scholarly journals Spectral risk measure of holding stocks in the long run

2020 ◽  
Vol 295 (1) ◽  
pp. 75-89
Author(s):  
Zsolt Bihary ◽  
Péter Csóka ◽  
Dávid Zoltán Szabó
Keyword(s):  
Stock Price ◽  
Risk Measures ◽  
Risk Measure ◽  
Stable Process ◽  
Important Special Case ◽  
Finite Moment ◽  
Holding Period ◽  
Long Run ◽  
Spectral Risk Measures ◽  
Spectral Risk Measure

AbstractWe investigate how the spectral risk measure associated with holding stocks rather than a risk-free deposit, depends on the holding period. Previous papers have shown that within a limited class of spectral risk measures, and when the stock price follows specific processes, spectral risk becomes negative at long periods. We generalize this result for arbitrary exponential Lévy processes. We also prove the same behavior for all spectral risk measures (including the important special case of Expected Shortfall) when the stock price grows realistically fast and when it follows a geometric Brownian motion or a finite moment log stable process. This result would suggest that holding stocks for long periods has a vanishing downside risk. However, using realistic models, we find numerically that spectral risk initially increases for a significant amount of time and reaches zero level only after several decades. Therefore, we conclude that holding stocks has spectral risk for all practically relevant periods.

scholarly journals The theory and application of spectral risk measures in Vietnam

2017 ◽  
Vol 24 (04) ◽  
pp. 29-45
Author(s):  
Hai Ho Hong ◽  
Hoa Nguyen Thi
Keyword(s):  
Risk Aversion ◽  
Portfolio Management ◽  
Value At Risk ◽  
Utility Theory ◽  
Risk Measures ◽  
Risk Measure ◽  
Coherent Risk ◽  
Spectral Risk Measures ◽  
Spectral Risk Measure ◽  
Current Risk

This paper aims to provide a new risk measure for portfolio management in Vietnam by incorporating investor’s risk aversion into current risk measures such as value at risk (VaR) and expected shortfall (ES). This measure shares several desirable characteristics with the coherent risk measures, as illustrated in Artzner et al. (1997). In Vietnam, our study makes the first attempt to utilize distortion theory, instead of utility theory, to facilitate the adoption of risk aversion level in the popular risk measures. We find that spectral risk measure is more flexible and effective to different groups of risk-adverse investors, compared to the more monotonic and conventional VaR and ES measures

scholarly journals Minimizing spectral risk measures applied to Markov decision processes

2021 ◽  
Author(s):  
Nicole Bäuerle ◽  
Alexander Glauner
Keyword(s):  
Minimization Problem ◽  
Risk Measures ◽  
Risk Measure ◽  
Sufficient Conditions ◽  
Planning Horizon ◽  
Insurance Company ◽  
Existence Of A Solution ◽  
Discounted Cost ◽  
Spectral Risk Measures ◽  
Markov Decision

AbstractWe study the minimization of a spectral risk measure of the total discounted cost generated by a Markov Decision Process (MDP) over a finite or infinite planning horizon. The MDP is assumed to have Borel state and action spaces and the cost function may be unbounded above. The optimization problem is split into two minimization problems using an infimum representation for spectral risk measures. We show that the inner minimization problem can be solved as an ordinary MDP on an extended state space and give sufficient conditions under which an optimal policy exists. Regarding the infinite dimensional outer minimization problem, we prove the existence of a solution and derive an algorithm for its numerical approximation. Our results include the findings in Bäuerle and Ott (Math Methods Oper Res 74(3):361–379, 2011) in the special case that the risk measure is Expected Shortfall. As an application, we present a dynamic extension of the classical static optimal reinsurance problem, where an insurance company minimizes its cost of capital.

