Replicating portfolio approach to capital calculation

The replicating portfolio (RP) approach to the calculation of capital for life insurance portfolios is an industry standard. The RP is obtained from projecting the terminal loss of discounted asset–liability cash flows on a set of factors generated by a family of financial instruments that can be efficiently simulated. We provide the mathematical foundations and a novel dynamic and path-dependent RP approach for real-world and risk-neutral sampling. We show that our RP approach yields asymptotically consistent capital estimators if the chaotic representation property holds. We illustrate the tractability of the RP approach by three numerical examples.     

Multivariate tests of the zero-beta CAPM

A ‘cross-sectional regression test’ (CSRT) of the CAPM is developed and its connection to the Hotelling T² test of multivariate statistical analysis is explored. Algebraic relations between the CSRT, the likehood ratio test and the Langrange multiplier test are derived and a useful small-sample bound on the distribution function of the CSRT is obtained. An application of the CSRT suggests that the CRSP equally-weighted index is inefficient, but that the inefficiency is not explained by a firm size-effect from February to December.     

Mathematical foundation of the replicating portfolio approach

In the last few years, the first theoretical foundations for replicating portfolios – probably the most prevailing technique for risk capital calculation in life insurance – have been given in a series of papers by Beutner, Pelsser and Schweizer. In these papers, the asymptotic behaviour of replicating portfolios concerning the approximation of the terminal value (TVL) and the fair value distribution of the liabilities (FVL) has been investigated in detail. We complement this line of research by providing results on approximations based on a finite number of replicating instruments. We do so by providing the link between the approximation error of the TVL distribution, the FVL distribution and the error in the resulting risk capital figure, either value at risk or some coherent risk measure. We further allow for a variety of practically relevant formulations of the replication problem, including cash flow matching approaches. In contrast to the existing literature, all our results apply to approaches both under the risk-neutral and the real-world measure. Our strongest bounds are due to the observation that in discrete time, the measure change from the real-world to the risk-neutral measure can be both bounded below and above by a suitable constant in the first period.     

A portfolio balance approach to the Canadian-U.S. exchange rate

An empirical portfolio balance model based on Branson and Henderson [Branson, W. H., & Henderson, D. W. (1985). The specification and influence of assets markets. In: Jones R. W., Kenen, P. B. (Eds.), Handbook of International Economics, Volume 2, Elsevier, Amsterdam] is specified for the Canadian-U.S. exchange rate over the floating exchange rate period. Empirical implementation reveals two cointegrating vectors that closely, although not perfectly, match the home and foreign asset demands of the theoretical model. Furthermore, the exchange rate is important in the error correction process. Finally, although the significance is quantitatively and statistically modest, a simplified version of the empirical model resulting from general-to-specific procedures is able to beat a random walk at some out-of-sample forecast horizons.     

A Markov-switching COGARCH approach to cryptocurrency portfolio selection and optimization

Financial Markets and Portfolio Management - Blockchain is a new technology slowly integrating our economy with cryptocurrencies such as Bitcoin and many more applications. Bitcoin and other...     

A simple nonparametric approach to low-dimension,shortfall-based portfolio selection

This paper develops a simple, low-dimension portfolio selection rule based on minimizing the probability of realizing a return below some pre-determined benchmark or target rate. Unlike most shortfall-based methods, which employ approximations to the shortfall probability, this method operates directly on the complementary Heaviside function representation of the in-sample shortfall probability. Thus, no behavioral assumptions, other than the notion of shortfall minimization, enter the portfolio selection process.     

A geometric approach to portfolio optimization in models with transaction costs

We consider a continuous-time stochastic optimization problem with infinite horizon, linear dynamics, and cone constraints which includes as a particular case portfolio selection problems under transaction costs for models of stock and currency markets. Using an appropriate geometric formalism we show that the Bellman function is the unique viscosity solution of a HJB equation.Mathematics Subject Classification (1991): 60G44JEL Classification: G13, G11This research was done at Munich University of Technology supported by a Mercator Guest Professorship of the German Science Foundation (Deutsche Forschungsgemeinschaft). The authors also express their thanks to Mark Davis, Steve Shreve, and Michael Taksar for useful discussions concerning the principle of dynamic programming.     

Thematic portfolio optimization: challenging the core satellite approach

In recent years, thematic exchange-traded funds (ETF) have increased in economic significance. Investors in thematic ETFs have more than just financial objectives and gain a non-monetary added value from a thematic portion in their portfolios. Therefore, traditional portfolio optimization models which target only financial criteria cannot suit these investors’ needs anymore. Nevertheless, to account for their thematic interests, investors adapt a core satellite strategy in which conventional core portfolios and thematic satellite portfolios are combined. Thus, these portfolios are separately optimized without further considering inter-portfolio correlation effects. Since modern portfolio theory has originally been established to, inter alia, optimize these correlation effects, portfolios can only be efficient by chance. Therefore, this study targets the correlation effects between conventional and thematic portfolios and uses a tri-criterion thematic portfolio optimization model as an overall framework. Throughout a two-part analysis with tradable ETFs and a simulation with 250,000 draws and 1,750,000 portfolio optimizations performed, the status quo is compared to the tri-criterion model. Quantifying the suboptimality, simulation results show a mean portfolio improvement of 6.23% measured as relative yield enhancement. Further, our analysis concludes that the more narrowly a theme is defined and the more particular it is, relative yield enhancements can increase up to 46.88%.

