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21 pages, 1481 KiB

Open AccessArticle

Determining Safe Withdrawal Rates for Post-Retirement via a Ruin-Theory Approach

by Diba Daraei and Kristina Sendova

Risks 2024, 12(4), 70; https://doi.org/10.3390/risks12040070 - 19 Apr 2024

Cited by 1 | Viewed by 2150

To ensure a comfortable post-retirement life and the ability to cover living expenses, it is of utmost importance for individuals to have a clear understanding of how long their pre-retirement savings will last. In this research, we employ a ruin-theory approach to model [...] Read more.

To ensure a comfortable post-retirement life and the ability to cover living expenses, it is of utmost importance for individuals to have a clear understanding of how long their pre-retirement savings will last. In this research, we employ a ruin-theory approach to model the inflows and the outflows of retirees’ portfolios. We track all transactions within the portfolios of retired clients sourced by a registered investment provider to Canada’s Financial Wellness Lab at Western University. By utilizing an advanced ruin model, we calculate the mean and the median time it takes for savings to be exhausted, the probabilities of exhaustion of funds within the retirees’ expected remaining lifetime while accounting for the observed withdrawal rates, and the deficit at ruin if a retiree has used up all of their savings. We also account for gender as well as for the risk tolerance of retired clients using a K-Means clustering algorithm. This allows us to compare the financial outcomes for female and male retirees and to enhance some findings in the literature. In the final phase of our study, we compare the results obtained by our methodology to the 4% rule which is a widely used approach for post-retirement spending. Our results show that most retirees can withdraw safely more than they currently do (around 2.5%). A withdrawal rate of about 4.5% is proved to be safe, but it might not provide sufficient income for most retirees since it yields approximately CAD 20,000 per year for male retirees in the highest risk tolerance group who withdraw about 4.5% annually. Full article

(This article belongs to the Special Issue Optimal Investment and Risk Management)

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32 pages, 755 KiB

Open AccessArticle

Asymptotic Methods for Transaction Costs

by Eberhard Mayerhofer

Risks 2024, 12(4), 64; https://doi.org/10.3390/risks12040064 - 4 Apr 2024

Viewed by 1227

Abstract

We propose a general approximation method for the determination of optimal trading strategies in markets with proportional transaction costs, with a polynomial approximation of the residual value function. The method is exemplified by several problems, from optimally tracking benchmarks and hedging the log [...] Read more.

We propose a general approximation method for the determination of optimal trading strategies in markets with proportional transaction costs, with a polynomial approximation of the residual value function. The method is exemplified by several problems, from optimally tracking benchmarks and hedging the log contract to maximizing utility from terminal wealth. Strategies are also approximated by practically executable, discrete trades. We identify the necessary trade-off between the trading frequency and trade size to ensure satisfactory agreement with the theoretically optimal, continuous strategies of infinite activity. Full article

(This article belongs to the Special Issue Optimal Investment and Risk Management)

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16 pages, 379 KiB

Open AccessArticle

Intangible Assets and Analysts’ Overreaction and Underreaction to Earnings Information: Empirical Evidence from Saudi Arabia

by Taoufik Elkemali

Risks 2024, 12(4), 63; https://doi.org/10.3390/risks12040063 - 2 Apr 2024

Cited by 2 | Viewed by 1747

Abstract

Several prior studies indicate that financial analysts exhibit systematic underreaction to information; others illustrate systematic overreaction. We assume that cognitive biases influence analysts’ behavior and that these misreactions are not systematic, but they depend on the nature of news. As cognitive biases intensify [...] Read more.

Several prior studies indicate that financial analysts exhibit systematic underreaction to information; others illustrate systematic overreaction. We assume that cognitive biases influence analysts’ behavior and that these misreactions are not systematic, but they depend on the nature of news. As cognitive biases intensify in situations of high ambiguity, we distinguish between bad and good news and investigate the impact of intangible assets—synonymous with high uncertainty and risk—on financial analysts’ reactions. We explore the effect of information conveyed by prior-year earnings announcements on the current-year forecast error. Our findings in the Saudi financial market reveal a tendency for overreaction to positive prior-year earnings change (good performance) and positive prior-year forecast errors (good surprise). Conversely, there is an underreaction to the negative prior-year earnings change (bad performance) and negative prior-year forecast error (bad surprise). Notably, analysts exhibit systematic optimism rather than systematic underreaction or overreaction. The results also highlight that the simultaneous phenomena of overreaction and underreaction is more pronounced in high intangible asset firms compared to low intangible asset firms. Full article

