Cryptocurrencies (CCs) have risen rapidly in market capitalization over the last years. Despite striking price volatility, their high average returns have drawn attention to CCs as alternative investment assets for portfolio and risk management. We investigate the utility gains for different types of investors when they consider cryptocurrencies as an addition to their portfolio of traditional assets. We consider risk-averse, return-seeking as well as diversificationpreferring investors who trade along different allocation frequencies, namely daily, weekly or monthly. Out-of-sample performance and diversification benefits are studied for the most popular portfolio-construction rules, including mean-variance optimization, risk-parity, and maximum-diversification strategies, as well as combined strategies. To account for low liquidity in CC markets, we incorporate liquidity constraints via the LIBRO method. Our results show that CCs can improve the risk-return profile of portfolios. In particular, a maximum-diversification strategy (maximizing the Portfolio Diversification Index, PDI) draws appreciably on CCs, and spanning tests clearly indicate that CC returns are non-redundant additions to the investment universe. Though our analysis also shows that illiquidity of CCs potentially reverses the results.
This research mainly explores the characteristics of different strategies and whether VIX INDEX positively influences the investment portfolio in any period. Our portfolio has six significant cryptocurrencies, VIX INDEX and gold. We perform parameter estimation on all raw data and bring the two types into different investment strategies, complete them effectively according to other characteristics, and compare the results. At the same time, we make two different portfolios, one contains VIX INDEX, and one does not have VIX INDEX. We use different portfolios in different portfolio strategies an…
This paper studies long term investing by an investor that maximizes either expected utility from terminal wealth or from consumption. We introduce the concepts of a generalized stochastic discount factor (SDF) and of the minimum price to attain target payouts. The paper finds that the dynamics of the SDF needs to be captured and not the entire market dynamics, which simplifies significantly practical implementations of optimal portfolio strategies. We pay particular attention to the case where the SDF is equal to the inverse of the growth-optimal portfolio in the given market. Then, optimal w…
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）
Portfolio management is essential for any investment decision. Yet, traditional methods in the literature are ill-suited for the characteristics and dynamics of cryptocurrencies. This work presents a method to build an investment portfolio consisting of more than 1500 cryptocurrencies covering 6 years of market data. It is centred around Topological Data Analysis (TDA), a recent approach to analyze data sets from the perspective of their topological structure. This publication proposes a system combining persistence landscapes to identify suitable investment opportunities in cryptocurrencies. …
This article develops a model that takes into account skewness risk in risk parity portfolios. In this framework, asset returns are viewed as stochastic processes with jumps or random variables generated by a Gaussian mixture distribution. This dual representation allows us to show that skewness and jump risks are equivalent. As the mixture representation is simple, we obtain analytical formulas for computing asset risk contributions of a given portfolio. Therefore, we define risk budgeting portfolios and derive existence and uniqueness conditions. We then apply our model to the equity/bond/vo…
We propose a new method of valuation of portfolios and their respective investing strategies. To this end we define a canonical ensemble of portfolios that allows to use the formalism thermodynamics.
Cryptocurrencies return cross-predictability and technological similarity yield information on risk propagation and market segmentation. To investigate these effects, we build a time-varying network for cryptocurrencies, based on the evolution of return cross-predictability and technological similarities. We develop a dynamic covariate-assisted spectral clustering method to consistently estimate the latent community structure of cryptocurrencies network that accounts for both sets of information. We demonstrate that investors can achieve better risk diversification by investing in cryptocurren…
This paper studies an optimal investing problem for a retiree facing longevity risk and living standard risk. We formulate the investing problem as a portfolio choice problem under a time-varying risk capacity constraint. We derive the optimal investment strategy under the specific condition on model parameters in terms of second-order ordinary differential equations. We demonstrate an endogenous number that measures the expected value to sustain the spending post-retirement. The optimal portfolio is nearly neutral to the stock market movement if the portfolio's value is higher than this numbe…
By exploiting a bipartite network representation of the relationships between mutual funds and portfolio holdings, we propose an indicator that we derive from the analysis of the network, labelled the Average Commonality Coefficient (ACC), which measures how frequently the assets in the fund portfolio are present in the portfolios of the other funds of the market. This indicator reflects the investment behavior of funds' managers as a function of the popularity of the assets they held. We show that $ACC$ provides useful information to discriminate between funds investing in niche markets and t…