scholarly journals LIQUIDITY RISK AND INSTABILITIES IN PORTFOLIO OPTIMIZATION

2016 ◽  
Vol 19 (05) ◽  
pp. 1650035 ◽  
Author(s):  
FABIO CACCIOLI ◽  
IMRE KONDOR ◽  
MATTEO MARSILI ◽  
SUSANNE STILL
Keyword(s):  
Portfolio Optimization ◽  
Risk Measures ◽  
Risk Measure ◽  
Estimation Error ◽  
Coherent Risk Measures ◽  
Important Special Case ◽  
Coherent Risk ◽  
Finite Samples ◽  
Impact Function ◽  
The Impact

We show that including a term which accounts for finite liquidity in portfolio optimization naturally mitigates the instabilities that arise in the estimation of coherent risk measures on finite samples. This is because taking into account the impact of trading in the market is mathematically equivalent to introducing a regularization on the risk measure. We show here that the impact function determines which regularizer is to be used. We also show that any regularizer based on the norm [Formula: see text] with [Formula: see text] makes the sensitivity of coherent risk measures to estimation error disappear, while regularizers with [Formula: see text] do not. The [Formula: see text] norm represents a border case: its “soft” implementation does not remove the instability, but rather shifts its locus, whereas its “hard” implementation (including hard limits or a ban on short selling) eliminates it. We demonstrate these effects on the important special case of expected shortfall (ES) which has recently become the global regulatory market risk measure.

scholarly journals Optimization Problem of Insurance Investment Based on Spectral Risk Measure and RAROC Criterion

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Xia Zhao ◽  
Hongyan Ji ◽  
Yu Shi
Keyword(s):  
Risk Aversion ◽  
Optimization Problem ◽  
Risk Measures ◽  
Risk Measure ◽  
Risk Attitude ◽  
Investment Strategy ◽  
Marginal Effect ◽  
Investment Ratio ◽  
Spectral Risk Measure ◽  
The Impact

This paper introduces spectral risk measure (SRM) into optimization problem of insurance investment. Spectral risk measure could describe the degree of risk aversion, so the underlying strategy might take the investor's risk attitude into account. We establish an optimization model aiming at maximizing risk-adjusted return of capital (RAROC) involved with spectral risk measure. The theoretical result is derived and empirical study is displayed under different risk measures and different confidence levels comparatively. The result shows that risk attitude has a significant impact on investment strategy. With the increase of risk aversion factor, the investment ratio of risk asset correspondingly reduces. When the aversive level increases to a certain extent, the impact on investment strategies disappears because of the marginal effect of risk aversion. In the case of VaR and CVaR without regard for risk aversion, the investment ratio of risk asset is increasing significantly.

scholarly journals Pricing of Margin Call Stock Loan Based on the FMLS

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Kaili Xiang ◽  
Peng Hu ◽  
Xiao Li
Keyword(s):  
Free Boundary ◽  
Normal Distribution ◽  
Stock Price ◽  
Empirical Test ◽  
Stable Process ◽  
Standard Normal Distribution ◽  
Asymmetric Distribution ◽  
Finite Moment ◽  
The Impact ◽  
Stock Loan

In common stock loan, lenders face the risk that their loans will not be repaid if the stock price falls below loan, which limits the issuance and circulation of stock loans. The empirical test suggests that the log-return series of stock price in the US market reject the normal distribution and admit instead a subclass of the asymmetric distribution. In this paper, we investigate the model of the margin call stock loan problem under the assumption that the return of stock follows the finite moment log-stable process (FMLS). In this case, the pricing model of the margin call stock loan can be described by a space-fractional partial differential equation with a time-varying free boundary condition. We transform the free boundary problem to a linear complementarity problem, and the fully-implicit finite difference method that we used is unconditionally stable in both the integer and fractional order. The numerical experiments are carried out to demonstrate differences of the margin call stock loan model under the FMLS and the standard normal distribution. Last, we analyze the impact of key parameters in our model on the margin call stock loan evaluation and give some reasonable explanation.

