Quadratic minimization with portfolio and terminal wealth constraints

We address a problem of stochastic optimal control drawn from the area of mathematical finance. The goal is to minimize the expected value of a general quadratic loss function of the wealth at close of trade when there is a specified convex constraint on the portfolio over the trading interval, together with a specified almost-sure lower-bound on the wealth at close of trade. We use a variational approach of Rockafellar which leads naturally to an appropriate vector space of dual variables, a dual functional on the space of dual variables such that the dual problem of maximizing the dual functional is guaranteed to have a solution (i.e. a Lagrange multiplier) when a simple and natural Slater condition holds for the terminal wealth constraint, and obtain necessary and sufficient conditions for optimality of a candidate wealth process. The dual variables are pairs, each comprising an Itô process paired with a member of the adjoint of the space of essentially bounded random variables measurable with respect to the event \(\sigma \)-algebra at close of trade. The necessary and sufficient conditions are used to construct an optimal portfolio in terms of the Lagrange multiplier. The dual problem simplifies to maximization of a concave function over the real line when the portfolio is unconstrained but the terminal wealth constraint is maintained.     

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.     

Dynamically consistent investment under model uncertainty: the robust forward criteria

We combine forward investment performance processes and ambiguity-averse portfolio selection. We introduce robust forward criteria which address ambiguity in the specification of the model, the risk preferences and the investment horizon. They encode the evolution of dynamically consistent ambiguity-averse preferences.We focus on establishing dual characterisations of the robust forward criteria, which is advantageous as the dual problem amounts to the search for an infimum whereas the primal problem features a saddle point. Our approach to duality builds on ideas developed in Schied (Finance Stoch. 11:107–129, 2007) and ?itkovi? (Ann. Appl. Probab. 19:2176–2210, 2009). We also study in detail the so-called time-monotone criteria. We solve explicitly the example of an investor who starts with logarithmic utility and applies a quadratic penalty function. Such an investor builds a dynamic estimate of the market price of risk \(\hat{\lambda}\) and updates her stochastic utility in accordance with the so-perceived elapsed market opportunities. We show that this leads to a time-consistent optimal investment policy given by a fractional Kelly strategy associated with \(\hat{\lambda}\) and with the leverage being proportional to the investor’s confidence in her estimate.     

Prognose des Abwicklungsergebnisses mittels Chain-Ladder-Verfahren für abhängige Run-Off-Portfolios

In the present paper we analyse how the estimators from Merz u. Wüthrich (2007) could be generalised to the case of N correlated run-off triangles. The simultaneous view on N correlated subportfolios is motivated by the fact, that in practice a run-off portfolio often has to be divided in subportfolios, so that the homogeneity assumption of the claims reserving method on each subportfolio is satisfied. We derive an explicit formula for the process-variance, the estimation-error and the prediction error made by the forecast for the claims development result with the Chain-Ladder method. We illustrate the results by an example.     

Tukey’s transformational ladder for portfolio management

Over the past half-century, the empirical finance community has produced vast literature on the advantages of the equally weighted Standard and Poor (S&P 500) portfolio as well as the often overlooked disadvantages of the market capitalization weighted S&P 500’s portfolio (see Bloomfield et al. in J Financ Econ 5:201–218, 1977; DeMiguel et al. in Rev Financ Stud 22(5):1915–1953, 2009; Jacobs et al. in J Financ Mark 19:62–85, 2014; Treynor in Financ Anal J 61(5):65–69, 2005). However, portfolio allocation based on Tukey’s transformational ladder has, rather surprisingly, remained absent from the literature. In this work, we consider the S&P 500 portfolio over the 1958–2015 time horizon weighted by Tukey’s transformational ladder (Tukey in Exploratory data analysis, Addison-Wesley, Boston, 1977): \(1/x^2,\,\, 1/x,\,\, 1/\sqrt{x},\,\, \text {log}(x),\,\, \sqrt{x},\,\, x,\,\, \text {and} \,\, x^2\), where x is defined as the market capitalization weighted S&P 500 portfolio. Accounting for dividends and transaction fees, we find that the 1/\(x^2\) weighting strategy produces cumulative returns that significantly dominate all other portfolio returns, achieving a compound annual growth rate of 18% over the 1958–2015 horizon. Our story is furthered by a startling phenomenon: both the cumulative and annual returns of the \(1/x^2\) weighting strategy are superior to those of the 1 / x weighting strategy, which are in turn superior to those of the \(1/\sqrt{x}\) weighted portfolio, and so forth, ending with the \(x^2\) transformation, whose cumulative returns are the lowest of the seven transformations of Tukey’s transformational ladder. The order of cumulative returns precisely follows that of Tukey’s transformational ladder. To the best of our knowledge, we are the first to discover this phenomenon.     

A Direct Test of the Free Cash Flow Hypothesis: Evidence from Real Estate Transactions

This paper tests (Jensen The American Economic Review, 76, 323–329 1986) free cash flow hypothesis using data on real estate transactions. We find that firms with either higher free cash flow or higher cash reserve pay more fore real estate, which is consistent with the free cash flow hypothesis. We also find that the agency costs of free cash flow associated with real estate transactions are more severe when firms have lower Tobin’s Q. Furthermore, we find that among the commonly used corporate governance measures, only equity compensation is effective in mitigating the agency problem of free cash flow.     

Small-time ruin for a financial process modulated by a Harris recurrent Markov chain

We consider a nonstandard ruin problem where: (i) the increments of the process are heavy-tailed and Markov-dependent, modulated by a general Harris recurrent Markov chain; (ii) ruin occurs when a positive boundary is attained within a sufficiently small time. Our main result provides sharp asymptotics for the small-time probability of ruin, viz., P(sup? _{n≤δ u} S _n ≥u), where {S _n } denotes the discrete partial sums of the process and δ∈(0,1/μ), where μ is the mean drift. We apply our results to obtain risk estimates which quantify, e.g., repetitive operational risk losses or the extremal behavior for a GARCH(1,1) process.     

Portfolio optimisation under non-linear drawdown constraints in a semimartingale financial model

A drawdown constraint forces the current wealth to remain above a given function of its maximum to date. We consider the portfolio optimisation problem of maximising the long-term growth rate of the expected utility of wealth subject to a drawdown constraint, as in the original setup of Grossman and Zhou (Math. Finance 3:241–276, 1993). We work in an abstract semimartingale financial market model with a general class of utility functions and drawdown constraints. We solve the problem by showing that it is in fact equivalent to an unconstrained problem with a suitably modified utility function. Both the value function and the optimal investment policy for the drawdown problem are given explicitly in terms of their counterparts in the unconstrained problem.     

Second order multiscale stochastic volatility asymptotics: stochastic terminal layer analysis and calibration

Multiscale stochastic volatility models have been developed as an efficient way to capture the principal effects on derivative pricing and portfolio optimization of randomly varying volatility. The recent book by Fouque et al. (Multiscale Stochastic Volatility for Equity, Interest-Rate and Credit Derivatives, 2011) analyzes models in which the volatility of the underlying is driven by two diffusions – one fast mean-reverting and one slowly varying – and provides a first order approximation for European option prices and for the implied volatility surface, which is calibrated to market data. Here, we present the full second order asymptotics, which are considerably more complicated due to a terminal layer near the option expiration time. We find that to second order, the implied volatility approximation depends quadratically on log-moneyness, capturing the convexity of the implied volatility curve seen in data. We introduce a new probabilistic approach to the terminal layer analysis needed for the derivation of the second order singular perturbation term, and calibrate to S&P 500 options data.     

<Emphasis Type="Italic">Shariah</Emphasis>-compliant equities: Empirical evaluation of performance in the European market during credit crunch

Islamic finance is based on the Islamic Jurisprudence as prescribed by the Shariah, and has witnessed significant growth and development in the recent decades. During the period of economic slowdown and following the financial crisis during FY 2007–2009, it was claimed that Islamic financial system seemed to be better in coping with economic slowdowns than conventional financial systems. The article analyses whether the same holds true for Shariah-compliant equities in the market, that is, whether Shariah-compliant equities perform better in the market as compared to the general market. Three portfolios are constructed based on the constituents of S&P Europe 350 to represent the overall market, the market without the financial firms and the market of Shariah-compliant equities. It is found that the portfolio of Shariah-compliant equities outperforms the other two portfolios in all aspects of analysis. However, it slightly underperforms the market portfolio when there is an upward growth trend in the economy. The findings of this article are very relevant for policymakers, investors and fund managers to determine policy matters, deciding on investment and marketing strategy for Islamic capital market products.     

Enhancement of value investing strategies based on financial statement variables: the German evidence

This paper examines the added-value of combining traditional valuation ratios with each other as well as with some financial statement variables in the German stock markets during the 2000–2015 period. The results show that combination pays off and, moreover, that the benefits of combination are greater in Germany than in most other developed stock markets. Particularly, we find strong evidence of the added-value of using Piotroski’s F-score as a supplementary selection criterion for value stocks as well as for low-accrual stocks. Our results show further that the F-score also boosts the efficacy of other valuation ratios besides the book-to-price ratio. In addition, the inclusion of F-score besides a relative value measure tends to increase the average market equity of portfolio firms. The decomposition of the full-sample-period performance into separate bull- and bear-period performance shows clearly that the better performance of F-score-boosted portfolios is mostly attributable to their outperformance during bearish periods, even though on average, they also generate higher bull-period returns than the comparable value portfolios formed without F-score. The use of F-score as a supplementary criterion also increases the proportion of stocks that earn above-market-average returns during the subsequent holding period. For the first time in the financial literature, we also document a strong relationship between high F-score stocks and momentum stocks.     

Strong Increases in Downside Risk Aversion

A ranking of risk preferences is of economic interest insofar as it leads to unambiguous comparative statics predictions, and for this to be the case, the ranking must be a strict partial ordering. The ranking by greater risk aversion meets this demand at the second order, and yields a variety of well-known predictions concerning the effect of greater risk aversion on demands for insurance and risky assets, among many other applications. There has been less success at the third order, where ranking preferences by aversion to downside risk has not produced a strict partial ordering. The problem is that account has not been taken of the fact that an increase in downside risk aversion must induce changes in risk aversion as well. We propose a definition of stronger downside risk aversion that does yield a strict partial ordering by requiring a nested increase in both second- and third-order risk aversion, so that v is more strongly downside risk averse than u if v is more risk averse and more downside risk averse than u. We demonstrate that v being more strongly downside risk averse than u is characterized by v never liking any change in the probability distribution for y that induces a third-order stochastic dominance deterioration in the distribution for u(y). We apply the definition to obtain intuitive comparative statics predictions in the precautionary saving problem, and relate the definition to alternatives proposed in the literature.     

The efficiency of IPO issuing mechanisms and market conditions: evidence in China

This study conducts a comparison analysis on the efficiency of bookbuilding and secondary market proportional offering (hereafter, SMP offering) in the China stock market. SMP offering as described in this paper is not a follow-on offering, but an initial offering applicable to investors in the secondary market. Specifically, as a unique type of fixed price offering, SMP offering only allows the existing investors who are holding shares (of any listed firms) in the secondary market to subscribe to IPO shares. The amount of IPO shares available to be subscribed by the existing investors is proportional to market value of shares held by them in the secondary market. We find some interesting evidence showing that, compared with bookbuilding, SMP offering is more efficient for pricing IPOs, particularly, in a volatile market. SMP offering leads to lower underpricing and lower cross-sectional variation of short-run returns of IPOs. Also, SMP offering is better able to counteract adverse market conditions in the form of low market return and/or high market volatility. Our results are robust to various alternative tests, e.g., the Heckman (Econometrica 47:153–161, 1979) two-stage procedure and an out-of-sample test, after controlling for the problem of endogeneity and for the influence of the exchange of listing, respectively.     

Diversification benefits of risk portfolio models: a case of Taiwan’s stock market

How to construct effective investment strategies is a core issue for modern finance. In this paper, we investigate the benefits of various models by rebalancing portfolios using the daily stock return data in Taiwan. We further consider investment constraints in portfolios to ensure the feasibility of their applications. Using five performance criteria, we find the risk models, particularly the CVaR, yield higher ex ante and ex post performance than a naïve buy-and-hold portfolio. The two-stage regressions show that high return benefits are associated with a bear market while high reduction in risk is positively related to high volatility. Though VaR is regarded as a standard model applied in the real world, our findings suggest that CVaR can serve as a good alternative.     

Impact of website characteristics on relationship quality: a comparison of banks financial cooperatives

This study seeks to investigate differences exhibited by bank customers and members of financial cooperatives respecting website characteristics (website design, convenience, information quality, ease of use and security/confidentiality) and their impact on online relationship quality (composed of trust, commitment and satisfaction). An online survey was conducted with 476 banking sector customers (banks and financial cooperatives), followed by a confirmatory factors analysis and multigroup analysis using EQS 6.2 software. Results evidence a significant difference in terms of website design and security/confidentiality. The impact of these variables on relationship quality proves significantly higher in the case of banks. This study submits that web strategies used by banks and financial cooperatives to develop online relationship quality may vary based on the type of organization.     

Model Predictive Control for Optimal Pairs Trading Portfolio with Gross Exposure and Transaction Cost Constraints

Model predictive control (MPC) is a flexible yet tractable technique in control engineering that recently has gained much attention in the area of finance, particularly for its application to portfolio optimization. In this paper, we extend the MPC with linear feedback setting in Yamada and Primbs (in: Proceedings of the IEEE conference on decision and control, pp 5705–5710, 2012) by incorporating the following two important and practical issues: The first issue is gross exposure (GE), which is the total value of long and short positions invested in risky assets (or stocks) as a proportion of the wealth possessed by a hedge fund. This quantity measures the leverage of a hedge fund, and the fund manager may limit the amount of leverage by imposing an upper bound, i.e., a GE constraint. The second issue is related to transaction costs, where the MPC algorithm may require frequent trades of many stocks leading to large transaction costs in practice. Here we assume that the transaction cost is proportional to the change in the amount of money (i.e., the change of absolute values of long or short positions) invested in each stock. We formulate the MPC strategy based on a conditional mean-variance problem which we show reduces to a convex quadratic problem, even with gross exposure and proportional transaction cost constraints. Based on numerical experiments using Japanese stock data, we demonstrate that the incorporation of the transaction cost constraint improves the empirical performance of the wealth in terms of Sharpe ratio, which may be improved further by adding the GE constraint.     

Do Stars Shine? Comparing the Performance Persistence of Star Sell-Side Analysts Listed by Institutional Investor,the Wall Street Journal,and StarMine

We investigate the profitability persistence of the investment recommendations from analysts listed in four different star rankings, Institutional Investor magazine, StarMine’s “Top Earnings Estimators” and “Top Stock Pickers”, and The Wall Street Journal, and show the predictive power of each evaluation methodology. We found that only Buy and Strong Buy recommendations from the entire group of Star analysts outperform those of the Non-Stars in the year after election, while Sell and Strong Sell recommendations performed as those of the Non-Stars. We document that the highest average monthly abnormal return of holding a long-short portfolio, 0.97 %, is obtained by following the recommendations of the group of star sell-side analysts rated by StarMine’s “Top Earnings Estimators” during the period from 2003 to 2014. Since earnings are one of the main drivers of stock prices, the results obtained are in line with the notion that focusing on superior earnings forecasts is one of the top requirements for successful stock picks.     

Tests of investor learning models using earnings innovations and implied volatilities

This paper investigates alternative models of learning to explain changes in uncertainty surrounding earnings innovations. As a proxy for investor uncertainty, we use model-free implied volatilities; as a proxy for earnings innovations, representing signals of firm performance likely to drive investor perceptions of uncertainty, we use quarterly unexpected earnings benchmarked to the consensus forecast. We document that uncertainty declines on average after the release of quarterly earnings announcements and this decline is attenuated by the magnitude of the earnings innovation. This latter result is consistent with models that incorporate signal magnitude as a factor driving changes in uncertainty. Most important, we document that signals deviating sufficiently from expectations lead to net increases in uncertainty. Critically, this result suggests that models allowing for posterior variance to be greater than prior variance even after signal revelation [e.g., regime shifts in Pastor and Veronesi (Annu Rev Financ Econ 1:361–381, 2009)] better describe how investors incorporate new information.     

Examining the impact of the attractiveness of alternatives on customers’ perceptions of price tolerance: Moderation and mediation analyses

The current literature provides mixed support for the positive influence of competitors on customers’ perceptions of price tolerance (Herrmann et al, Psychology & Marketing, 2004 21(7), 533–551). This paper examines a number of mediators and moderators of this relationship, such as positive switching barriers, negative switching barriers and customer satisfaction. A total of 162 valid responses was collected from the financial brokerage context by means of a random sample. The data were analysed using the Partial-least square (PLS) approach to structural equation modelling. The findings show that customers’ satisfaction with the service provider partially mediates the positive effect of alternatives on price tolerance. Negative, not positive, switching barriers were found to weaken the effect on price tolerance of the attractiveness of alternatives.