Doug I. Jones

Doug I. Jones

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我们提供的利率理论portfolio theory及其相关学科的代写,服务范围广, 其中包括但不限于:

  • Statistical Inference 统计推断
  • Statistical Computing 统计计算
  • Advanced Probability Theory 高等概率论
  • Advanced Mathematical Statistics 高等数理统计学
  • (Generalized) Linear Models 广义线性模型
  • Statistical Machine Learning 统计机器学习
  • Longitudinal Data Analysis 纵向数据分析
  • Foundations of Data Science 数据科学基础


An individual security’s expected returns are almost always based on estimates provided by analysts. The techniques used for obtaining these forecasts are contained in Chapters 17, 18, and 19, which discuss valuation models, earnings estimation, and efficient markets. In this section, we discuss some characteristics of these forecasts that need to be taken into account when forming portfolios.

Researchers have found that forecasts of analysts across the stocks they follow tend to be too optimistic and too diverse, having too high a mean and too much dispersion. Nevertheless, researchers have found that analysts’ estimates do have information content [see, e.g., Elton, Gruber, and Grossman (1986)]. However, there is substantial error. A useful way to think about the information is that these are nuggets of gold in a large pile of rock. If this information is used directly as input into a portfolio optimizer, then the extreme estimates will result in a portfolio that includes very few securities, frequently heavily concentrated in only one or two. These heavily concentrated portfolios will have high risk. Given the substantial error in forecasts of expected return, the extra return from these portfolios is likely to be small, and given the higher risk, the portfolios are likely to perform poorly. The object then is to devise techniques that still utilize the information in the forecasts but result in well-diversified portfolios.

Diversification serves three purposes. First, diversified portfolios have lower risk than more concentrated portfolios selected from the set of diverse forecasts. Second, it is generally believed that analysts’ estimates have some information content but with lots of random noise. If the errors are uncorrelated, then a larger portfolio reduces the amount of random noise and increases the chance that the extra return is observed. Third, increasing the number of securities and reducing the amount invested in any single one reduces the amount invested in a security due to the extreme estimate of one analyst.

The easiest way to ensure diversification is to put upper limits on the amount invested in each security. A $2 \%$ upper limit will guarantee at least 50 securities in any given portfolio. A $1 \%$ limit would guarantee 100 securities. Upper limits are useful and are a common feature in most analysis. The difficulty is that many securities will be at the upper limit. If we believe securities with high forecasted expected returns are more desirable on average, then we would like to hold these securities in higher proportions. An upper limit of $1 \%$ to ensure at least 100 securities in the portfolio may be harmful if some of the securities with highest forecasted expected returns or desirable risk characteristics are securities in which we would like to invest more heavily. How else can one ensure reasonable diversification while allowing higher allocations to some securities?

One way to do this is to allow higher upper bounds but to process analysts’ data to reduce some of the extreme variability. The simplest way to make forecasts less extreme and avoid the difficulties caused by this is to move all the forecasts part way to the mean and adjust the whole distribution of analysts’ estimates so that it has a mean consistent with what we believe is appropriate for the type of securities being examined.

For example, if we employ analysts who forecast a $16 \%$ return for the average equity security and we forecast a market return of $12 \%$ for equities, we can first lower all analysts’ individual estimates by $4 \%^8$ Then, to get rid of the extreme forecasts, we can adjust all forecasts toward the mean. For example, if an analyst’s forecast is an expected return of $20 \%$ for stock ABC, we would first adjust the forecasts so all of the forecasts have a mean consistent with our beliefs or, in this case, reduce it by $4 \%$ to $16 \%$. Then we further adjust it by some percentage (e.g., $50 \%$ ) of the difference of the forecast from the forecasted mean. Thus the forecast would be $16-(1 / 2) 4=14$ for $\mathrm{ABC}$. This type of adjustment preserves the rank order of the forecasts and, by making them less extreme, results in a more diversified portfolio. The difficulty with this simple adjustment is that if one believes that the securities differ in risk, the simple adjustment does not preserve the rank order of what analysts believe are good purchases (e.g., an expected return more than commensurate with their risk).

金融代写|利率理论代写portfolio theory代考|PORTFOLIO ANALYSIS WITH DISCRETE DATA

Often analysts’ information about expected return comes in the form of discrete rankings rather than an estimate of expected return. For example, one common ranking used by industry is to place a stock in one of the following five categories:

  1. strong buy
  2. buy
  3. hold
  4. sell
  5. strong sell
    If this is the form of analyst information, then different techniques for forming portfolios are required.

The optimum way to utilize these data depends on how one believes the groups were formed in the first place. In most cases, the belief is that they were formed without any consideration of the risk characteristics of the securities. In this case, there is no single optimum method for utilizing these data. However, there are a number of methods that are sensible.

One technique that can be used is to construct an index fund out of the top group or groups. To construct an index fund, one would decide on the return-generating process that best fits the data (see Chapters 7 and 8 ) and then determine the sensitivities of the market to the factors in the model. Once these are determined, one would construct a portfolio from the top-ranked securities with the same sensitivity as the market to each of the factors and that has minimal residual risk. Such a portfolio has some nice characteristics. First, if the rankings contain no information, then one has constructed a portfolio that should mimic an index fund. Second, if there is information in the rankings, then the portfolio should have volatility similar to the market and be highly correlated with the market (move up and down with the market) but have extra return. In other words, such a portfolio would perform like an enhanced return index fund. The only condition under which the portfolio would not perform well is if the information in the rankings were perverse, that is, the highest-ranked securities were actually the worst securities to hold.



