Mean–CVaR portfolio selection: A nonparametric estimation framework

Yao, Haixiang; Li, Zhongfei; Lai, Yongzeng

doi:10.1016/j.cor.2012.11.007

Cited by 64 publications

(22 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The core of the theory is telling us the truth that investors should consider the risk and return together and determine the allocations of funds among investment alternatives on the basis of the trade-off between them [2]. In the past three decades, numerous researchers had contributed to the development of modern portfolio theory and proposed many optimization models and selection approaches for portfolio selection problem based on the trade-off analysis between reward and risk; see [3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

A Parametric Sharpe Ratio Optimization Approach for Fuzzy Portfolio Selection Problem

Liu¹,

Li²

2017

Mathematical Problems in Engineering

View full text Add to dashboard Cite

When facing to make a portfolio decision, investors may care more about every portfolio's performance on a return and risk tradeoff. In this paper, a new low partial moment measurement that only punishes the loss risk is defined for selection variables based on L-S integral. Furthermore, a new performance measure for portfolio evaluation is proposed to generalize the Sharpe ratio in the fuzzy context. With the optimal performance criterion, a new parametric Sharpe ratio portfolio optimization model is developed wherein uncertain returns are presented as parametric interval-valued fuzzy variables. To make the proposed model easy to solve, we transform the fractional programming into an equivalent form and solve it with domain decomposition method (DDM). Finally, we apply the proposed performance measure into a portfolio selection problem, compare the computational results in different cases, and analyze the influence of different parameters on the optimal portfolio.

show abstract

Section: Introductionmentioning

confidence: 99%

A Parametric Sharpe Ratio Optimization Approach for Fuzzy Portfolio Selection Problem

Liu¹,

Li²

2017

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…Inspired by Yao et al (), we prove that KEM CVaR hedge model is a convex optimization.Theorem KEM CVaR hedge model (i.e., equation (6)) is a convex optimization model.Proof Because the feasible set is a nonempty convex set, we only need to prove that the Hessian matrix of the objective function

{\overset{false^}{F}}_{α} ((),, h, v)

is positive semi‐definite. Differentiate

{\overset{false^}{F}}_{α} ((),, h, v)

with respect to R t and by the definition of R t we have

\frac{\partial {\overset{false^}{F}}_{α} ((),, h, v)}{\partial R_{t}} = - \frac{1}{Tα} \sum_{t = 1}^{T} ((), ((), r_{p, t} + v) g ((), R_{t}) + {bR}_{t} g ((), R_{t})) = 0

Differentiate R t with respect to h and v and we have

\frac{\partial R_{t}}{\partial v} = - \frac{1}{b}, \frac{\partial R_{t}}{\partial h} = \frac{r_{2, t}}{b} + \frac{v + r_{p, t}}{b^{2}} \frac{\partial b}{\partial h}

Next, we take derivative of

{\overset{false^}{F}}_{α} ((),, h, v)

on v and h , respectively, and make use of equation (7) and equation (8), we get:

\frac{\partial {\overset{false^}{F}}_{α} ((),, h, v)}{\partial v} = 1 - \frac{1}{Tα} \sum_{t = 1}^{T} G ((), R_{t})

…”

Section: Methodsmentioning

confidence: 94%

Nonparametric Kernel Method to Hedge Downside Risk

Huang

Ding

2019

Int Rev Finance

View full text Add to dashboard Cite

We propose a nonparametric kernel estimation method (KEM) that determines the optimal hedge ratio by minimizing the downside risk of a hedged portfolio, measured by conditional value‐at‐risk (CVaR). We also demonstrate that the KEM minimum‐CVaR hedge model is a convex optimization. The simulation results show that our KEM provides more accurate estimations and the empirical results suggest that, compared to other conventional methods, our KEM yields higher effectiveness in hedging the downside risk in the weather‐sensitive markets.

show abstract

“…A portfolio selection model based on fuzzy-value-at-risk is given in [10] and developed a particle swarm optimization algorithm to find the best solution. An alternative risk measure is given in [11,12], named as Conditional-Value-at-Risk (also known as Expected Shortfall, Expected Tail Loss). CVaR is thoroughly identical to VaR measure of risk for normal distributions and has better attributes than VaR.…”

Section: Related Workmentioning

confidence: 99%

A Novel Framework for Portfolio Selection Model Using Modified ANFIS and Fuzzy Sets

Kumar

Doja

2018

Computers

View full text Add to dashboard Cite

This paper proposes a novel framework for solving the portfolio selection problem. This framework is excogitated using two newly parameters obtained from an existing basic mean variance model. The scheme can prove entirely advantageous for decision-making while using computed values of these significant parameters. The framework combines effectiveness of the mean-variance model and another significant parameter called Conditional-Value-at-Risk (CVaR). It focuses on extracting two newly parameters viz. αnew and βnew, which are demarcated from results obtained from mean-variance model and the value of CVaR. The method intends to minimize the overall cost, which is computed in the framework using quadratic equations involving these newly parameters. The new structure of ANFIS is designed by changing existing structure of ANFIS and this new structure contains six layers instead of existing five-layered structure. Fuzzy sets are harnessed for the design of the second layer of this new ANFIS structure. The output parameter acquired from the sixth layer of the new ANFIS structure serves as an important index for an investor in the decision-making. The numerical results acquired from the framework and the new six-layered structure is presented and these results are assimilated and compared with the results of the existing ANFIS structure.

show abstract

Mean–CVaR portfolio selection: A nonparametric estimation framework

Cited by 64 publications

References 36 publications

A Parametric Sharpe Ratio Optimization Approach for Fuzzy Portfolio Selection Problem

A Parametric Sharpe Ratio Optimization Approach for Fuzzy Portfolio Selection Problem

Nonparametric Kernel Method to Hedge Downside Risk

A Novel Framework for Portfolio Selection Model Using Modified ANFIS and Fuzzy Sets

Contact Info

Product

Resources

About