(This article belongs to the Special Issue Optimal Investment and Risk Management)

17 pages, 469 KiB

Open AccessArticle

The Role of Longevity-Indexed Bond in Risk Management of Aggregated Defined Benefit Pension Scheme

by Xiaoyi Zhang, Yanan Li and Junyi Guo

Risks 2024, 12(3), 49; https://doi.org/10.3390/risks12030049 - 6 Mar 2024

Viewed by 1685

Abstract

Defined benefit (DB) pension plans are a primary type of pension schemes with the sponsor assuming most of the risks. Longevity-indexed bonds have been used to hedge or transfer risks in pension plans. Our objective is to study an aggregated DB pension plan’s [...] Read more.

Defined benefit (DB) pension plans are a primary type of pension schemes with the sponsor assuming most of the risks. Longevity-indexed bonds have been used to hedge or transfer risks in pension plans. Our objective is to study an aggregated DB pension plan’s optimal risk management problem focusing on minimizing the solvency risk over a finite time horizon and to investigate the investment strategies in a market, comprising a longevity-indexed bond and a risk-free asset, under stochastic nominal interest rates. Using the dynamic programming technique in the stochastic control problem, we obtain the closed-form optimal investment strategy by solving the corresponding Hamilton–Jacobi–Bellman (HJB) equation. In addition, a comparative analysis implicates that longevity-indexed bonds significantly reduce solvency risk compared to zero-coupon bonds, offering a strategic advantage in pension fund management. Besides the closed-form solution and the comparative study, another novelty of this study is the extension of actuarial liability (AL) and normal cost (NC) definitions, and we introduce the risk neutral valuation of liabilities in DB pension scheme with the consideration of mortality rate. Full article

(This article belongs to the Special Issue Optimal Investment and Risk Management)

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16 pages, 2151 KiB

Open AccessFeature PaperArticle

Market Equilibrium and the Cost of Capital with Heterogeneous Investment Horizons

by Moshe Levy and Haim Levy

Risks 2024, 12(3), 44; https://doi.org/10.3390/risks12030044 - 29 Feb 2024

Cited by 2 | Viewed by 1707

Abstract

Expected returns, variances, betas, and alphas are all non-linear functions of the investment horizon. This seems to be a fatal conceptual problem for the capital asset pricing model (CAPM), which assumes a unique common horizon for all investors. We show that under the [...] Read more.

Expected returns, variances, betas, and alphas are all non-linear functions of the investment horizon. This seems to be a fatal conceptual problem for the capital asset pricing model (CAPM), which assumes a unique common horizon for all investors. We show that under the standard assumptions, the theoretical CAPM equilibrium surprisingly holds with the 1-period parameters, even when investors have heterogeneous and possibly much longer horizons. This is true not only for risk-averse investors, but for any investors with non-decreasing preferences, including prospect theory investors. Thus, the widespread practice of using monthly betas to estimate the cost of capital is theoretically justified. Full article

(This article belongs to the Special Issue Optimal Investment and Risk Management)

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17 pages, 2295 KiB

Open AccessArticle

Centrality-Based Equal Risk Contribution Portfolio

by Shreya Patki, Roy H. Kwon and Yuri Lawryshyn

Risks 2024, 12(1), 8; https://doi.org/10.3390/risks12010008 - 2 Jan 2024

Viewed by 2278

Abstract

This article combines the traditional definition of portfolio risk with minimum-spanning-tree-based “interconnectedness risk” to improve equal risk contribution portfolio performance. We use betweenness centrality to measure an asset’s importance in a market graph (network). After filtering the complete correlation network to a minimum [...] Read more.

