有限资产投资组合模型比较：线性 vs 二次

下载需积分: 5 | PDF格式 | 309KB | 更新于2024-07-09 | 152 浏览量 | 举报

本文主要探讨了在实际投资环境中，线性与二次投资组合选择模型的运用及性能比较。研究涉及了三个模型：有限资产马科维茨（LAM）、有限资产平均半绝对偏差（LAMSAD）以及有限资产条件风险价值（LACVaR）。这些模型考虑了投资组合中资产的数量限制和权重基数约束。通过混合整数线性编程（Mixed Integer Linear Programming, MILP）和混合整数二次编程（Mixed Integer Quadratic Programming, MIQP）来解决这些问题。文章中提到，LAMSAD和LACVaR模型使用先进的商业代码求解，而LAM模型则采用了商业代码和作者提出的新方法。令人惊讶的是，对于中大型规模的投资组合，使用新方法解决二次LAM模型比使用商业求解器解决线性LACVaR和LAMSAD模型更为高效。新方法的优势在于，它可以在不增加计算成本的情况下找到三目标问题的所有极值点。在样本外性能的比较中，研究发现三个模型与等权重投资组合之间没有明显的优劣关系。相比于之前的研究所示，等权重投资组合并未显示出比这三个提议的模型更具优势。实证结果基于文献中常用的一些新旧公开数据集，提供了丰富的对比分析。这篇研究论文对金融投资领域的投资组合优化提供了深入的理解，特别是对于有限投资组合情况下的线性与二次模型的效率和性能差异。这些模型的比较和实际应用有助于投资者根据特定的约束和目标，选择最适合自己的投资策略。此外，该研究也强调了新的优化算法在处理复杂投资组合问题时的潜力，为未来的模型改进和技术发展提供了方向。

展开

Linear vs. Quadratic portfolio 5

x is the vector whose components x

are the fractions of a given capital invested

in asset i in the portfolio we are selecting.

We assume that n assets are available and, adopting a standard approximation,

we have that R

(x) =



i=1

is the portfolio return at time t, with t = 1, ..., T .

2.1 The Limited Asset Markowitz model

We denote by µ



t=1

, and by σ

the covariance of returns of asset i and

asset j. We also denote by ρ the required level of return for the portfolio. The

classical Mean-Variance (MV) model reads:

Min



i=1



j=1



i=1

= ρ



i=1

= 1

≥ 0 i = 1, . . . , n

(1)

This is a convex quadratic programming problem which can be solved by a num-

ber of eﬃcient algorithms with a moderate computational eﬀort even for large

instances. We denote by ϕ(ρ) the optimal value of (1) as a function of ρ. Let

min

denote the value of



i=1

at an optimal solution of the problem ob-

tained by deleting the ﬁrst constraint in (1), and let ρ

max

= max{µ

, . . . , µ

Then the graph of ϕ(ρ) on the interval [ρ

min

, ρ

max

] coincides with the set of all

non-dominated (or eﬃcient) portfolios (eﬃcient frontier), and is usually approxi-

mated by solving (1) for several (equally spaced) values of ρ in [ρ

min

, ρ

max

]. The

following proposition and corollary can be found in [15].

Proposition 1 [15]. The convexity of (1) implies that, for ρ ≥ ρ

min

, the function

ϕ(ρ) is increasing and convex.

Corollary 1 [15]. The solution of (1) does not change if we replace the expected

return constraint with



i=1

≥ ρ.

Note that for every solution ¯x of problem (1) the point (



i=1

¯x



i=1



j=1

¯x

)

is an eﬃcient point of the multi-objective problem of minimizing risk and maximiz-

ing return. Conversely, every such eﬃcient point can be obtained in this manner

for some ρ.

We now add to the MV model the realistic constraint that no more than K

assets should be held in the portfolio (a cardinality constraint), and furthermore

that the quantity x

of each asset that is included in the portfolio should b e limited

within a given interval [ℓ

, u

] (a quantity constraint or buy-in threshold). Thus we

obtain the following Limited Asset Markowitz model:

Electronic copy available at: https://ssrn.com/abstract=2365855

下载后可阅读完整内容，剩余20页未读，立即下载

身份认证购VIP最低享 7 折!

30元优惠券

weixin_38610012

粉丝: 3

有限资产投资组合模型比较：线性 vs 二次

连续时间均值-方差投资组合选择：随机LQ框架

自融资投资组合模型的旋转算法：降低方差风险

Rao二次熵与最大分散化指数：投资组合风险管理

有关组合投资优化的数学模型

非光滑凹交易成本下的均值-CVaR投资组合优化研究

广义互补主元算法：凸二次规划的高效求解与组合投资应用

多风险资产优化组合模型：理论与应用

MATLAB线性和混合整数线性规划毕业设计源码

FAANG公司资产组合创建与优化实践

【CVX案例研究】：线性与二次规划在CVX中的高效实现

最新资源