Trading Cryptocurrencies Using Second Order Stochastic Dominance

This research is the first attempt to customize a trading system that is based on second order stochastic dominance (SSD) to five known cryptocurrencies’ daily data: Bitcoin, Ethereum, XRP, Binance Coin, and Cardano. Results show that our system can predict price trends of cryptocurrencies, trade them profitably, and in most cases outperform the buy and hold (B&H) simple strategy. Our system’s best performance was achieved trading XRP, Binance Coin, Ethereum, and Bitcoin. Although our system has also generated a positive net profit (NP) for Cardano, it failed to outperform the B&H strategy. For all currencies, the system better predicted long trends than short trends.

The Truncated Burr X-G Family of Distributions: Properties and Applications to Actuarial and Financial Data

In this article, the “truncated-composed” scheme was applied to the Burr X distribution to motivate a new family of univariate continuous-type distributions, called the truncated Burr X generated family. It is mathematically simple and provides more modeling freedom for any parental distribution. Additional functionality is conferred on the probability density and hazard rate functions, improving their peak, asymmetry, tail, and flatness levels. These characteristics are represented analytically and graphically with three special distributions of the family derived from the exponential, Rayleigh, and Lindley distributions. Subsequently, we conducted asymptotic, first-order stochastic dominance, series expansion, Tsallis entropy, and moment studies. Useful risk measures were also investigated. The remainder of the study was devoted to the statistical use of the associated models. In particular, we developed an adapted maximum likelihood methodology aiming to efficiently estimate the model parameters. The special distribution extending the exponential distribution was applied as a statistical model to fit two sets of actuarial and financial data. It performed better than a wide variety of selected competing non-nested models. Numerical applications for risk measures are also given.

Basic Geometric Dispersion Theory of Decision Making Under Risk: Asymmetric Risk Relativity, New Predictions of Empirical Behaviors, and Risk Triad

Many studies have spotlighted significant applications of expected utility theory (EUT), cumulative prospect theory (CPT), and mean-variance in assessing risks. We illustrate that these models and their extensions are unable to predict risk behaviors accurately in out-of-sample empirical studies. EUT uses a nonlinear value (utility) function of consequences but is linear in probabilities, which has been criticized as its primary weakness. Although mean-variance is nonlinear in probabilities, it is symmetric, contradicts first-order stochastic dominance, and uses the same standard deviation for both risk aversion and risk proneness. In this paper, we explore a special case of geometric dispersion theory (GDT) that is simultaneously nonlinear in both consequences and probabilities. It complies with first-order stochastic dominance and is asymmetric to represent the mixed risk-averse and risk-prone behaviors of the decision makers. GDT is a triad model that uses expected value, risk-averse dispersion, and risk-prone dispersion. GDT uses only two parameters, z and zX; these constants remain the same regardless of the scale of risk problem. We compare GDT to several other risk dispersion models that are based on EUT and/or mean-variance, and identify verified risk paradoxes that contradict EUT, CPT, and mean-variance but are easily explainable by GDT. We demonstrate that GDT predicts out-of-sample empirical risk behaviors far more accurately than EUT, CPT, mean-variance, and other risk dispersion models. We also discuss the underlying assumptions, meanings, and perspectives of GDT and how it reflects risk relativity and risk triad. This paper covers basic GDT, which is a special case of general GDT of Malakooti [Malakooti (2020) Geometric dispersion theory of decision making under risk: Generalizing EUT, RDEU, & CPT with out-of-sample empirical studies. Working paper, Case Western Reserve University, Cleveland.].

Investigation of the Calendar Effect

This chapter aims to examine calendar anomaly in selected sample countries by using second-order stochastic dominance (SSD) approach. Day-of-the-week and month-of-the-year effects are analysed for a group of 5 developed and 5 developing country indexes to estimate efficient (inefficient) weekdays and months for the period between 1988 and 2016. Then, back-testing procedure is applied for each sample country to compare performance of index returns for 2017-2019 with the strategy arisen by estimation results. Findings suggest that Monday and Friday returns are inefficient and efficient respectively in all developing countries where different results obtained for developed ones. In monthly analysis, December returns found efficient in 8 indexes including S&P 500. However, October is inefficient for all indexes. Positive January effect seems disappeared in most cases. Back-testing results indicate that in a bearish market condition SSD strategy outperforms index returns in general for daily and monthly comparison.