Lessons from naïve diversification about the risk-reward trade-off

Studies of naïve diversification show that average total portfolio risk declines asymptotically as number of stocks increases. Recent work shows that a significant amount of idiosyncratic risk remains, even for portfolios with large numbers of stocks. The corresponding shocks are non-trivial. For example, more than half of all equal-weighted portfolios with 100 stocks have better than a 16 percent chance of an annual shock at least as large as about half of the annualized mean excess return on the U.S. total stock market index over July 1963–June 2018. I perform a simulation analysis of portfolio reward-to-risk as well as the components of total portfolio risk. On average, investors do not appear to be rewarded for exposure to non-systematic risk. The cross-sectional distribution of the true Sharpe ratio rises and its dispersion shrinks significantly as the number of stocks in the portfolio increases, whereas the cross-sectional distribution of the true non-systematic risk falls and its dispersion shrinks significantly as the number of stocks in the portfolio increases. This pattern appears regardless of the true asset pricing model for generating security returns, the portfolio weighting method, or specification of security alphas.     

Jump risk and cross section of stock returns: evidence from China’s stock market

Various studies have confirmed the existence of jumps in different financial markets. However, there is sparse theoretical or empirical effort to examine the dynamic relation between jump risk and cross-sectional expected stock returns. We follow a stylized SDF-based diffusion-jump model to examine its testable implications about the relation between cross-section expected excess returns and variations in jump intensities across stocks. The zero-cost portfolio, exploiting the return spreads between the top and bottom decile portfolios formed on jump intensity, could earn an annualized return as high as 24% with an annualized Sharpe ratio of 1.67. A Fama-MacBeth test shows that stock excess returns monotonically decrease in jump intensity even after controlling for other common risk factors.     

Hedging inflation with individual US stocks: A long-run portfolio analysis

This paper examines whether individual stocks can act as inflation hedgers. We focus on longer investment horizons and construct in- and out-of-sample portfolios based on the long-run relationship (cointegration) of stock prices with respect to consumer prices. Empirical evidence suggests that investors are better off by holding a portfolio of stocks with higher long-run betas as part of asset selection and allocation strategy. Stocks that outperform inflation tend to be drawn from the Energy and Industrial sectors. Finally, we observe that the companies average inflation hedging ability declined steadily over the past ten years, while the number of firms that hedge inflation has decreased considerably after the recent downturn of the US economy.     

The behavior of MENA oil and non-oil producing countries in international portfolio optimization

It is well documented in developed economies that portfolio investment across national borders brings benefits of increasing returns and/or reducing risk. Dividing MENA stock markets into two main groups (oil producing and non-oil producing countries), this study examines the potential role of each group in providing diversification benefits for international investors. In addition, the behavior of the long and the short-run Efficient Frontiers (EFs) constructed by each of the sub-groups and the combined MENA markets is explored. Multi-objective international portfolio models are proposed under Mean-Variance and Mean-Lower Partial Moment frameworks, and the Multiple Fitness Function Genetic Algorithm (MFFGA) is used to find the EFs of optimal portfolios. The findings indicate that the stock markets of oil producing countries can be considered as a potential avenue for international portfolio diversification for investors not only from the same countries but also from the other MENA markets. It was also found that international portfolios constructed from the combination of MENA equity markets are more stable compared to the portfolios of sub-group markets. Further, the findings indicate that the behavior of short-term EFs in the MENA region cannot be predicted by the behavior of long-term EFs.     

Homeownership and mixed-asset portfolio allocations

Homeownership represents both a consumption and an investment decision for individuals. Considering the investment benefits of the home, we estimate the total returns and risk associated with the investment in single-family homes. Then, using a mean–variance utility function, we consider the impact of homeownership and mortgage loan financing on the optimal asset allocation decisions of individuals and contrast this with advice that does not include the home as part of the portfolio. While optimal portfolio weights are dependant upon both the degree of risk aversion of the individual investor and the relative importance of the home in the overall net worth picture, we show that, in general, the higher the home-to-net worth ratio, the higher the optimal portfolio allocation to stock. For most investors, including the home in the optimization decision leads to higher allocations to risky stock than suggested by traditional advice that ignores the home.     

