200 research outputs found
Continuous-Time Markowitz's Model with Transaction Costs
A continuous-time Markowitz's mean-variance portfolio selection problem is
studied in a market with one stock, one bond, and proportional transaction
costs. This is a singular stochastic control problem,inherently in a finite
time horizon. With a series of transformations, the problem is turned into a
so-called double obstacle problem, a well studied problem in physics and
partial differential equation literature, featuring two time-varying free
boundaries. The two boundaries, which define the buy, sell, and no-trade
regions, are proved to be smooth in time. This in turn characterizes the
optimal strategy, via a Skorokhod problem, as one that tries to keep a certain
adjusted bond-stock position within the no-trade region. Several features of
the optimal strategy are revealed that are remarkably different from its
no-transaction-cost counterpart. It is shown that there exists a critical
length in time, which is dependent on the stock excess return as well as the
transaction fees but independent of the investment target and the stock
volatility, so that an expected terminal return may not be achievable if the
planning horizon is shorter than that critical length (while in the absence of
transaction costs any expected return can be reached in an arbitrary period of
time). It is further demonstrated that anyone following the optimal strategy
should not buy the stock beyond the point when the time to maturity is shorter
than the aforementioned critical length. Moreover, the investor would be less
likely to buy the stock and more likely to sell the stock when the maturity
date is getting closer. These features, while consistent with the widely
accepted investment wisdom, suggest that the planning horizon is an integral
part of the investment opportunities.Comment: 30 pages, 1 figur
Portfolio selection of stochastic differential equation with jumps under regime switching.
In this thesis, we are interested in the stochastic differential equation with jumps under regime switching. Firstly, we investigate a continuous-time version of the mean-variance portfolio selection model with jumps under regime switching. The portfolio selection proposed and analyzed for a market consisting of one bank account an d multiple stocks. The random regime switching is assumed to be independent of the underlying Brownian motion and jump processes. Secondly, we consider the problem of pricing contigent claims on a stock whose price process is modeled by a Levy process. Since the market is incomplete and there is not a unique equivalent martingale measure. We study approaches to pricing options. Finally, we investigate a continuous-time version Markowitz's mean-variance portfolio selection problem which is studied in a market with one bank account, one stock and proportional transaction costs. This is a singular stochastic control problem. Via a series of transformations, the problem is turned into a double obstacle problem
Comparison of portfolios: research on fundamental indices and recurrent indices
Treball Final de Grau en Finances i Comptabilitat. Codi: FC1049. Curs acadรจmic: 2021-2022Portfolios constructed on the basis of fundamental metrics have been the subject of research
over the years and are an area of great interest in portfolio investment.They have been
constructed according to the Market capitalization and the naรฏve portfolio. Moreover, They
have been studied and analyzed by different economists as well as compared by investors
with the recurrent and most used portfolios.
Since there has been a growing interest in this topic in recent years, this research presents
different studies by researchers who have conducted empirical studies in which it is
compared constructed portfolios by fundamental metrics with the most recurrent portfolios
that got different results and therefore different conclusions.
So far, there are still disagreements about which of these strategies performs best. That is
why the main objective of this project is to find out which portfolio has the best results among
all of them that have been analyzed. Hence this project focuses on portfolios based on
fundamental factors and compares them with the portfolios used by investors or analysts.
The portfolios based on fundamental metrics that have been studied in this work are:
portfolio based on Return on Assets, portfolio based on Return on Equity and portfolio based
on the fundamental metric Debt to Equity
The portfolio is constructed with 35 companies that have been part of the Ibex 35 during the
period from 2018 to 2020
Risk measures and their applications in asset management
Several approaches exist to model decision making under risk, where risk can be broadly defined as the effect of variability of random outcomes. One of the main approaches in the practice of decision making under risk uses mean-risk models; one such well-known is the classical Markowitz model, where variance is used as risk measure. Along this line, we consider a portfolio selection problem, where the asset returns have an elliptical distribution. We mainly focus on portfolio optimization models constructing portfolios with minimal risk, provided that a prescribed expected return level is attained. In particular, we model the risk by using Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). After reviewing the main properties of VaR and CVaR, we present short proofs to some of the well-known results. Finally, we describe a computationally efficient solution algorithm and present numerical results.conditional value-at-risk;elliptical distributions;mean-risk;portfolio optimization;value-at-risk
๋ณ๋์ฑ ์ํ๊ณผ ์ ๋ขฐ๋ ์ํ์ ๊ณ ๋ คํ ์ต์ ์ ์๊ตฌ์ฑ ๋์ถ ๋ฐฉ๋ฒ๋ก ์ฐ๊ตฌ
ํ์๋
ผ๋ฌธ (๋ฐ์ฌ) -- ์์ธ๋ํ๊ต ๋ํ์ : ๊ณต๊ณผ๋ํ ํ๋๊ณผ์ ๊ธฐ์ ๊ฒฝ์ยท๊ฒฝ์ ยท์ ์ฑ
์ ๊ณต, 2020. 8. ์ด์ข
์.Long-term power planning has been focused primarily on cost minimization, which was the same in other countries as in Korea. Since 2000, several studies applied Markowitz's portfolio theory to the portfolio of power generation sources. However, many of the earlier studies only concentrated on finding the efficient frontier of the portfolio, and there has not been a study on the trade-off ratio value between the cost and its volatility. Therefore, in earlier studies, the optimal portfolios from the efficiency frontier were found through scenario analysis, and not the real value of the policymaker's trade-off ratio.
The primary aim of this paper is to estimate reasonably the exchange ratio between costs and their volatility in the analysis of the optimal power mix using the mean-variance model. This study started from the microeconomic foundation, which the policy makers used to establish the power plan to maximize their social welfare, estimate the marginal rate of substitution (MRS) between these elements using the time series of the power structure in Korea, and derive the optimal power portfolio from this. The secondary aim of this paper is to include in the analysis model the reliability risks that must be considered in the optimal power generation mix. Several studies describe power generation assets in the same way as securities traded in the capital market, but it is very important to maintain power supply reliability as well as minimize cost, and avoid volatility in real-world power plant investment. In this study, the reliability risk was defined as the loss of load probability, and the mean-variance portfolio model was expanded by including it as an element of the social welfare function of policy-makers in establishing a power plan.
The findings of the study are as follows: First, from the perspective of cost and volatility, the ratio of substitution between the two factors gradually changed from 1992 to 2014 to take more volatility risk. This was a major reason for the expansion of combined cycle gas turbine, which was eco-friendly and continuously improved in thermal efficiency since the 1990s, whereas diversifying power sources with nuclear power and coal after the oil shock in the 1970s.
Second, the actual power generation portfolio was gradually approaching the optimal portfolio during the analysis period, but the share of LNG combined cycle power generation has increased significantly compared to the optimum level since 2011 when a large-scale power outage occurred in Korea. This can be attributed to the fact that in the early 2010s, the approval for the construction of LNG combined cycle power plants increased significantly to cope with the electricity crisis because of a short construction time.
Third, when considering power reliability, the ratio of the optimal power generation portfolio was found to increase in proportion to peak-load generator, especially LNG, as compared to the volatility-risk-only model. This is because the combined power generation technology is composed of several gas turbines and a steam turbine, and the unit capacity per generator is small, which has a considerable diversification effect even in the event of generator failure.
Based on these results, it is expected that the proportion of LNG in the power generation portfolio will have to be increased in the future. This is because policy makers are gradually changing the viewpoint of allowing volatility risk in their utility, and LNG CC is superior to other power sources in terms of reliability. In particular, the expansion of renewable power sources, which will increase the risk of reliability, is expected to require more LNG facilities in the future.์ง๊ธ๊น์ง ์ฅ๊ธฐ ์ ์๊ณํ์ ์ฃผ๋ก ๋น์ฉ์ต์ํ๋ฅผ ๋ฐํ์ผ๋ก ์ด๋ฃจ์ด์ ธ์๋ค. ํ์ง๋ง, 2000๋
๋ ์ดํ๋ถํฐ Markowitz์ ํฌํธํด๋ฆฌ์ค ์ด๋ก ์ ๋ฐ์ ์ค๋น์ ํฌํธํด๋ฆฌ์ค์ ์ ์ฉํ๋ ์ฐ๊ตฌ๊ฐ ๋ณธ๊ฒฉ์ ์ผ๋ก ์ด๋ฃจ์ด์ง๊ธฐ ์์ํ๋ฉด์ ํฐ ๋ณํ๊ฐ ๋ํ๋ฌ๋ค. ๊ทธ๋ฌ๋ ์ ํ์ ๋ง์ ์ฐ๊ตฌ๋ค์ ๋ฐ์ ๋น์ฉ์ ํ๊ท ๊ณผ ๋ถ์ฐ์ ํตํด ํฌํธํด๋ฆฌ์ค์ ํจ์จ ๊ฒฝ๊ณ๋ฅผ ์ฐพ๋๋ฐ ์ฃผ๋ ๋ชฉ์ ์ ๋์๊ณ , ๊ทธ ๋ ์์ ๊ฐ์ ๊ตํ๋น์จ์ด ์ด๋ป๊ฒ ๋๋์ง์ ๋ํ ์ฐ๊ตฌ๋ ์ด๋ฃจ์ด์ง์ง ์์๋ค. ๊ทธ๋์ ํจ์จ๊ฒฝ๊ณ๋ก๋ถํฐ ์ต์ ์ ์๊ตฌ์ฑ์ ์ฐพ์๋ด๋ ๋ฐฉ๋ฒ์ ์๋๋ฆฌ์ค ๊ธฐ๋ฒ์ ์์กดํ๊ฑฐ๋, ์ ํต์ ์ธ CAPM ๋ชจํ์ ์ด์ฉํ์ฌ ์์ฅ ํฌํธํด๋ฆฌ์ค๋ฅผ ๋์ถํ๋๋ฐ ๊ทธ์ณค๋ค.
๋ณธ ๋
ผ๋ฌธ์ ์ฒซ ๋ฒ์งธ ๋ชฉ์ ์ ํ๊ท -๋ถ์ฐ ๋ชจํ์ ์ ์ฉํ ์ต์ ์ ์ ๋ฏน์ค๋ฅผ ๋ถ์ํจ์ ์์ด์, ๋น์ฉ์ ํ๊ท ๊ณผ ๊ทธ ๋ณ๋์ฑ ๊ฐ์ ๊ตํ ๋น์จ, ์ฆ trade-off ๊ด๊ณ๋ฅผ ํฉ๋ฆฌ์ ์ผ๋ก ์ถ์ ํ๋๋ฐ ์๋ค. ๋ ๋ฒ์งธ ๋ชฉ์ ์ ์ต์ ์ ์๊ตฌ์ฑ์ ๊ณ ๋ คํจ์ ์์ด์, ์ ๋ ฅ์ฐ์
์์ ๋ฐ๋์ ๊ณ ๋ คํด์ผํ๋ ์ ๋ขฐ๋ ์ํ์ ๋ถ์ ๋ชจํ์ ๋ฐ์ํ๋ ๊ฒ์ด๋ค. ๊ธฐ์กด์ ๋ง์ ์ฐ๊ตฌ๋ค์ ๋ฐ์ ์์ฐ์ด ๋ง์น ์๋ณธ์์ฅ์์ ๊ฑฐ๋๋๋ ์ ๊ฐ์ฆ๊ถ๊ณผ ๊ฐ์ ๋ฐฉ์์ผ๋ก ๋ถ์๋์์ผ๋, ํ์ค์ ๋ฐ์ ์ค๋น ํฌ์๋ ๋น์ฉ์ต์ํ์ ๋ณ๋์ฑ ํํผ๋ฟ๋ง ์๋๋ผ, ์ ๋ ฅ ์ ๋ขฐ๋๋ฅผ ์ ์งํ๋ ๊ฒ์ด ๋งค์ฐ ์ค์ํ๋ค. ๋ณธ ๋
ผ๋ฌธ์์๋ ์ ๋ขฐ๋ ์ํ์ ๊ณต๊ธ์ง์ฅํ๋ฅ (LOLP)๋ก ์ ์ํ์ฌ, ์ ์๊ณํ์ ์๋ฆฝํ๋ ์ ์ฑ
๋น๊ตญ์์ ํจ์ฉํจ์์ ํ ์์๋ก ๋ฐ์ํ์ฌ ํ๊ท -๋ถ์ฐ ํฌํธํด๋ฆฌ์ค ๋ชจํ์ ํ์ฅ์์ผฐ๋ค. ๋ชจํ์ ๋ฏธ์์ ๊ธฐ์ด๋ ๋ณ๋์ฑ ์ํ๋ง์ ๊ณ ๋ คํ 1์ํ ๋ชจํ๊ณผ ๋์ผํ๋ฉฐ, ์ฐ๋ฆฌ๋๋ผ์ LOLPํจ์๋ฅผ ์ฐ์ถํ๊ธฐ ์ํ์ฌ ๋ชฌํ
์นด๋ฅผ๋ก ์๋ฎฌ๋ ์ด์
์ ์ด์ฉํ์๋ค.
์ด๋ฌํ ์ฐ๊ตฌ๋ชฉํ์ ๋ฐฉ๋ฒ๋ก ์ผ๋ก๋ถํฐ ์ป์ ๊ฒฐ๊ณผ๋ ๋ค์๊ณผ ๊ฐ๋ค. ์ฒซ์งธ, ๋น์ฉ๊ณผ ๋น์ฉ์ ๋ณ๋์ฑ์ ๊ด์ ์์ ์ ์ฑ
์
์์๊ฐ ๋ฐ๋ผ๋ณด๋ ๋ ์์๊ฐ์ ๋์ฒด ๋น์จ์ 1992~2014๋
๋์ ์ ์ฐจ ๋ณ๋์ฑ์ ํ์ฉํ๋ ์ชฝ์ผ๋ก ์ ํธ๊ฐ ๋ณ๊ฒฝ๋์๋ค. ์ด๋1970๋
๋ ์ค์ผ์ผํฌ ์ดํ ์์๋ ฅ๊ณผ ์ํ์ผ๋ก ๋ฐ์ ์์ ๋ค๊ฐํ๋ฅผ ์๋ํ์๋ค๊ฐ, 1990๋
๋ ์ดํ๋ถํฐ ์นํ๊ฒฝ์ ์ด๊ณ ๋ฐ์ ํจ์จ์ด ์ง์์ ์ผ๋ก ๊ฐ์ ๋ LNG ๋ณตํฉ๋ฐ์ ์ด ํ๋๋๋ฐ ํฐ ์ด์ ๊ฐ ์์๋ค. ๋์งธ, ์ค์ ์ ์๊ตฌ์ฑ์ ๋ถ์๊ธฐ๊ฐ ๋์ ์ ์ฐจ ์ต์ ํฌํธํด๋ฆฌ์ค์ ๊ทผ์ ํด์ง๊ณ ์์์ผ๋, ๋๊ท๋ชจ ์ํ์ ์ ์ด ๋ฐ์ํ์๋ 2011๋
์ดํ๋ก LNG ๋ณตํฉ ๋ฐ์ ์ ๋น์ค์ด ์ต์ ์ ๋นํด ํจ์ฌ ๋์ด๋ฌ๋ค. ์ด๋ 2010๋
๋ ์ด, ์ ๋ ฅ ์๊ธ์๊ธฐ์ ๋์ํ์ฌ ๊ฑด์ค ๊ธฐ๊ฐ์ด ์งง์ LNG ๋ณตํฉ๋ฐ์ ์ ๊ฑด์ค ์น์ธ์ด ์๋น์ ๋์ด๋๋ฐ ๊ทธ ์์ธ์ ์ฐพ์ ์ ์๋ค. ์
์งธ, ์ ๋ ฅ์ ๋ขฐ๋๋ฅผ ๊ณ ๋ คํ ๊ฒฝ์ฐ ์ต์ ์ ์๊ตฌ์ฑ ๋น์จ์ ๋ณ๋์ฑ๋ง ๊ณ ๋ คํ ๋ชจํ๋ณด๋ค ํผํฌ๋ฐ์ ์ค๋น, ๊ทธ ์ค์์๋ ํนํ LNG์ ๋น์ค์ด ๋์ด๋๋ ๊ฒ์ผ๋ก ๋ํ๋ฌ๋ค. ์ด๋ ๋ณตํฉ๋ฐ์ ๊ธฐ์ ์ด ์ฌ๋ฌ ๋์ ๊ฐ์ค ํฐ๋น๊ณผ ์คํํฐ๋น์ผ๋ก ์ด๋ฃจ์ด์ ธ, ๋ฐ์ ๊ธฐ๋น ๋จ์ ๊ธฐ ์ฉ๋์ด ์์ ๊ณ ์ฅ ๋ฐ์์๋ ์๋นํ ๋ถ์ฐ ํจ๊ณผ๊ฐ ์๊ธฐ ๋๋ฌธ์ด๋ค.
์ด๋ฌํ ๊ฒฐ๊ณผ๋ฅผ ๋ฐํ์ผ๋ก ์ ์๊ตฌ์ฑ์์ ์ ์ฑ
์ ์์ฌ์ ์ ๋์ถํ๋ฉด, ํฅํ ์ ์๊ตฌ์ฑ์๋ ํ์ฌ๋ณด๋ค LNG์ ๋น์ค์ด ๋ ๋์ด๋์ผ ํ ๊ฒ์ผ๋ก ๋ณด์ธ๋ค. ์ด๋ ์ ์ฑ
์
์์์ ํจ์ฉ๋ ๋น์ฉ์ ๋ณ๋์ฑ์ ์ ์ฐจ ํ์ฉํ๋ ๊ด์ ์ผ๋ก ๋ณํ๊ณ ์๊ณ , ์ ๋ขฐ๋ ์ธก๋ฉด์์๋ ๋ค๋ฅธ ์ ์์ ๋นํ์ฌ ์ฐ์ํ ํน์ฑ์ด ์๊ธฐ ๋๋ฌธ์ด๋ค. ํนํ, ์จ์ค๊ฐ์ค ๋ฐฐ์ถ ๋น์ฉ์ ์ฆ๊ฐ์ ์ ๋ขฐ๋ ์ํ์ ์ฆ๊ฐ์ํฌ ์ ์ฌ์ ์ ์์ ์ ์ฑ
์ ํ๋๋ ์์ผ๋ก ๋ ๋ง์ LNG์ค๋น๋ฅผ ํ์๋ก ํ ๊ฒ์ผ๋ก ์์๋๋ค.Chapter 1. Introduction 1
1.1 Research Background 1
1.2 Research Objectives 4
1.3 Research Outline 6
Chapter 2. Literature Review 7
2.1 Portfolio Theory 7
2.1.1 Markowitzs Concept 8
2.1.2 Capital Asset Pricing Model 10
2.2 Application to Power Generation Mix 14
2.2.1 Application to Global Case 14
2.2.2 Application to Korean Case 19
2.3 Estimation of the Trade-off Ratio 23
2.4 Limitations of Previous Research and Research Motivation 25
Chapter 3. Methodology 29
3.1 Volatility Risk Only Model (1-risk model) 29
3.1.1 Microeconomic Foundation 29
3.1.2 Econometric Method 35
3.2 Reliability Risk Added Model (2-risk model) 40
3.2.1 Measure of Reliability risk 40
3.2.2 Microeconomic Foundation 45
Chapter 4. Empirical Studies 56
4.1 Data Specification 56
4.1.1 Investment Cost 56
4.1.2 O&M and Fuel cost 59
4.1.3 Total Supply Cost 61
4.2 Estimation of 1-risk Model 63
4.2.1 Estimation of Covariance Matrix 63
4.2.2 Estimation of Share Equation 69
4.2.3 Empirical Results and Discussion 70
4.3 Estimation of 2-risk Model 79
4.3.1 Calculation of LOLP 79
4.3.2 Estimation of Share Equation 84
4.3.3 Empirical Results and Discussion 86
4.4 Implication for Electric Power Industry Policy 94
4.4.1 Revisit to the CAPM 95
4.4.2 Intermittency of Renewable Energy 102
4.4.3 Future Portfolio Including Renewable Energy 107
Chapter 5. Summary and Conclusion 111
5.1 Concluding Remarks and Contribution 111
5.2 Limitation and Future Studies 115
Bibliography 116
Appendix 1 : Deriving Optimal Share Equation 128
Appendix 2 : Deriving Derivatives of LOLP Function 130
Appendix 3 : Data Set 133
Appendix 4 : 8th Basic plan for supply and demand 135
Abstract (Korean) 139Docto
Efficient and robust estimation for financial returns: an approach based on q-entropy
We consider a new robust parametric estimation procedure, which minimizes an empirical version of the Havrda-Charvร t-Tsallis entropy. The resulting estimator adapts according to the discrepancy between the data and the assumed model by tuning a single constant q, which controls the trade-off between robustness and effciency. The method is applied to expected return and volatility estimation of financial asset returns under multivariate normality. Theoretical properties, ease of implementability and empirical results on simulated and financial data make it a valid alternative to classic robust estimators and semi-parametric minimum divergence methods based on kernel smoothing.q-entropy; robust estimation; power-divergence; financial returns
Efficient and robust estimation for financial returns: an approach based on q-entropy
We consider a new robust parametric estimation procedure, which minimizes an empirical version of the Havrda-Charv_at-Tsallis entropy. The resulting estimator adapts according to the discrepancy between the data and the assumed model by tuning a single constant q, which controls the trade-o_ between robustness and e_ciency. The method is applied to expected re- turn and volatility estimation of _nancial asset returns under multivariate normality. Theoretical properties, ease of implementability and empirical re- sults on simulated and _nancial data make it a valid alternative to classic robust estimators and semi-parametric minimum divergence methods based on kernel smoothingq-entropy, robust estimation, power-divergence, _nancial returns
A Heuristic Approach To The Index Tracking Problem: A Case Study Of The Tehran Exchange Price Index
Index tracking, the most popular form of passive fund management, is a portfolio
selection problem in which the return of one of the stock market indexes is reproduced by
creating a tracking portfolio consisting of a subset of the stocks included in the index.
Index tracking has been known as an NP-Hard problem, and sophisticated approaches
have been proposed in the literature to solve this problem. This paper presents an easyto-implement heuristic solution to this complex problem. The proposed approach was
implemented to develop a tracking portfolio of 438 stocks listed in the Tehran Exchange
Price Index. The numerical results indicate that the approach is able to identify quality
solutions within reasonable model runtime
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