Hierarchical AI Multi-Agent Fundamental Investing: Evidence from China's A-Share Market
Faculty of Business and Economics, University of Hong Kong（香港大学商学院）；Department of Mathematics, University of Hong Kong（香港大学数学系）；Department of Industrial Engineering and Decision Analytics, Hong Kong University of Science and Technology（香港科学与技术大学工业工程与决策分析系）
AllianceBernstein（联博集团）；University of Manchester（曼彻斯特大学）；University of California, Berkeley（加州大学伯克利分校）
The financial crisis of 2008 generated interest in more transparent, rules-based strategies for portfolio construction, with Smart beta strategies emerging as a trend among institutional investors. While they perform well in the long run, these strategies often suffer from severe short-term drawdown (peak-to-trough decline) with fluctuating performance across cycles. To address cyclicality and underperformance, we build a dynamic asset allocation system using Hidden Markov Models (HMMs). We test our system across multiple combinations of smart beta strategies and the resulting portfolios show …
We study portfolio optimization of four major cryptocurrencies. Our time series model is a generalized autoregressive conditional heteroscedasticity (GARCH) model with multivariate normal tempered stable (MNTS) distributed residuals used to capture the non-Gaussian cryptocurrency return dynamics. Based on the time series model, we optimize the portfolio in terms of Foster-Hart risk. Those sophisticated techniques are not yet documented in the context of cryptocurrency. Statistical tests suggest that the MNTS distributed GARCH model fits better with cryptocurrency returns than the competing GAR…
In this report we derive the strategic (deterministic) allocation to bonds and stocks resulting in the optimal mean-variance trade-off on a given investment horizon. The underlying capital market features a mean-reverting process for equity returns, and the primary question of interest is how mean-reversion effects the optimal strategy and the resulting portfolio value at the horizon. In particular, we are interested in knowing under which assumptions and on which horizons, the risk-reward trade-off is so favourable that the value of the portfolio is effectively bounded from below on the horiz…
Kelly's Criterion is well known among gamblers and investors as a method for maximizing the returns one would expect to observe over long periods of betting or investing. These ideas are conspicuously absent from portfolio optimization problems in the financial and automation literature. This paper will show how Kelly's Criterion can be incorporated into standard portfolio optimization models. The model developed here combines risk and return into a single objective function by incorporating a risk parameter. This model is then solved for a portfolio of 10 stocks from a major stock exchange us…
We consider portfolio optimization in futures markets. We model the entire futures price curve at once as a solution of a stochastic partial differential equation. The agents objective is to maximize her utility from the final wealth when investing in futures contracts. We study a class of futures price curve models which admit a finite-dimensional realization. Using this, we recast the portfolio optimization problem as a finite-dimensional control problem and study its solvability.
In recent years, cryptocurrencies have gone from an obscure niche to a prominent place, with investment in these assets becoming increasingly popular. However, cryptocurrencies carry a high risk due to their high volatility. In this paper, criteria based on historical cryptocurrency data are defined in order to characterize returns and risks in different ways, in short time windows (7 and 15 days); then, the importance of criteria is analyzed by various methods and their impact is evaluated. Finally, the future plan is projected to use the knowledge obtained for the selection of investment por…
In financial investing, universal portfolios are a means of constructing portfolios which guarantee a certain level of performance relative to a baseline, while making no statistical assumptions about the future market data. They fall under the broad category of regret minimization algorithms. This document covers an introduction and survey to universal portfolio techniques, covering some of the basic concepts and proofs in the area. Topics include: Constant Rebalanced Portfolios, Cover's Algorithm, Incorporating Transaction Costs, Efficient Computation of Portfolios, Including Side Informatio…
This paper presents hedging strategies for European and exotic options in a Levy market. By applying Taylor's Theorem, dynamic hedging portfolios are con- structed under different market assumptions, such as the existence of power jump assets or moment swaps. In the case of European options or baskets of European options, static hedging is implemented. It is shown that perfect hedging can be achieved. Delta and gamma hedging strategies are extended to higher moment hedging by investing in other traded derivatives depending on the same underlying asset. This development is of practical importan…
Cryptocurrency markets have attracted many interest for global investors because of their novelty, wide online availability, increasing capitalization and potential profits. In the econophysics tradition we show that many of the most available cryptocurrencies have return statistics that do not follow Gaussian distributions but heavy--tailed distributions instead. Entropy measures are also applied showing that portfolio diversification is a reasonable practice for decreasing return uncertainty.