This article combines the traditional definition of portfolio risk with minimum-spanning-tree-based “interconnectedness risk” to improve equal risk contribution portfolio performance. We use betweenness centrality to measure an asset’s importance in a market graph (network). After filtering the complete correlation network to a minimum spanning tree, we calculate the centrality score and convert it to a centrality heuristic. We develop an adjusted variance–covariance matrix using the centrality heuristic to bias the model to assign peripheral assets in the minimum spanning tree higher weights. We test this methodology using the constituents of the S&P 100 index. The results show that the centrality equal risk portfolio can improve upon the base equal risk portfolio returns, with a similar level of risk. We observe that during bear markets, the centrality-based portfolio can surpass the base equal risk portfolio risk. Full article

(This article belongs to the Special Issue Optimal Investment and Risk Management)

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21 pages, 557 KiB

Open AccessFeature PaperArticle

Bidual Representation of Expectiles

by Alejandro Balbás, Beatriz Balbás, Raquel Balbás and Jean-Philippe Charron

Risks 2023, 11(12), 220; https://doi.org/10.3390/risks11120220 - 15 Dec 2023

Cited by 2 | Viewed by 1675

Abstract

Downside risk measures play a very interesting role in risk management problems. In particular, the value at risk (VaR) and the conditional value at risk (CVaR) have become very important instruments to address problems such as risk optimization, capital requirements, portfolio selection, pricing [...] Read more.

Downside risk measures play a very interesting role in risk management problems. In particular, the value at risk (VaR) and the conditional value at risk (CVaR) have become very important instruments to address problems such as risk optimization, capital requirements, portfolio selection, pricing and hedging issues, risk transference, risk sharing, etc. In contrast, expectile risk measures are not as widely used, even though they are both coherent and elicitable. This paper addresses the bidual representation of expectiles in order to prove further important properties of these risk measures. Indeed, the bidual representation of expectiles enables us to estimate and optimize them by linear programming methods, deal with optimization problems involving expectile-linked constraints, relate expectiles with VaR and CVaR by means of both equalities and inequalities, give VaR and CVaR hyperbolic upper bounds beyond the level of confidence, and analyze whether co-monotonic additivity holds for expectiles. Illustrative applications are presented. Full article

(This article belongs to the Special Issue Optimal Investment and Risk Management)

24 pages, 659 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Option Pricing and Portfolio Optimization under a Multi-Asset Jump-Diffusion Model with Systemic Risk

by Roman N. Makarov

Risks 2023, 11(12), 217; https://doi.org/10.3390/risks11120217 - 13 Dec 2023

Viewed by 2287

Abstract

We explore a multi-asset jump-diffusion pricing model, combining a systemic risk asset with several conditionally independent ordinary assets. Our approach allows for analyzing and modeling a portfolio that integrates high-activity security, such as an exchange trading fund (ETF) tracking a major market index [...] Read more.

We explore a multi-asset jump-diffusion pricing model, combining a systemic risk asset with several conditionally independent ordinary assets. Our approach allows for analyzing and modeling a portfolio that integrates high-activity security, such as an exchange trading fund (ETF) tracking a major market index (e.g., S&P500), along with several low-activity securities infrequently traded on financial markets. The model retains tractability even as the number of securities increases. The proposed framework allows for constructing models with common and asset-specific jumps with normally or exponentially distributed sizes. One of the main features of the model is the possibility of estimating parameters for each asset price process individually. We present the conditional maximum likelihood estimation (MLE) method for fitting asset price processes to empirical data. For the case with common jumps only, we derive a closed-form solution to the conditional MLE method for ordinary assets that works even if the data are incomplete and asynchronous. Alternatively, to find risk-neutral parameters, the least-square method calibrates the model to option values. The number of parameters grows linearly in the number of assets compared to the quadratic growth through the correlation matrix, which is typical for many other multi-asset models. We delve into the properties of the proposed model, its parameter estimation using the MLE method and least-squares technique, the evaluation of VaR and CVaR metrics, the identification of optimal portfolios, and the pricing of European-style basket options. We propose a Laplace-transform-based approach to computing Value at Risk (VaR) and conditional VaR (also known as the expected shortfall) of portfolio returns. Additionally, European-style basket options written on the extreme and average stock prices or returns can be evaluated semi-analytically. For numerical demonstration, we examine a combination of the SPDR S&P 500 ETF (as a systemic risk asset) with eight ordinary assets representing diverse industries. Using historical assets and options prices, we estimate the real-world and risk-neutral parameters of the model with common jumps, construct several optimal portfolios, and evaluate various basket options with the eight assets. The results affirm the robustness and efficiency of the estimation and evaluation methodologies. Computational results are compared with Monte Carlo estimates. Full article

(This article belongs to the Special Issue Optimal Investment and Risk Management)

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