     

From insurance risk to credit portfolio management: a new approach to pricing CDOs

We present a new approach for pricing collateralized debt obligations (CDOs) which takes into account the issue of the market incompleteness. In particular, we develop a suitable extension of the actuarial framework proposed by Bayraktar et al. [Valuation of mortality risk via the instantaneous Sharpe ratio: Applications to life annuities. J. Econ. Dyn. Control, 2009, 33, 676–691], Milevsky et al. [Financial valuation of mortality risk via the instantaneous Sharpe-ratio: Applications to pricing pure endowments. Working Paper, 2007. Available at: http://arxiv.org/abs/0705.1302], Young [Pricing life insurance under stochastic mortality via the instantaneous Sharpe ratio: Theorems and proofs. Technical Report, 2007. Available at: http://arxiv.org/abs/0705.1297] and Young [Pricing life insurance under stochastic mortality via the instantaneous Sharpe ratio. Insurance: Math. Econ., 2008, 42, 691–703], which is based on the so-called instantaneous Sharpe ratio. Such a procedure allows us to incorporate the attitude of investors towards risk in a direct and rational way and, in addition, is also suitable for dealing with the often illiquid CDO market. Numerical experiments are presented which reveal that the market incompleteness can have a strong effect on the pricing of CDOs, and allows us to explain the high bid-ask spreads that are frequently observed in the markets.     

Systemic risk contributions: A credit portfolio approach

We put forward a framework for measuring systemic risk and attributing it to individual banks. Systemic risk is coherently measured as the expected loss to depositors and investors when a systemic event occurs. The risk contributions are calculated so as to ensure a full risk allocation among institutions. Applying our methodology to a panel of 54–86 of the world’s major commercial banks for a 13-year time span with monthly frequency not only allows us to closely match the list of G-SIBs; we can also use individual risk contributions to compute bank-specific surcharges: systemic capital charges as well as countercyclical buffers. We therefore address both dimensions of systemic risk – cross-sectional and time-series – in a single integrated approach. As the analysis of risk drivers confirms, the main focus of macroprudential supervision should be on a solid capital base throughout the financial cycle and de-correlation of banks’ asset values.     

Dynamic hedge fund portfolio construction: A semi-parametric approach

In this article, we evaluate alternative optimization frameworks for constructing portfolios of hedge funds. We compare the standard mean–variance optimization model with models based on CVaR, CDaR and Omega, for both conservative and aggressive hedge fund investment strategies. In order to implement the CVaR, CDaR and Omega optimization models, we propose a semi-parametric methodology, which is based on extreme value theory, copula and Monte Carlo simulation. We compare the semi-parametric approach with the standard, non-parametric approach, used to compute CVaR, CDaR and Omega, and the benchmark parametric approach, based on both static and dynamic mean–variance optimization. We report two main findings. The first is that the CVaR, CDaR and Omega models offer a significant improvement in terms of risk-adjusted portfolio performance over the parametric mean–variance model. The second is that semi-parametric estimation of the CVaR, CDaR and Omega models offers a very substantial improvement over non-parametric estimation. Our results are robust to the choice of target return, risk limit and estimation sample size.     

A synthetic factor approach to the estimation of value-at-risk of a portfolio of interest rate swaps

In this paper we decompose the interest rate swap yield curves of 10 major currencies into their common factors and find that the first two factors, interpreted as parallel shift and rotation, explain between 97.1% and 98.6% of the variation in the interest rate swap rates across all 10 currencies. The main contribution of the paper however is that we then model these two factors as simplified synthetic factors so that they may be used to develop an innovative approach to the computation of Value-at-Risk (VaR) for a portfolio of interest rate swaps.     

Marriage and other risky assets: A portfolio approach

We study the joint impact of gender and marital status on financial investments by testing the hypothesis that marriage represents – in a portfolio framework – a sort of safe asset and that this attribute may change over time. We show that married individuals have a higher propensity to invest in risky assets than single ones, that this marital status gap is stronger for women and that, for women only, it evolves and declines at the end of the sample period. Next we explore a number of possible explanations of the observed gender differences by controlling for background factors that capture the evolution of family and society. We find that both the higher female marital status gap and its time variability vanish for those women who are employed. Our empirical investigation is based on a dataset drawn from the 1993–2006 Bank of Italy Survey of Household Income and Wealth.     