单个证券的预期回报几乎总是基于分析师提供的估计。用于获得这些预测的技术包含在第 17、18 和 19 章中,它们讨论了估值模型、收益估计和有效市场。在本节中,我们将讨论在形成投资组合时需要考虑的这些预测的一些特征。

研究人员发现,分析师对他们关注的股票的预测往往过于乐观和过于多样化,均值过高且离差太大。然而,研究人员发现分析师的估计确实具有信息内容 [参见,例如,Elton、Gruber 和 Grossman (1986)]。但是,存在很大的错误。考虑这些信息的一个有用方法是,这些是一大堆岩石中的金块。如果将此信息直接用作投资组合优化器的输入,那么极端估计将导致投资组合中包含的证券很少,而且通常只集中在一两个证券中。这些高度集中的投资组合将具有高风险。鉴于预期回报预测存在重大错误,这些投资组合的额外回报可能很小,考虑到更高的风险,投资组合可能表现不佳。然后,目标是设计仍然利用预测中的信息但会产生充分多样化的投资组合的技术。


确保多元化的最简单方法是对每种证券的投资金额设定上限。2% 的上限2%将保证任何给定投资组合中至少有 50 种证券。1 1%限制将保证 100 种证券。上限很有用,并且是大多数分析中的常见特征。难的是很多证券都会涨停。如果我们认为具有高预期预期回报的证券平均而言更受欢迎,那么我们希望持有这些证券的比例更高。上限为1%确保投资组合中至少有 100 种证券可能是有害的,如果某些具有最高预测预期收益或理想风险特征的证券是我们想要加大投资的证券的话。在允许对某些证券进行更高配置的同时,还能如何确保合理的多元化?


例如,如果我们聘请的分析师预测股票的平均回报率为 ,而我们预测股票的然后,到摆脱极端预测,我们可以将所有预测调整为均值。例如,如果分析师的预测是股票 ABC 的预期回报率为,我们将首先调整预测,以便所有预测的均值与我们的信念一致,或者在这种情况下,将其降低 4至。然后我们进一步调整它一些百分比(例如,16%12%4%820%4%16%50%) 预测与预测平均值的差异。的预测为。这种类型的调整保留了预测的排名顺序,并通过降低它们的极端性,使投资组合更加多元化。这种简单调整的困难在于,如果有人认为证券的风险不同,那么简单的调整就不会保留分析师认为是好的购买(例如,预期回报与其风险相称)的排名顺序。16−(1/2)4=14ABC

金融代写|利率理论代写portfolio theory代考|PORTFOLIO ANALYSIS WITH DISCRETE DATA


  1. 强买
  2. 抓住
  3. 强势卖出


可以使用的一种技术是从一个或多个顶级组构建指数基金。要构建指数基金,需要确定最适合数据的回报生成过程(参见第 7 章和第 8 章),然后确定市场对模型中的因素的敏感性。一旦确定了这些因素,就可以从排名靠前的证券中构建一个投资组合,该证券与市场对每个因素的敏感性相同,并且剩余风险最小。这样的投资组合具有一些不错的特征。首先,如果排名不包含任何信息,那么就构建了一个应该模仿指数基金的投资组合。第二,如果排名中有信息,那么投资组合应该具有与市场相似的波动性并且与市场高度相关(随市场上下波动)但有额外的回报。换句话说,这样的投资组合将像增强回报指数基金一样发挥作用。投资组合表现不佳的唯一条件是排名中的信息有悖常理,即排名最高的证券实际上是持有最差的证券。

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术语 广义线性模型(GLM)通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归,以及方差分析和方差分析(仅含固定效应)。



有限元是一种通用的数值方法,用于解决两个或三个空间变量的偏微分方程(即一些边界值问题)。为了解决一个问题,有限元将一个大系统细分为更小、更简单的部分,称为有限元。这是通过在空间维度上的特定空间离散化来实现的,它是通过构建对象的网格来实现的:用于求解的数值域,它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统,以模拟整个问题。然后,有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。





随机过程,是依赖于参数的一组随机变量的全体,参数通常是时间。 随机变量是随机现象的数量表现,其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值(如1秒,5分钟,12小时,7天,1年),因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中,往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录,以得到其自身发展的规律。


多元回归分析渐进(Multiple Regression Analysis Asymptotics)属于计量经济学领域,主要是一种数学上的统计分析方法,可以分析复杂情况下各影响因素的数学关系,在自然科学、社会和经济学等多个领域内应用广泛。


MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中,其中问题和解决方案以熟悉的数学符号表示。典型用途包括:数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发,包括图形用户界面构建MATLAB 是一个交互式系统,其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题,尤其是那些具有矩阵和向量公式的问题,而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问,这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展,得到了许多用户的投入。在大学环境中,它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域,MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要,工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数(M 文件)的综合集合,可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。


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