Debt Structure Adjustments and Long-run Stock Price Performance

2000 ◽  
Author(s):  
Sudip Datta ◽  
Mai E. Iskandar-Datta ◽  
Kartik Raman
Keyword(s):  
Stock Price ◽  
Debt Structure ◽  
Price Performance ◽  
Long Run

scholarly journals Financial Crises, Macroeconomic Variables, and Long-Run Risk: An Econometric Analysis of Stock Returns Correlations (2000 to 2019)

2021 ◽  
Vol 14 (3) ◽  
pp. 127
Author(s):  
Marco Tronzano
Keyword(s):  
Stock Returns ◽  
Risk Premium ◽  
Financial Crises ◽  
Stock Price ◽  
Financial Risk ◽  
Swiss Franc ◽  
Chinese Stock Market ◽  
Stock Market Index ◽  
Defensive Role ◽  
Long Run

This paper focuses on four major aggregate stock price indexes (SP 500, Stock Europe 600, Nikkei 225, Shanghai Composite) and two “safe-haven” assets (Gold, Swiss Franc), and explores their return co-movements during the last two decades. Significant contagion effects on stock markets are documented during almost all financial crises; moreover, in line with the recent literature, the defensive role of gold and the Swiss Franc in asset portfolios is highlighted. Focusing on a new set of macroeconomic and financial series, a significant impact of these variables on stock returns correlations is found, notably in the case of the world equity risk premium. Finally, long-run risks are detected in all asset portfolios including the Chinese stock market index. Overall, this empirical evidence is of interest for researchers, financial risk managers and policy makers.

scholarly journals Modified Mean-Variance Risk Measures for Long-Term Portfolios

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 111
Author(s):  
Hyungbin Park
Keyword(s):  
Risk Measures ◽  
Risk Measure ◽  
Investment Strategy ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Volatility Model ◽  
Variance Risk ◽  
Investment Portfolios ◽  
Mean Variance

This paper proposes modified mean-variance risk measures for long-term investment portfolios. Two types of portfolios are considered: constant proportion portfolios and increasing amount portfolios. They are widely used in finance for investing assets and developing derivative securities. We compare the long-term behavior of a conventional mean-variance risk measure and a modified one of the two types of portfolios, and we discuss the benefits of the modified measure. Subsequently, an optimal long-term investment strategy is derived. We show that the modified risk measure reflects the investor’s risk aversion on the optimal long-term investment strategy; however, the conventional one does not. Several factor models are discussed as concrete examples: the Black–Scholes model, Kim–Omberg model, Heston model, and 3/2 stochastic volatility model.

scholarly journals Portfolio Optimization Constrained by Performance Attribution

2021 ◽  
Vol 14 (5) ◽  
pp. 201
Author(s):  
Yuan Hu ◽  
W. Brent Lindquist ◽  
Svetlozar T. Rachev
Keyword(s):  
Portfolio Optimization ◽  
Asset Allocation ◽  
Value At Risk ◽  
Risk Measures ◽  
Risk Measure ◽  
Selection Effect ◽  
Conditional Value At Risk ◽  
Positive Role ◽  
Performance Attribution ◽  
Dow Jones Industrial Average

This paper investigates performance attribution measures as a basis for constraining portfolio optimization. We employ optimizations that minimize conditional value-at-risk and investigate two performance attributes, asset allocation (AA) and the selection effect (SE), as constraints on asset weights. The test portfolio consists of stocks from the Dow Jones Industrial Average index. Values for the performance attributes are established relative to two benchmarks, equi-weighted and price-weighted portfolios of the same stocks. Performance of the optimized portfolios is judged using comparisons of cumulative price and the risk-measures: maximum drawdown, Sharpe ratio, Sortino–Satchell ratio and Rachev ratio. The results suggest that achieving SE performance thresholds requires larger turnover values than that required for achieving comparable AA thresholds. The results also suggest a positive role in price and risk-measure performance for the imposition of constraints on AA and SE.

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