Managing Market Risk and Controlling VAR

2018 ◽  
pp. 113-131
Keyword(s):  
Efficient Frontier ◽  
Market Risk ◽  
Sharpe Ratio ◽  
Optimal Portfolio ◽  
Return Variance ◽  
Simulation Results ◽  
Investment Portfolios ◽  
Mean Variance ◽  
Portfolio Return ◽  
Correlated Assets

The market risk management in a portfolio selection of correlated assets is considered in this chapter. The chapter elaborates how to construct and select an optimal portfolio of correlated assets in order to control VAR considering the risk associated limits. Stochastic optimisation is used to construct the efficient frontier of minimal mean variance investment portfolios with maximal return and a minimal acceptable risk. Monte Carlo simulation is utilised to stochastically calculate and measure the portfolio return, Variance, Standard Deviation, VAR and Sharpe Ratio of the efficient frontier portfolios. Six Sigma process capability metrics are also stochastically calculated against desired specified target limits for VAR and Sharpe Ratio of the Efficient Frontier portfolios. Simulation results are analysed and the optimal portfolio is selected from the Efficient Frontier based on the criteria of maximum Sharpe Ratio.

Petroleum Exploration Risk in Prospect Portfolio Selection

2017 ◽  
pp. 40-65
Keyword(s):  
Standard Deviation ◽  
Portfolio Selection ◽  
Six Sigma ◽  
Efficient Frontier ◽  
Sharpe Ratio ◽  
Petroleum Exploration ◽  
Management Approach ◽  
Portfolio Optimisation ◽  
Exploration Risk ◽  
Return Variance

Presented method is applied to petroleum exploration for prospect portfolio selection to achieve investment objectives controlling risk. DMAIC framework applies stochastic techniques to risk management. Optimisation resolves Efficient Frontier of portfolios for desired range of expected return with initially defined increment. Simulation measures Efficient Frontier portfolios calculating mean return, variance, standard deviation, Sharpe Ratio, and Six Sigma metrics versus pre-specified target limits. Analysis considers mean return, Six Sigma metrics and Sharpe Ratio and selects the portfolio with maximal Sharpe Ratio as initially the best portfolio. Optimisation resolves Efficient Frontier in a narrow interval with smaller increments. Simulation measures Efficient Frontier performance including mean return, variance, standard deviation, Sharpe Ratio, and Six Sigma metrics versus pre-specified target. Analysis identifies the maximal Sharpe Ratio portfolio, i.e. the best portfolio for implementation. Selected prospects in the portfolio are individual projects. So, Project Management approach is used for control.

scholarly journals Mean-Variance Portfolio Selection with Tracking Error Penalization

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1915
Author(s):  
William Lefebvre ◽  
Grégoire Loeper ◽  
Huyên Pham
Keyword(s):  
Portfolio Selection ◽  
Tracking Error ◽  
Efficient Frontier ◽  
Minimum Variance ◽  
Sharpe Ratio ◽  
Portfolio Strategy ◽  
The Mean ◽  
Mean Variance Portfolio ◽  
Mean Variance ◽  
Variance Criterion

This paper studies a variation of the continuous-time mean-variance portfolio selection where a tracking-error penalization is added to the mean-variance criterion. The tracking error term penalizes the distance between the allocation controls and a reference portfolio with same wealth and fixed weights. Such consideration is motivated as follows: (i) On the one hand, it is a way to robustify the mean-variance allocation in the case of misspecified parameters, by “fitting" it to a reference portfolio that can be agnostic to market parameters; (ii) On the other hand, it is a procedure to track a benchmark and improve the Sharpe ratio of the resulting portfolio by considering a mean-variance criterion in the objective function. This problem is formulated as a McKean–Vlasov control problem. We provide explicit solutions for the optimal portfolio strategy and asymptotic expansions of the portfolio strategy and efficient frontier for small values of the tracking error parameter. Finally, we compare the Sharpe ratios obtained by the standard mean-variance allocation and the penalized one for four different reference portfolios: equal-weights, minimum-variance, equal risk contributions and shrinking portfolio. This comparison is done on a simulated misspecified model, and on a backtest performed with historical data. Our results show that in most cases, the penalized portfolio outperforms in terms of Sharpe ratio both the standard mean-variance and the reference portfolio.

