### 金融代写|量化风险管理代写Quantitative Risk Management代考|BUSA90315

statistics-lab™ 为您的留学生涯保驾护航 在代写量化风险管理Quantitative Risk Management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。我们的专家在代写量化风险管理Quantitative Risk Management代写方面经验极为丰富，各种代写量化风险管理Quantitative Risk Management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|量化风险管理代写Quantitative Risk Management代考|Risk Management in Essence

A hyperbola forms the efficient frontier if no risk-free asset is available (assumption that most portfolio manager considers as being closer to reality). Assuming the existence of a risk-free asset, the efficient frontier is a straight line. Formally, for a risk level given $q \in[0, \infty)$, the efficient frontier is obtained by minimising the following expression:
$$w^{T} \Sigma w-q * R^{T} w$$
where

• $w$ is a vector of portfolio weights and $\sum_{i} w_{i}=1$. Note that negative weights indicate the sale of a security.;
• $\Sigma$ is the covariance matrix for the returns on the assets in the portfolio;
• $q \geq 0$ is the risk level factor,
• $R$ is a vector of expected returns,
• $w^{T} \Sigma w$ is the variance of portfolio’s return,
• $R^{T} w$ is the expected return of the portfolio.
Remark 3.2.2 The two mutual fund theorem (Merton 1972) states that any portfolio on the efficient frontier can be generated by holding a combination of any two given portfolios on the frontier; the latter two given portfolios are the “mutual funds” in the theorem’s name. So in the absence of a risk-free asset, an investor can achieve any desired efficient portfolio even if all that is accessible is a pair of efficient mutual funds. If the location of the desired portfolio on the frontier is between the locations of the two mutual funds, both mutual funds will be held in positive quantities. If the desired portfolio is outside the range spanned by the two mutual funds, then one of the mutual funds must be sold short (held in negative quantity) while the size of the investment in the other mutual fund must be greater than the amount available for investment (the excess being funded by the borrowing from the other fund).

## 金融代写|量化风险管理代写Quantitative Risk Management代考|Risk-Free Asset and the Capital Allocation Line

The risk-free asset is the asset that pays a risk-free rate assuming that this asset exists. In practice, short-term government securities are used as a risk-free asset, because they pay a fixed rate of interest and have exceptionally low default risk. The risk-free asset is constant and is mechanically uncorrelated with any other asset. Consequently, when combined with any other asset or portfolio of assets, the change in return is linearly related to the change in risk as the proportions in the combination vary.

When a risk-free asset is introduced, the half-line shown in the figure is the new efficient frontier. It is tangent to the hyperbola at the pure risky portfolio with the highest Sharpe ratio. Its vertical intercept represents a portfolio with $100 \%$ of holdings in the risk-free asset; the tangency with the hyperbola represents a portfolio with no risk-free holdings and $100 \%$ of assets held in the portfolio occurring at the tangency point; points between those points are portfolios containing positive amounts of both the risky tangency portfolio and the risk-free asset; and points on the half-line beyond the tangency point are leveraged portfolios involving negative holdings of the risk-free asset (the latter has been sold short-in other words, the investor has borrowed at the risk-free rate) and an amount invested in the tangency portfolio equal to more than $100 \%$ of the investor’s initial capital. This efficient half-line is called the capital allocation line (CAL), and its formula can be shown to be
$$E\left(R_{C}\right)=R_{F}+\sigma_{C} \frac{E\left(R_{P}\right)-R_{F}}{\sigma_{P}}$$
In this formula $\mathrm{P}$ is the sub-portfolio of risky assets at the tangency with the Markowitz curve, $F$ is the risk-free asset, and $C$ is a combination of portfolios $P$ and $F$.

By the diagram, the introduction of the risk-free asset as a possible component of the portfolio has improved the range of risk-expected return combinations available, because everywhere except at the tangency portfolio the half-line gives a higher expected return than the hyperbola does at every possible risk level. The fact that all points on the linear efficient locus can be achieved by a combination of holdings of the risk-free asset and the tangency portfolio is known as the one mutual fund theorem, where the mutual fund referred to is the tangency portfolio.

## 金融代写|量化风险管理代写Quantitative Risk Management代考|Risk Management Through MPT

The specific risk is the risk associated with individual assets. As introduced above, these risks can be reduced through diversification. The specific risk is diversifiable, unique, unsystematic, and therefore traditionally denoted idiosyncratic risk. The

systematic risk refers to the risk common to all securities. The systematic risk cannot be diversified, assuming a single market. The systematic risk is therefore equivalent to the risk of the market portfolio.

Since a security will be purchased only if it improves the risk-expected return characteristics of the market portfolio, the relevant measure of the risk of a security is the risk it adds to the market portfolio, and not its risk in isolation. In this context, the volatility of the asset and its correlation with the market portfolio are historically observed and are therefore given. (There are several approaches to asset pricing that attempt to price assets by modelling the stochastic properties of the moments of assets’ returns – these are broadly referred to as conditional asset pricing models.)
Systematic risks within one market can be managed through a strategy of using both long and short positions within one portfolio, creating a “market neutral” portfolio. Market neutral portfolios, therefore will have a correlations of zero.

## 金融代写|量化风险管理代写Quantitative Risk Management代考|Risk Management in Essence

• 在是投资组合权重的向量，并且∑一世在一世=1. 请注意，负权重表示出售证券。
• Σ是投资组合中资产收益的协方差矩阵；
• q≥0是风险水平因子，
• R是预期收益的向量，
• 在吨Σ在是投资组合收益的方差，
• R吨在是投资组合的预期收益。
备注 3.2.2 两个共同基金定理 (Merton 1972) 指出，有效前沿上的任何投资组合都可以通过在前沿上持有任意两个给定投资组合来产生；后两个给定的投资组合是定理名称中的“共同基金”。因此，在没有无风险资产的情况下，即使只有一对高效的共同基金，投资者也可以实现任何期望的高效投资组合。如果边界上所需投资组合的位置在两个共同基金的位置之间，则两个共同基金都将以正数持有。如果所需的投资组合超出两个共同基金的范围，

## 有限元方法代写

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## 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。