Robust tracking error portfolio selection with worst-case downside risk measures

This paper proposes downside risk measure models in portfolio selection that captures uncertainties both in distribution and in parameters. The worst-case distribution with given information on the mean value and the covariance matrix is used, together with ellipsoidal and polytopic uncertainty sets, to build-up this type of downside risk model. As an application of the models, the tracking error portfolio selection problem is considered. By lifting the vector variables to positive semidefinite matrix variables, we obtain semidefinite programming formulations of the robust tracking portfolio models. Numerical results are presented in tracking SSE50 of the Shanghai Stock Exchange. Compared with the tracking error variance portfolio model and the equally weighted strategy, the proposed models are more stable, have better accumulated wealth and have much better Sharpe ratio in the investment period for the majority of observed instances.     

The costs of suboptimal dynamic asset allocation: General results and applications to interest rate risk, stock volatility risk, and growth/value tilts

The recent theoretical asset allocation literature has derived optimal dynamic investment strategies in various advanced models of asset returns. But how sensitive is investor welfare to deviations from the theoretically optimal strategy? Will unsophisticated investors do almost as well as sophisticated investors? This paper develops a general theoretical framework for answering such questions and applies it to three specific models of interest rate risk, stochastic stock volatility, and mean reversion and growth/value tilts of stock portfolios. Among other things, we find that growth/value tilts are highly valuable, but the hedging of time-varying stock risk premia is less important.     

Alternative estimation method of earnings growth rate for PEGR strategy

The ambiguous return pattern for the PEGR (the ratio of the stock’s price/earnings to its estimated earnings growth rate) strategy has been documented in literature for the US stock markets. As stock prices and earnings per share (EPS) are objective data, earnings growth rate, however, is estimated by analyst whose method partial explains the PEGR vague return pattern. The purpose of this study is not to deny or substitute analysts’ estimation, but rather, to provide a simple and popular method, log-linear regression model, to forecast the earnings growth rate (G), and examine whether the typical PEGR effect, such as PER (price/earnings ratio) or PBR (price/book ratio) effect, exists by using our alternative estimation method. Our evidence indeed shows that returns on the lowest PEGR portfolio not only dominate over all higher PEGR portfolios, but also beat the market with stochastic dominance (SD) analysis, which is consistent with our prediction. Our results, at least, imply that using the log-linear regression model to construct the PEGR-sorted portfolios can benefit investors and the model is also a good choice for analysts in their forecasting.     

基于对冲基金的投资组合新架构研究

本文在分析传统的投资对冲基金组合架构存在不足的基础上,提出了新的资产组合构架模型,并通过美国市场的数据论证了对冲基金为何不是一个纯粹超额收益的制造者而更多是一个风险溢价的提供者以及将对冲基金与传统资产有机整合到一起的好处,为投资者优化资产投资组合提供了新的方法。     

Time and frequency connectedness and portfolio diversification between cryptocurrencies and renewable energy stock markets during COVID-19

The assessment of the time and frequency connectedness between cryptocurrencies and renewable energy stock markets is of key interest for portfolio diversification. In this paper, we utilize weekly data from 07 August 2015 to 26 March 2021 to document the dynamics and portfolio diversification from a fresh cryptocurrencies-renewable energy perspective. Our time-frequency domain spillovers results reveal that renewable energy stocks are the main spillover contributors in the connectedness system and the short-run spillovers dominate their long-run counterparts. Furthermore, investors can gain more profits through short-run transactions in our portfolio design and we can optimize portfolios by investing a large portion in cryptocurrencies. A fascinating fact is that the COVID-19 pandemic can reverse the effectiveness of our hedging strategy.     