Research and Development Risk in Projects Selection

2017 ◽  
pp. 66-91
Keyword(s):  
Standard Deviation ◽  
Six Sigma ◽  
Efficient Frontier ◽  
Sharpe Ratio ◽  
Management Approach ◽  
Portfolio Optimisation ◽  
Expected Return ◽  
Return Variance ◽  
Stochastic Techniques ◽  
Development Risk

Elaborated method is applied to R&D for project portfolio selection to achieve investment objectives controlling risk. DMAIC framework applies stochastic techniques to risk management. Optimisation resolves Efficient Frontier of portfolios for desired range of expected return with initially defined increment. Simulation measures Efficient Frontier portfolios calculating mean return, variance, standard deviation, Sharpe Ratio, and Six Sigma metrics versus pre-specified target limits. Analysis considers mean return, Six Sigma metrics and Sharpe Ratio and selects the portfolio with maximal Sharpe Ratio as initially the best portfolio. Optimisation resolves Efficient Frontier in a narrow interval with smaller increments. Simulation measures Efficient Frontier performance including mean return, variance, standard deviation, Sharpe Ratio, and Six Sigma metrics versus pre-specified target. Analysis identifies the maximal Sharpe Ratio portfolio, i.e. the best portfolio for implementation. Selected projects in the portfolio are individual projects. So, Project Management approach is used for control.

scholarly journals Continuous-Time Mean-Variance Portfolio Selection under the CEV Process

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Hui-qiang Ma
Keyword(s):  
Portfolio Selection ◽  
Continuous Time ◽  
Stock Price ◽  
Efficient Frontier ◽  
Optimal Portfolio ◽  
Portfolio Strategy ◽  
Cev Process ◽  
The Mean ◽  
Mean Variance Portfolio ◽  
Mean Variance

We consider a continuous-time mean-variance portfolio selection model when stock price follows the constant elasticity of variance (CEV) process. The aim of this paper is to derive an optimal portfolio strategy and the efficient frontier. The mean-variance portfolio selection problem is formulated as a linearly constrained convex program problem. By employing the Lagrange multiplier method and stochastic optimal control theory, we obtain the optimal portfolio strategy and mean-variance efficient frontier analytically. The results show that the mean-variance efficient frontier is still a parabola in the mean-variance plane, and the optimal strategies depend not only on the total wealth but also on the stock price. Moreover, some numerical examples are given to analyze the sensitivity of the efficient frontier with respect to the elasticity parameter and to illustrate the results presented in this paper. The numerical results show that the price of risk decreases as the elasticity coefficient increases.

scholarly journals Seleção de Carteiras: Escolha entre modelos baseada em persistência de performance

2020 ◽  
Vol 18 (1) ◽  
pp. 91
Author(s):  
Ricardo De Souza Tavares ◽  
João Frois Caldeira
Keyword(s):  
Portfolio Selection ◽  
Selection Procedure ◽  
Sharpe Ratio ◽  
Suggested Approach ◽  
Average Return ◽  
The Mean ◽  
Investment Portfolios ◽  
Mean Variance

<p>This essay presents an alternative to the problem of choosing between strategies for building investment portfolios. We propose a new portfolio selection procedure, dividing the sample into three equal parts (for estimations initiations, training, and evaluation outside the sample) in which, at each point of time, the strategy with the best performance is chosen in a window of p recent observations for a given criterion. We considered as criteria the mean, variance, and Sharpe ratio, aiming to construct sequences of allocation choices that best adapted to the different contexts and databases analyzed. Results indicate that the suggested approach was capable of generating allocation sequences with good performance in terms of average return and Sharpe ratio.</p>

scholarly journals Optimization Stock Portfolio With Mean-Variance and Linear Programming: Case In Indonesia Stock Market

