金融代写|投资组合代写Investment Portfolio代考|FINC3017

金融代写|投资组合代写Investment Portfolio代考|PORTFOLIO CONSTRAINTS COMMONLY USED IN PRACTICE

Institutional features and investment policy decisions often lead to more complicated constraints and portfolio management objectives than those present in the original formulation of the mean-variance problem. For example, many mutual funds are managed relative to a particular benchmark or asset universe (e.g., S\&P 500, Russell 1000) so that their tracking error relative to the benchmark is kept small. ${ }^3$ A portfolio manager might also be restricted on how concentrated the investment portfolio can be in a particular industry or sector. These restrictions, and many more, can be modeled by adding constraints to the original formulation.

In this section, we describe constraints that are often used in combination with the mean-variance problem in practical applications. Specifically, we distinguish between linear, quadratic, nonlinear, and combinatorial/ integer constraints.

Throughout this section, we denote the current portfolio weights by $\mathbf{w}_0$ and the targeted portfolio weights by w, so that the amount to be traded is $\mathbf{x}=\mathbf{w}-\mathbf{w}_0$.

High portfolio turnover can result in large transaction costs that make portfolio rebalancing inefficient. One possibility is to limit the amount of turnover allowed when performing portfolio optimization. The most common turnover constraints limit turnover on each individual asset
$$\left|x_i\right| \leq U_i$$
or on the whole portfolio
$$\sum_{i \in I}\left|x_i\right| \leq U_{\text {portfolio }}$$
where $I$ denotes the available investment universe. Turnover constraints are often imposed relative to the average daily volume (ADV) of a stock. For example, we might want to restrict turnover to be no more than $5 \%$ of average daily volume. Modifications of these constraints, such as limiting turnover in a specific industry or sector, are also frequently applied.

金融代写|投资组合代写Investment Portfolio代考|Risk Factor Constraints

In practice, it is very common for portfolio managers to use factor models to control for different risk exposures to risk factors such as market, size, and style. ${ }^4$ Let us assume that security returns have a factor structure with $K$ risk factors, that is
$$R_i=\alpha_i+\sum_{k=1}^K \beta_{i k} F_k+\varepsilon_i$$
where $F_k, k=1, \ldots, K$ are the $K$ factors common to all the securities, $\beta_{i k}$ is the sensitivity of the $i$-th security to the $k$-th factor, and $\varepsilon_i$ is the nonsystematic return for the $i$-th security.

To limit a portfolio’s exposure to the k-th risk factor, we can impose the constraint
$$\sum_{i=1}^N \beta_{i k} w_i \leq U_k$$
where $U_k$ denotes maximum exposure allowed. To construct a portfolio that is neutral to the $k$-th risk factor (for example, market neutral) we would use the constraint
$$\sum_{i=1}^N \beta_{i k} w_i=0$$

金融代写|投资组合代写Investment Portfolio代考|Risk Factor Constraints

$$R_i=\alpha_i+\sum_{k=1}^K \beta_{i k} F_k+\varepsilon_i$$

$$\sum_{i=1}^N \beta_{i k} w_i \leq U_k$$

$$\sum_{i=1}^N \beta_{i k} w_i=0$$

myassignments-help数学代考价格说明

1、客户需提供物理代考的网址，相关账户，以及课程名称，Textbook等相关资料~客服会根据作业数量和持续时间给您定价~使收费透明，让您清楚的知道您的钱花在什么地方。

2、数学代写一般每篇报价约为600—1000rmb，费用根据持续时间、周作业量、成绩要求有所浮动(持续时间越长约便宜、周作业量越多约贵、成绩要求越高越贵)，报价后价格觉得合适，可以先付一周的款，我们帮你试做，满意后再继续，遇到Fail全额退款。

3、myassignments-help公司所有MATH作业代写服务支持付半款，全款，周付款，周付款一方面方便大家查阅自己的分数，一方面也方便大家资金周转，注意:每周固定周一时先预付下周的定金，不付定金不予继续做。物理代写一次性付清打9.5折。

Math作业代写、数学代写常见问题

myassignments-help擅长领域包含但不是全部: