Static Portfolio Research Articles

Determinants of stock market participation

AbstractThe low degree of stock market participation (SMP) is one of the big puzzles in finance. Numerous determinants have been proposed. We put these determinants into a structure that is derived from a standard static portfolio model. Then we discuss arguments put forward regarding specific SMP determinants and the empirical evidence that has been provided. The focus of our survey is on the identification of a causal impact of determinants on SMP via shocks. We summarize the evidence by suggesting established and likely SMP determinants and providing an outlook for future research and policy.

A Semi-Static Replication Method for Bermudan Swaptions under an Affine Multi-Factor Model

We present a semi-static replication algorithm for Bermudan swaptions under an affine, multi-factor term structure model. In contrast to dynamic replication, which needs to be continuously updated as the market moves, a semi-static replication needs to be rebalanced on just a finite number of instances. We show that the exotic derivative can be decomposed into a portfolio of vanilla discount bond options, which mirrors its value as the market moves and can be priced in closed form. This paves the way toward the efficient numerical simulation of xVA, market, and credit risk metrics for which forward valuation is the key ingredient. The static portfolio composition is obtained by regressing the target option’s value using an interpretable, artificial neural network. Leveraging the universal approximation power of neural networks, we prove that the replication error can be arbitrarily small for a sufficiently large portfolio. A direct, a lower bound, and an upper bound estimator for the Bermudan swaption price are inferred from the replication algorithm. Additionally, closed-form error margins to the price statistics are determined. We practically study the accuracy and convergence of the method through several numerical experiments. The results indicate that the semi-static replication approaches the LSM benchmark with basis point accuracy and provides tight, efficient error bounds. For in-model simulations, the semi-static replication outperforms a traditional dynamic hedge.

Consolidated learning: a domain-specific model-free optimization strategy with validation on metaMIMIC benchmarks

For many machine learning models, a choice of hyperparameters is a crucial step towards achieving high performance. Prevalent meta-learning approaches focus on obtaining good hyperparameter configurations with a limited computational budget for a completely new task based on the results obtained from the prior tasks. This paper proposes a new formulation of the tuning problem, called consolidated learning, more suited to practical challenges faced by model developers, in which a large number of predictive models are created on similar datasets. In such settings, we are interested in the total optimization time rather than tuning for a single task. We show that a carefully selected static portfolio of hyperparameter configurations yields good results for anytime optimization, while maintaining the ease of use and implementation. Moreover, we point out how to construct such a portfolio for specific domains. The improvement in the optimization is possible due to the more efficient transfer of hyperparameter configurations between similar tasks. We demonstrate the effectiveness of this approach through an empirical study for the XGBoost algorithm and the newly created metaMIMIC benchmarks of predictive tasks extracted from the MIMIC-IV medical database. In the paper, we show that the potential of consolidated learning is considerably greater due to its compatibility with many machine learning application scenarios.

Lifestyle, Longevity, and Legacy Risks with Annuities in Retirement Portfolio Decumulation

Investors planning for retirement balance three Ls: (1) lifestyle risk, hoping to maintain a consumption stream that provides a chosen standard of living; (2) longevity risk, hoping to remain solvent throughout their lifetime; and (3) legacy risk, hoping to leave a bequest to their heirs. We solve this multiple objective problem for a wide range of consumption and annuitization scenarios. For each scenario, we apply dynamic programming to optimally evolve the investments in the non-annuitized portion of the portfolio so as to minimize longevity risk. Our dynamic programming approach has the advantages of (1) generating results that are far superior to what standard Monte Carlo methods, static portfolios, and target date fund glide paths can provide and (2) not requiring utility functions, which are hard to specify for individuals. We show that investors who want to minimize their longevity and legacy risk and who are unable to annuitize their full consumption stream are best off avoiding even partial annuitization of their portfolio. For investors who are able to annuitize their full consumption stream, we quantify their longevity versus legacy risk trade-offs, enabling them to select the best annuity for their needs.

Improved Dynamic Portfolio Selection Model with DCC-GARCH: Evidence from the U.S. Stock Market

As an important financial instrument in real financial market, the selection and management of portfolio has always been a significant and hot issue in the field of economics. This study collects data of stocks daily returns in the real US stock market to test whether DCC-GARCH model can improve the performance of portfolio return compared with the original static model when the assumption of fixed covariance matrix is relaxed. This study also compares the performance of improved portfolio with that of S&P500. The result shows that portfolio returns obtained by the dynamic model outperform the original static portfolio and market performance by a large margin. This shows that, without taking into account transaction costs, an effective way to enhance the traditional mean-variance model is to fit and predict the dynamic covariance using DCC-GARCH model.

Surplus Optimization in Defined Benefit Pensions Using the Regime‐Switching Model: Occupational Pension Plans in South Korea*

AbstractWe assume a hypothetical defined benefit (DB) pension plan that reflects the characteristics of the occupational pension in South Korea and propose a surplus optimization strategy using a regime‐switching model. Using conditional surplus at risk, we construct an optimized portfolio that limits extreme tail risks. Furthermore, we identify the surplus risk and return conditional on global macroeconomic status using a hidden Markov model. The main results are that (i) the DB pension portfolio should move from principal‐protected products to diverse capital market products, and (ii) the DB pension portfolio using the regime‐switching model outperforms an unconditional static portfolio.

Stock market prediction and portfolio composition using a hybrid approach combined with self-adaptive evolutionary algorithm

This work presents a new approach to maximize financial market investment returns. It incorporates two Evolutionary Algorithms (EAs) combined with fundamental and technical investment strategies. The first EA (simple) maintains its evolutionary parameters static during evolution. The second (self-adaptive) introduces the variation operators’ parameters’ values in the representation for them to evolve. The EA is responsible for optimizing the weight that financial ratios from the F-Score have on composing static/dynamic portfolios. Furthermore, it is also responsible for defining the importance that selected technical indicators have on revealing the best timing for market positions placement. Results showed that both cases surpassed the S&P500 returns, performing their best results using a self-adaptive EA combined with a static portfolio and a sliding window of 2 years of train/test. The technical case study showed better results in “bear markets” since it predicted some market declines. Its best subtest achieved returns on average 2.2x and in its best 3.5x higher than the benchmark. Its Sharpe Ratio achieved, on average, 4.9x and in its best 9x higher results than the benchmark. The fundamental case study displayed best in the “bull market”, achieving high market prices. Its best subtest achieved returns on average 2.4x and in its best 3.2x higher than the benchmark. Its Sharpe Ratio achieved, on average, 4.4x and in its best 6.5x higher results than the benchmark.

Recovering subjective probability distributions

AbstractThis study proposes a direct estimation method for recovering subjective probability distributions from option prices. We find that the subjective cumulative distribution function and subjective statistics are represented as static portfolios composed of plain vanilla options. The portfolio weights of the options are determined by the levels of the reciprocal of the pricing kernel and their differentiation. Using options data, we investigate the historical behavior of subjective probability distributions of returns on the S&P 500 index. We also analyze subjective equity risk premiums and subjective variance risk premiums, which can be regarded as ex ante risk premiums.

Timing Excess Returns: A Cross-Universe Approach to Alpha

We present a simple model that uses time series momentum in order to construct strategies that systematically outperform their benchmark. The simplicity of our model is elegant: We only require a benchmark time series and several related investable indizes, not requiring regression or other models to estimate our parameters. We find that our one size fits all approach delivers significant outperformance in both equity and bond markets while meeting the ex-ante risk requirements, nearly doubling yearly returns vs. the MSCI World and Bloomberg Barclays Euro Aggregate Corporate Bond benchmarks in a long-only backtest. We then combine both approaches into an absolute return strategy by benchmarking vs. the Eonia Total Return Index and find significant outperformance at a sharpe ratio of 1.8. Furthermore, we demonstrate that our model delivers a benefit versus a static portfolio with fixed mean weights, showing that timing of excess return momentum has a sizeable benefit vs. static allocations. This also applies to the passively investable equity factors, where we outperform a static factor exposure portfolio with statistical significance. Also, we show that our model delivers an alpha after deducting transaction costs.

Constrained Dynamic Mean-Variance Portfolio Selection in Continuous-Time

This paper revisits the dynamic MV portfolio selection problem with cone constraints in continuous-time. We first reformulate our constrained MV portfolio selection model into a special constrained LQ optimal control model and develop the optimal portfolio policy of our model. In addition, we provide an alternative method to resolve this dynamic MV portfolio selection problem with cone constraints. More specifically, instead of solving the correspondent HJB equation directly, we develop the optimal solution for this problem by using the special properties of value function induced from its model structure, such as the monotonicity and convexity of value function. Finally, we provide an example to illustrate how to use our solution in real application. The illustrative example demonstrates that our dynamic MV portfolio policy dominates the static MV portfolio policy.

Dynamic optimization for multi-goals wealth management

We develop a dynamic programming methodology that seeks to maximize investor outcomes over multiple, potentially competing goals (such as upgrading a home, paying college tuition, or maintaining an income stream in retirement), even when financial resources are limited. Unlike Monte Carlo approaches currently in wide use in the wealth management industry, our approach uses investor preferences to dynamically make the optimal determination for fulfilling or not fulfilling each goal and for selecting the investor’s investment portfolio. This can be computed quickly, even for numerous investor goals spread over different or concurrent time periods, where each goal may be all-or-nothing or may allow for partial fulfillment. The probabilities of attaining each (full or partial) goal under the optimal scenario are also computed, so the investor can ensure the algorithm accurately reflects their preference for the relative importance of each of their goals. This approach vastly outperforms static portfolio strategies and target-date funds, widely used in the wealth management industry.

Time-Varying Mean-Variance Portfolio Selection under Transaction Costs and Cardinality Constraint Problem via Beetle Antennae Search Algorithm (BAS)

The Markowitz mean-variance portfolio selection is widely acclaimed as a very important investment strategy. A popular option to solve the static mean-variance portfolio selection (MVPS) problem is based on the use of quadratic programming (QP) methods. On the other hand, the static portfolio selection under transaction costs (PSTC) problem is usually approached with nonlinear programming (NLP) methods. In this article, we define and study the time-varying mean-variance portfolio selection under transaction costs and cardinality constraint (TV-MVPSTC-CC) problem as a time-varying nonlinear programming (TVNLP) problem. The TV-MVPSTC-CC also comprises the properties of a moving average. These properties make the TV-MVPSTC-CC an even greater analysis tool suitable to evaluate investments and identify trading opportunities across a continuous-time period. Using the Beetle Antennae Search (BAS) algorithm, we also provide an online solution to the static NLP problem. To the best of our knowledge, this is an innovative approach that incorporates modern meta-heuristic optimization techniques to provide an online, thus more realistic, solution to the TV-MVPSTC-CC problem. In this way, we present an online solution to a time-varying financial problem while eliminating the restrictions of static methods. Our approach is also verified by numerical experiments and computer simulations as an excellent alternative to traditional approaches.

Does Carbon Risk Matter? Evidence of Carbon Premium in EU Energy-Intensive Companies

In this paper we have assessed the impact of the European Union’s Emissions Trading Scheme (EU ETS) on the level of the carbon premium. The aim of the study is to determine whether there is a stable carbon premium in energy-intensive sectors. Unlike other studies, our research sample included not only companies in the energy sector, but also entities classified as energy-intensive. In the research, we used our own criterion for allocating companies to a clean and dirty portfolio, which made it possible to make the estimation of the carbon premium more resistant to changes in the rules for allocation of emission allowances. We detected a positive, statistically significant carbon premium in the years 2003–2012 and a negative one in the years 2013–2015, but we did not detect a statistically significant carbon premium in the period 2016–2019. This means that there are no grounds for concluding that there is a stable, positive carbon premium for energy-intensive companies subject to the EU ETS over time. We have also noticed that a significant problem in studying the impact of the EU ETS on the carbon premium is the use of static portfolios of clean and dirty companies

A functional analysis approach to the static replication of European options

The replication of any European contingent claim by a static portfolio of calls and puts with strikes forming a continuum, formally proven by Carr and Madan [Towards a theory of volatility trading. In Volatility: New Estimation Techniques for Pricing Derivatives, edited by R.A. Jarrow, Vol. 29, pp. 417–427, 1998 (Risk books)], is part of the more general theory of integral equations. We use spectral decomposition techniques to show that exact payoff replication may be achieved with a discrete portfolio of special options. We discuss applications for fast pricing of vanilla options that may be suitable for large option books or high frequency option trading, and for model pricing when the characteristic function of the underlying asset price is known.

Static Replication of European Standard Dispersion Options

The replication of any European contingent claim by a static portfolio of calls and puts with strikes forming a continuum, formally proven by Carr and Madan (1998), extends to options written on the Euclidean norm of a vector of n asset performances. With the help of integral equation techniques we derive replicating portfolios for calls, puts and indeed any claim contingent on standard dispersion using vanilla basket calls whose basket weights span an n-dimensional continuum. Consequently multi-asset standard dispersion options admit a model-free price enforced by arbitrage, just as single-asset European claims do.