2010 ◽  
Vol 1 (1) ◽  
pp. 15
Author(s):  
Yen Sun
Keyword(s):  
Linear Programming ◽  
Stock Market ◽  
Stock Exchange ◽  
Efficient Frontier ◽  
Risk Averse ◽  
Market Return ◽  
Stock Portfolios ◽  
Stock Portfolio ◽  
Mean Variance ◽  
Portfolio Return

It is observed that the number of Indonesia’s domestic investor who involved in the stock exchange is very less compare to its total number of population (only about 0.1%). As a result, Indonesia Stock Exchange (IDX) is highly affected by foreign investor that can threat the economy. Domestic investor tends to invest in risk-free asset such as deposit in the bank since they are not familiar yet with the stock market and anxious about the risk (risk-averse type of investor). Therefore, it is important to educate domestic investor to involve in the stock exchange. Investing in portfolio of stock is one of the best choices for risk-averse investor (such as Indonesia domestic investor) since it offers lower risk for a given level of return. This paper studies the optimization of Indonesian stock portfolio. The data is the historical return of 10 stocks of LQ 45 for 5 time series (January 2004 – December 2008). It will be focus on selecting stocks into a portfolio, setting 10 of stock portfolios using mean variance method combining with the linear programming (solver). Furthermore, based on Efficient Frontier concept and Sharpe measurement, there will be one stock portfolio picked as an optimum Portfolio (Namely Portfolio G). Then, Performance of portfolio G will be evaluated by using Sharpe, Treynor and Jensen Measurement to show whether the return of Portfolio G exceeds the market return. This paper also illustrates how the stock composition of the Optimum Portfolio (G) succeeds to predict the portfolio return in the future (5th January – 3rd April 2009). The result of the study observed that optimization portfolio using Mean-Variance (consistent with Markowitz theory) combine with linear programming can be applied into Indonesia stock’s portfolio. All the measurements (Sharpe, Jensen, and Treynor) show that the portfolio G is a superior portfolio. It is also been found that the composition (weights) stocks of optimum portfolio (G) can be used to predict the forward return (5th January – 3rd April 2009). It is shown that the stock portfolio return of 5th January – 3rd April 2009) has exceeded the market return for the same period of time based on Sharpe and Treynor measurement. 

scholarly journals A Probabilistic-Based Portfolio Resampling Under the Mean-Variance Criterion

2021 ◽  
Vol 6 (1) ◽  
pp. 45-56
Author(s):  
Anmar Al Wakil
Keyword(s):  
Estimation Error ◽  
Confidence Region ◽  
Three Dimensional ◽  
Efficient Frontier ◽  
Parameter Estimates ◽  
Three Dimensional Representation ◽  
The Mean ◽  
Mean Variance ◽  
Portfolio Return ◽  
Global Mean

Abstract An abundant amount of literature has documented the limitations of traditional unconstrained mean-variance optimization and Efficient Frontier (EF) considered as an estimation-error maximization that magnifies errors in parameter estimates. Originally introduced by Michaud (1998), empirical superiority of portfolio resampling supposedly lies in the addressing of parameter uncertainty by averaging forecasts that are based on a large number of bootstrap replications. Nevertheless, averaging over resampled portfolio weights in order to obtain the unique Resampled Efficient Frontier (REF, U.S. patent number 6,003,018) has been documented as a debated statistical procedure. Alternatively, we propose a probabilistic extension of the Michaud resampling that we introduce as the Probabilistic Resampled Efficient Frontier (PREF). The originality of this work lies in addressing the information loss in the REF by proposing a geometrical three-dimensional representation of the PREF in the mean-variance-probability space. Interestingly, this geometrical representation illustrates a confidence region around the naive EF associated to higher probabilities; in particular for simulated Global-Mean-Variance portfolios. Furthermore, the confidence region becomes wider with portfolio return, as is illustrated by the dispersion of simulated Maximum-Mean portfolios.