Decentralized Finance (DeFi) is a new financial industry built on blockchain technologies. Decentralized financial services have consequently increased the ability to lend, borrow, and invest in decentralized investment vehicles, allowing investors to bypass third party intermediaries. DeFi's promise is to reduce the cost of transaction and management fees whilst increasing trust between agents of the Financial Industry 3.0. This paper provides an overview of the different components of DeFi, as well as the risks involved in investing through these new vehicles. We will also propose an allocat…
Smart beta, also known as strategic beta or factor investing, is the idea of selecting an investment portfolio in a simple rule-based manner that systematically captures market inefficiencies, thereby enhancing risk-adjusted returns above capitalization-weighted benchmarks. We explore the idea of applying a smart strategy in reverse, yielding a "bad beta" portfolio which can be shorted, thus allowing long and short positions on independent smart beta strategies to generate beta neutral returns. In this article we detail the construction of a monthly reweighted portfolio involving two independe…
This article aims to combine factor investing and reinforcement learning (RL). The agent learns through sequential random allocations which rely on firms' characteristics. Using Dirichlet distributions as the driving policy, we derive closed forms for the policy gradients and analytical properties of the performance measure. This enables the implementation of REINFORCE methods, which we perform on a large dataset of US equities. Across a large range of parametric choices, our result indicates that RL-based portfolios are very close to the equally-weighted (1/N) allocation. This implies that th…
Among professionals and academics alike, it is well known that active portfolio management is unable to provide additional risk-adjusted returns relative to their benchmarks. For this reason, passive wealth management has emerged in recent decades to offer returns close to benchmarks at a lower cost. In this article, we first refine the existing results on the theoretical properties of oblique Brownian motion. Then, assuming that the returns follow skew geometric Brownian motions and that they are correlated, we describe some statistical properties for the \emph{ex-post}, the \emph{ex-ante} tr…
We study how to assess the potential benefit of diversifying an equity portfolio by investing within and across equity sectors. We analyse 20 years of US stock price data, which includes the global financial crisis (GFC) and the COVID-19 market crash, as well as periods of financial stability, to determine the `all weather' nature of equity portfolios. We establish that one may use the leading eigenvalue of the cross-correlation matrix of log returns as well as graph-theoretic diagnostics such as modularity to quantify the collective behaviour of the market or a subset of it. We confirm that f…
The fundamental principle in Modern Portfolio Theory (MPT) is based on the quantification of the portfolio's risk related to performance. Although MPT has made huge impacts on the investment world and prompted the success and prevalence of passive investing, it still has shortcomings in real-world applications. One of the main challenges is that the level of risk an investor can endure, known as \emph{risk-preference}, is a subjective choice that is tightly related to psychology and behavioral science in decision making. This paper presents a novel approach of measuring risk preference from ex…
Like ESG investing, climate change is an important concern for asset managers and owners, and a new challenge for portfolio construction. Until now, investors have mainly measured carbon risk using fundamental approaches, such as with carbon intensity metrics. Nevertheless, it has not been proven that asset prices are directly impacted by these fundamental-based measures. In this paper, we focus on another approach, which consists in measuring the sensitivity of stock prices with respect to a carbon risk factor. In our opinion, carbon betas are market-based measures that are complementary to c…
The proprietary nature of Hedge Fund investing means that it is common practise for managers to release minimal information about their returns. The construction of a Fund of Hedge Funds portfolio requires a correlation matrix which often has to be estimated using a relatively small sample of monthly returns data which induces noise. In this paper random matrix theory (RMT) is applied to a cross-correlation matrix C, constructed using hedge fund returns data. The analysis reveals a number of eigenvalues that deviate from the spectrum suggested by RMT. The components of the deviating eigenvecto…
This article studies the impact of carbon risk on stock pricing. To address this, we consider the seminal approach of Görgen \textsl{et al.} (2019), who proposed estimating the carbon financial risk of equities by their carbon beta. To achieve this, the primary task is to develop a brown-minus-green (or BMG) risk factor, similar to Fama and French (1992). Secondly, we must estimate the carbon beta using a multi-factor model. While Görgen \textsl{et al.} (2019) considered that the carbon beta is constant, we propose a time-varying estimation model to assess the dynamics of the carbon risk. More…
A continuous-path semimartingale market model with wealth processes discounted by a riskless asset is considered. The numeraire portfolio is the unique strictly positive wealth process that, when used as a benchmark to denominate all other wealth, makes all wealth processes local martingales. It is assumed that the numeraire portfolio exists and that its wealth increases to infinity as time goes to infinity. Under this setting, an initial enlargement of the filtration is performed, by including the overall minimum of the numeraire portfolio. It is established that all nonnegative wealth proces…
With the good development in the financial industry, the market starts to catch people's eyes, not only by the diversified investing choices ranging from bonds and stocks to futures and options but also by the general "high-risk, high-reward" mindset prompting people to put money in the financial market. People are interested in reducing risk at a given level of return since there is no way of having both high returns and low risk. Many researchers have been studying this issue, and the most pioneering one is Harry Markowitz's Modern Portfolio Theory developed in 1952, which is the cornerstone…
Stock price prediction is a challenging task and a lot of propositions exist in the literature in this area. Portfolio construction is a process of choosing a group of stocks and investing in them optimally to maximize the return while minimizing the risk. Since the time when Markowitz proposed the Modern Portfolio Theory, several advancements have happened in the area of building efficient portfolios. An investor can get the best benefit out of the stock market if the investor invests in an efficient portfolio and could take the buy or sell decision in advance, by estimating the future asset …
This note investigates the causes of the quality anomaly, which is one of the strongest and most scalable anomalies in equity markets. We explore two potential explanations. The "risk view", whereby investing in high quality firms is somehow riskier, so that the higher returns of a quality portfolio are a compensation for risk exposure. This view is consistent with the Efficient Market Hypothesis. The other view is the "behavioral view", which states that some investors persistently underestimate the true value of high quality firms. We find no evidence in favor of the "risk view": The returns…
