel 一样的电子表格软件来完成这份。你会发现在这些软件中除回归分析工具外，其自带的统计公式（比如 STDEV.P( ) 和 CORREL( )等）也很实用。可以用电子表格的“帮助”菜单来找出这些公式具体如何应用。





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Use of Optimiser

使用优化器

To use the embedded optimiser (entitled “Solver”) in Excel, select the Data tab and look in the analysis section. In your spreadsheet, you can make some initial guesses for the weights of each asset to be included in the portfolio. Calculate the required portfolio return, risk, performance ratio etc… based on these weights. In the pop-up Solver box, set the “set objective” to the cell containing the formula for the objective measure (eg the Sharpe ratio in the context of the optimal risky portfolio etc). Select “max” (or “min” if appropriate etc…). In the “by changing variable cells” field, select the cells containing asset weights. If you click the “solve” key, the optimiser will attempt to optimise the performance measure by adjusting the weights for each asset. It is likely that you will need some constraints for the optimisation (eg by using the “subject to the constraints” component). For example, ensure that the sum of the weights is constrained to equal one. Also, consider adding additional constraints if they prove appropriate in the context of the project.

如要使用 Excel 内置的优化器（名称为“规划求解”），在数据选项卡的分析组中找到。在电子表格中，你可以先猜测投资组合中每一项资产的权重，然后据此计算要求的投资组合收益、风险和业绩比率等等。在弹出的规划求解对话框中，在“设置目标”框中输入含有目标度量（比如优化风险投资组合的夏普比率等）公式的单元格，选择“最大值”（或“最小值”）。在“可变变量单元格”框中，选择包含资产权重的单元格。如果你单击了“求解”，优化器将尝试通过改变每一项资产的权重来优化业绩度量。你可能需要为优化设置一些约束条件（使用“遵守约束”），比如保证约束权重之和为一。此外如果在中适用，还可以考虑增加额外的约束条件。


Marking & Spreadsheets

评分和电子表格

We do not mark spreadsheet. Do not submit spreadsheet files or spreadsheet print outs with your project answer.

我们不对电子表格进行评分。在提交时，不要提交电子表格文件或者打印件。





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Appendix B: Mapping BKM 10th English version and 9th Chinese version
附录 B：BKM 课本英文第十版和中文第九版的页码对照

BKM 课本英文第十版相关章节 BKM 课本中文第九版相关章节



BKM 第 8 章 262-264 页 BKM 第 8 章 162-163 页
BKM 338-340 页 BKM 第 10 章 215-216 页
BKM 340-342 页 BKM 第 10 章 217-218 页
BKM 第 13 章 415 – 426 页 BKM 第 13 章 265-282 页