International portfolio diversification: an ICAPM approach with currency risk

This article investigates international stock market integration in four major developed economies, namely the United States, the Economic and Monetary Union of the European Union, Japan and the United Kingdom, and two Asian emerging, countries namely China and India, over the period from June 1994 to June 2009. To model stock market integration we estimate a dynamic version of the international capital asset pricing model (CAPM) in the absence of purchasing power parity. Conditional variance is modelled via a multivariate GARCH specification. To investigate the evolution of integration overtime we estimate the CAPM in sub-periods. In addition, we connect our results to the timing of world financial crises. Our findings show that the stock markets tend to move in parallel after June of 2002, although from 2002 to 2006 there have not been crises events. These results support the increasing globalization and interdependence of both emerging and developed markets in the recent decade, reducing the benefits of portfolio diversification.     

Nontraded asset valuation with portfolio constraints: a binomial approach

We provide a simple binomial framework to value American-stylederivatives subject to trading restrictions. The optimal investmentof liquid wealth is solved simultaneously with the early exercisedecision of the nontraded derivative. No-short-sales constraintson the underlying asset manifest themselves in the form of animplicit dividend yield in the risk-neutralized process forthe underlying asset. One consequence is that American calloptions may be optimally exercised prior to maturity even whenthe underlying asset pays no dividends. Applications to executivestock options (ESO) are presented: it is shown that the valueof an ESO could be substantially lower than that computed usingthe Black-Scholes model. We also analyze nontraded payoffs basedon a price that is imperfectly correlated with the price ofa traded asset.     

A differential evolution copula-based approach for a multi-period cryptocurrency portfolio optimization

Recent years have seen a growing interest among investors in the new technology of blockchain and cryptocurrencies and some early investors in this new type of digital assets have made significant gains. The heuristic algorithm, differential evolution, has been advocated as a powerful tool in portfolio optimization. We propose in this study two new approaches derived from the traditional differential evolution (DE) method: the GARCH-differential evolution (GARCH-DE) and the GARCH-differential evolution t-copula (GARCH-DE-t-copula). We then contrast these two models with DE (benchmark) in single and multi-period optimizations on a portfolio consisting of five cryptoassets under the coherent risk measure CVaR constraint. Our analysis shows that the GARCH-DE-t-copula outperforms the DE and GARCH-DE approaches in both single- and multi-period frameworks. For these notoriously volatile assets, the GARCH-DE-t-copula has shown risk-control ability, hereby confirming the ability of t-copula to capture the dependence structure in the fat tail.     

An approach to learning risk-based auditing

This paper presents a discussion of a risk-based auditing project that can be used in an undergraduate or graduate auditing course. The project gives students an opportunity to apply the concepts learned in their auditing class about risk-based auditing to a real world company. A number of companies are selected from a particular industry. Each student team is assigned a company and performs business risk analysis related to the entity and its environment using a structured questionnaire (template). The students are required to perform analytical procedures (ratio analysis) on the company and compare it to industry data or a competitor. Student evaluations of the project indicate that it helped them apply their audit knowledge, and was relevant to the auditing class.     

The effectiveness of the VaR-based portfolio insurance strategy: An empirical analysis

This paper proposes an approach to constructing the insured portfolios under the VaR-based portfolio insurance strategy (VBPI) and provides a comprehensive analysis of its hedging effectiveness in comparison with the buy-and-hold (B&H) as well as the constant proportion portfolio insurance (CPPI) strategies in the context of the Chinese market. The results show that both of the insurance strategies are able to limit the downward returns while retaining certain upside returns, and their capabilities of reshaping the return distributions increase as the guarantee or the confidence level rises. In general, the VBPI strategy tends to outperform the CPPI strategy in terms of both the degree of downside protection and the return performance.     

Time-consistency in managing a commodity portfolio: A dynamic risk measure approach

We address the problem of managing a storable commodity portfolio, that includes physical assets and positions in spot and forward markets. The vast amount of capital involved in the acquisition of a power plant or storage facility implies that the financing period stretches over a period of several quarters or years. Hence, an intertemporally consistent way of optimizing the portfolio over the planning horizon is required. We demonstrate the temporal inconsistency of static risk objectives based on final wealth and advocate the validity in our setting of a new class of recursive risk measures introduced by Epstein and Zin [Epstein, G., Zin, S., 1989. Substitution, risk aversion, and the temporal behavior of consumption and asset returns: A theoretical framework. Econometrica, 57 (4) 937–969] and Wang [Wang, T., 2000. A class of dynamic risk measures University of British Columbia]. These risk measures provide important insights on the trade-offs between date-specific risks (i.e., losses occurring at a point in time) and time-duration risks represented by the pair (return, risk) over a planning horizon; in a number of situations, they dramatically improve the efficiency of static risk objectives, as exhibited in numerical examples.