Arbitrage Bounds on Currency Basket Options

This article exploits arbitrage valuation bounds on currency basket options. Instead of using a sophisticated model to price these options, we consider a set of pricing models that are consistent with the prices of available hedging assets. In the absence of arbitrage, we identify valuation bounds on currency basket options without model specifications. Our results extend the work in the literature by seeking tight arbitrage valuation bounds on these options. Specifically, the valuation bounds are enforced by static portfolios that consist of both cross-currency options and individual options denominated in the numeraire currency.

Establishing the risk denominator in a Sharpe ratio framework for share selection from a momentum investment strategy approach

Background: Based on the static mean-variance portfolio optimisation theory, investors will choose the portfolio with the highest Sharpe ratio to achieve a higher expected utility. However, the traditional Sharpe ratio only accounts for the first two moments of return distributions, which can lead to false portfolio performance diagnostics with the presence of asymmetric, highly skewed returns. Aim: With many criticising the standard deviation's applicability and with no consensus on the ascendency of which other risk denominator to consult, this study contributes to the literature by validating the importance of consulting value-at-risk as the more commendable risk denominators for the Johannesburg Stock Exchange. Method: These results were derived from a novel index approach that produces a comprehensive risk-adjusted performance evaluation score. Results: Of the 24 Sharpe ratio variations under evaluation, this study identified the value-at-risk Sharpe ratio as the better variation, which led to more profi table share selections for long-only portfolios from a one-year and five-year momentum investment strategy perspective. However, the attributes of adjusting for skewness and kurtosis exhibited more promise from a three-year momentum investment strategy perspective. Conclusion: The results highlighted the ability to outperform the market, which further emphasised the importance of active portfolio management. However, the results also conrfimed that active and more passive equity portfolio managers will have to consult different Sharpe ratio variations to enhance the ability to outperform the market and a buy-and-hold strategy.

Decomposing Factor Momentum

Factor momentum returns do not stem from momentum in factor returns. To study the source of returns, this paper decomposes the factor momentum portfolio into a factor timing portfolio and a static portfolio, where the former dynamically collects the return due to serial correlations of factor returns and the latter passively collects factor premiums. Evidence from 210 stock return factors reveals that the static portfolio robustly accounts for a dominant fraction of the factor momentum return and outperforms in risk-adjusted returns, whereas factor return predictability is empirically too weak to produce timing benefits. The static portfolio survives the post-publication decline of factor performance but the factor momentum portfolio does not.

Time-varying minimum-cost portfolio insurance under transaction costs problem via Beetle Antennae Search Algorithm (BAS)

Abstract Portfolio insurance is a hedging strategy which is used to limit portfolio losses without having to sell off stock when stocks decline in value. Consequently, the minimization of the costs related to portfolio insurance is a very important investment strategy. On the one hand, a popular option to solve the static minimum-cost portfolio insurance problem is based on the use of linear programming (LP) methods. On the other hand, the static portfolio selection under transaction costs (PSTC) problem is usually approached by nonlinear programming (NLP) methods. In this article, we define and study the time-varying minimum-cost portfolio insurance under transaction costs (TV-MCPITC) problem in the form of a time-varying nonlinear programming (TV-NLP) problem. Using the Beetle Antennae Search (BAS) algorithm, we also provide an online solution to the static NLP problem. The online solution to a time-varying financial problem is a great technical analysis tool and along with fundamental analysis will enable the investors to make better decisions. To the best of our knowledge, an approach that incorporates modern meta-heuristic optimization techniques to provide a more realistic online solution to the TV-MCPITC problem is original. In this way, by presenting an online solution to a time-varying financial problem we highlight the limitations of static methods. Our approach is also verified by numerical experiments and computer simulations as an excellent alternative to conventional MATLAB methods.

Decomposing Factor Momentum

Factor momentum returns do not stem from momentum in factor returns. To study the source of returns, this paper decomposes the stock factor momentum portfolio into a factor timing portfolio and a static portfolio, where the former dynamically collects the return due to serial correlations of factor returns and the latter is designed to collect factor premiums. Sequential sorts of 210 factors show that the static portfolio robustly accounts for a dominant fraction of the total factor momentum return and outperforms in risk-adjusted returns, whereas factor return predictability is empirically too weak to produce significant timing benefits. The static portfolio survives the post-publication decay of factor returns but the factor momentum portfolio does not.