assignmentutor™您的专属作业导师

assignmentutor-lab™ 为您的留学生涯保驾护航 在代写风险和利率理论Market Risk, Measures and Portfolio Theory方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写风险和利率理论Market Risk, Measures and Portfolio Theory代写方面经验极为丰富，各种代写风险和利率理论Market Risk, Measures and Portfolio Theory相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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

## 金融代写|风险和利率理论代写Market Risk, Measures and Portfolio Theory代考|Adding a risk-free security

All portfolios built of the risk-free asset (with rate of return $R$ ) and any other asset are represented by a straight half-line starting from $(0, R)$ and passing though the corresponding points on the $(\sigma, \mu)$-plane (see Figure 2.6). The new feasible region is thus obtained by taking any point on the attainable set and linking it with the risk-free asset, as shown in Figure 2.8. To find the new efficient frontier we seek a line with the highest slope according to the preference relation. Note that it is reasonable to make the following restriction: the risk-free return is smaller than the expected return of the risk-minimising portfolio. Under this assumption there is a unique portfolio on the efficient frontier, called the market portfolio, such that the line with the highest slope passes through it (see Figure 2.9). This optimal line, called the capital market line, is tangent to the efficient frontier (as follows from the elementary geometric properties of hyperbolas). Denoting the expected return of the market portfolio by $\mu_{\mathrm{m}}$ and its risk by $\sigma_{\mathbf{m}}$, the capital market line is given by
$$\mu=R+\frac{\mu_{\mathrm{m}}-R}{\sigma_{\mathrm{m}}} \sigma .$$
Theorem $2.10$
The weights of the market portfolio are $\mathbf{m}=(w, 1-w)$, with
$$w=\frac{c}{c+d}, \quad 1-w=\frac{d}{c+d}$$
where
\begin{aligned} &c=\sigma_2^2\left(\mu_1-R\right)-\sigma_{12}\left(\mu_2-R\right), \ &d=\sigma_1^2\left(\mu_2-R\right)-\sigma_{12}\left(\mu_1-R\right) . \end{aligned}
Proof See page 33.

## 金融代写|风险和利率理论代写Market Risk, Measures and Portfolio Theory代考|Indifference curves

The dominance relation, where we prefer portfolios lying to the left upper side of the $(\sigma, \mu)$-plane, does not help us choose between two assets where one has higher expected return and higher risk, and the other is less risky but with lower return. It seems impossible to extend the relation to solve this decision problem so that this extension would be accepted by all investors. The relation is based on risk aversion, but the investors who, as assumed, share this attitude, may differ in the intensity of their aversion. An investor who is sensitive to risk may require much higher returns as a compensation for increased exposure. Another investor may be cornered, forced to accept risk to earn the return needed to fulfil the requirements created by his circumstances, or may be just less sensitive to risk. It is inevitable that we have to allow for the modelling of individual preferences.
Let us fix our attention on one particular investor, and fix one particular asset (or portfolio of assets). We assume that this investor can answer the following question: which assets are equally as attractive as the fixed one? The answer provides us with a certain set of assets. Since the preference relation is valid, two assets with the same expected returns and different risk will never be equally attractive; nor will be two assets with the same risk but different expected returns. Thus the intersection of this set by any line parallel to any of the axes can contain at most one element. So it is a graph of an increasing function. We assume in addition that this function is convex for each investor – in other words, to retain his peace of mind, the investor demands that a unit increase of risk be offset by more than one unit increase in return, as shown in Figure $2.10$ – and we call it an indifference curve.
We assume that indifference curves are level sets of a function
$$u: \mathbb{R}^2 \rightarrow \mathbb{R} \text {. }$$
We assume that a curve $\left{u=c_2\right}$ lies above $\left{u=c_1\right}$ for $c_1<c_2$. In other words, the higher the value of $u$, the higher the investor’s satisfaction with the investment. Given a set of attainable portfolios, an investor chooses the one placed on the best indifference curve. It is geometrically obvious as a result of convexity of the curves that the optimal portfolio is at the tangency point with the capital market line, for some indifference curve, as shown in Figure 2.11(a).

For another investor, who is less risk averse, that is, who has less steep indifference curves, the optimal portfolio may be different, as in Figure 2.11(b). It lies further to the right, which agrees with our intuition regarding the risk preferences of this investor.

# 风险和利率理论代写

## 金融代写|风险和利率理论代写市场风险、措施和投资组合理论代考|添加一个无风险的证券

$$\mu=R+\frac{\mu_{\mathrm{m}}-R}{\sigma_{\mathrm{m}}} \sigma .$$

$$w=\frac{c}{c+d}, \quad 1-w=\frac{d}{c+d}$$
，其中
\begin{aligned} &c=\sigma_2^2\left(\mu_1-R\right)-\sigma_{12}\left(\mu_2-R\right), \ &d=\sigma_1^2\left(\mu_2-R\right)-\sigma_{12}\left(\mu_1-R\right) . \end{aligned}

## 金融代写|风险和利率理论代写市场风险、度量和投资组合理论代考|无差异曲线

$$u: \mathbb{R}^2 \rightarrow \mathbb{R} \text {. }$$

## 有限元方法代写

assignmentutor™作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

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。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师