Investment Management Risk

2017 ◽  
pp. 13-39
Keyword(s):  
Portfolio Management ◽  
Value At Risk ◽  
Efficient Frontier ◽  
Sharpe Ratio ◽  
Portfolio Performance ◽  
Investment Management ◽  
Expected Return ◽  
Return Variance ◽  
Asset Portfolio ◽  
Investment Process

Proposed method is applied to Investment Management for portfolio selection to achieve investment objectives controlling risk. DMAIC framework applies stochastic techniques to investment risk management. Optimisation constructs Efficient Frontier of optimal portfolios with expected return in a predefined range with a determined increment. Simulation calculates and measures the portfolio return, Variance, Standard Deviation, Value at Risk (VAR), Sharpe Ratio and Beta of Efficient Frontier portfolios; Six Sigma capability metrics of investment process are calculated versus specified limits. Analysis allows for selection of the best Efficient Frontier portfolio with maximum Sharpe Ratio. Simulation sensitivity analysis identifies the riskiest asset. Portfolio revision considers options to improve the portfolio and replaces the asset with an option to reduce risk. Portfolio execution implements the revised portfolio. Ongoing portfolio management evaluates portfolio performance on regular basis and if required, revises the portfolio considering changes in the market and investor's position.

scholarly journals Portfolio theory in the selection of oil investment projects

2012 ◽  
Vol 19 (2) ◽  
pp. 265-272
Author(s):  
Jalimar Guimarães Simplício ◽  
Celso Funcia Lemme ◽  
Ricardo Pereira Câmara Leal
Keyword(s):  
Efficient Frontier ◽  
Investment Project ◽  
Optimization Procedure ◽  
Financial Assets ◽  
Investment Projects ◽  
The Mean ◽  
Project Portfolios ◽  
Investment Portfolios ◽  
Mean Variance ◽  
Selection Of

The objective of this article is to compare investment project selection using the efficient frontier in the mean-variance space based on optimization models introduced by Markowitz (1952) with the project ranking method according to the profitability index (PI). The selection of real assets by companies did not incorporate the mean-variance optimization procedure in the same way the selection of financial assets in investment portfolios did. The process of selection and formation of portfolios of investment projects for the oil area of a company in the energy industry was analyzed. Project portfolios formed according to the usual company practice of ranking by their PI were compared with those that result from applying mean-variance optimization through Monte Carlo simulation, which allows the computation of mean returns, variances, and covariances for the set of projects considered. The inefficiency of project portfolios obtained by ranking according to the PI compared to those obtained by the method of Markowitz suggests that there are opportunities to improve the process of selecting the set of projects to be implemented by companies.

scholarly journals ANALISIS EFISIENSI PENENTUAN PORTOFOLIO SAHAM PERUSAHAAN MANUFAKTUR DI PT. BURSA EFEK INDONESIA (BEI)

2017 ◽  
pp. 38-56
Author(s):  
Jonner Pangaribuan
Keyword(s):  
Stock Returns ◽  
Stock Price ◽  
Stock Exchange ◽  
Efficient Frontier ◽  
Positive Influence ◽  
Optimal Portfolio ◽  
Manufacturing Companies ◽  
Technical Documentation ◽  
Expected Return ◽  
Portfolio Return

companies, as well as the influence of optimal portfolios and efficient manufacturing companies on stock returns in IDX. Benefits gained for investors itself is as an input to invest in stocks is optimal. The population in this study are all companies listed on the Stock Exchange, and the samples used are as many as 152 shares of manufacturing companies are divided into two portfolios based on market capitalization and value of corporate assets. Data collection techniques used by technical documentation, that the financial statements of companies that have previously run for two years ie from 2002 to 2003 observations. The data analysis technique used is multiple linear regression. Based on the results of the regression can be concluded that the higher the premium market significantly increases the risk of a stock portfolio of manufacturing companies. Regression coefficient for the independent variable on the dependent variable ERM portfolio return has a positive influence on the company. From the observations made, the optimal portfolio is the portfolio to be done based on the value of assets, particularly as it offers a great asset portfolio return of 55 percent with a 100 percent risk. Obviously the determination of the optimal portfolio for an investor to do and are applied in the efficient frontier curve is in accordance with the preferences of the investor returns and are willing to bear the risk. Therefore, investors should consider the investment shares of SBI level, analyzing the stock price and the expected return on a portfolio that is offered, as well as selecting a portfolio of shares in accordance with the preferences of the investor.

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