Diversified behavioral portfolio as an alternative to Modern Portfolio Theory

The traditional mean–variance approach has been complemented by alternative theories that use risk measures different from standard deviation of returns or involve additional distributional features of returns like skewness and kurtosis. We propose a portfolio choice model that combines different distributional characteristics of the returns in the decision-making making process, considering preferences of investors which are modeled as non-statistical uncertainties of investors using fuzzy theory. We use 20 stocks of the S&P500 from January 2013 to December 2017. We assess the obtained portfolios’ performance, and the diversified behavioral portfolios outperform than the mean–variance portfolio. This methodological proposal can be seen as a strong managerial tool to make investment portfolio decisions.     

The Market Performance of Socially Responsible Investment during Periods of the Economic Cycle – Illustrated Using the Case of FTSE

The debate about socially responsible investment (SRI) portfolio performance compared with its non‐SRI counterparts remains inconclusive. This paper contributes to the debate by adding a new approach, examining the issue of a full economic circle through economic boom, recession and recovery. We compare stock performance of two value‐weighted investment portfolios: FTSE4Good (SRI portfolios) and FTSE 350 (conventional portfolios) from 2004 to 2011 including 2007 to 2009 financial crash. The results indicate the SRI portfolio performed better and recovered its value quicker in post‐crisis than the non‐SRI portfolio, indicating that SRI portfolios are more resilient to economic turmoil and market shocks. Copyright © 2015 John Wiley & Sons, Ltd.     

Catastrophe equity put options with floating strike prices

In this study, we extend the results in Cox et al. (2004) by considering floating strike prices, which are affected by accumulated losses. We employ a compound Poisson process to describe catastrophe losses and adopt a mean-reverting square root process to capture the volatility of the underlying stock. In the numerical section, we first compare the differences in the prices of the options with fixed and floating strike prices. In addition, we illustrate the variance of the portfolios consisting of the stock and options with alternative kinds of strike prices by holding the total cost of the options constant. Variance-optimal portfolios are also investigated. Interestingly, numerical results show that the portfolios consisting of the stock and options with floating strike prices have lower variances in all cases, even when we hold the total option costs constant.     

Sulla rigidita ‘della volatilita’ dell'ottimo portafoglio aleatorio al variare delle aspettative di mercato

Con riferimento al ben noto modello diagonale di Sharpe per le scelte di portafoglio, il presente lavoro si propone di fomire supporto teorico alla congettura (confermata da indagini sul mercato finanziario domestico) di una sostanziale rigidità della volatilità dell'ottimo portafoglio aleatorio al variare delle aspettative di mercato.

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Summary It is well known that one of the key theoretical supports to modern portfolio management derives from the so called diagonal model proposed by W. Sharpe.Precisely managers should build risky portfolios with high beta if the market is expected to rise and conversely with low betas if the market is expected to fall.Here on the contrary we discuss the theoretical bases of what seems to be a law of rigidity of the volatility of the optimal risky portfolio to variations ceteris paribus of the market expectations, quite likely prevailing on financial markets.Indeed this fact seems to be supported by empirical data regarding domestic stock market collected and discussed elsewhere (Stucchi 1988).This seems to suggest that the right response to change in market expectation is to change the bond-stock composition of the protfolio, rather then to act on the volatility of the stock (risky) portfolio.

     

Measuring the economic significance of mean-variance spanning

This paper investigates the economic significance of mean-variance spanning tests using three classical statistical tests in a unified framework. I show how to compute confidence intervals about the Sharpe ratios of tangent portfolios, the variance of return of minimum variance portfolios, as well as the certainty equivalent utility gains. I apply this statistical framework to the question of whether US investors should diversify internationally. The analysis suggests that a strong statistical rejection of the hypothesis that there is no improvement in the minimum variance portfolio’s standard deviation of return does not imply that there are no significant economic benefits to be made in terms of a substantial risk reduction. These results have important implications for empirical tests of mean-variance spanning as well as empirical assets pricing tests and minimum variance bounds on stochastic discount factors.     

Optimal portfolio choice in the presence of domestic systemic risk: empirical evidence from stock markets

In this paper, we empirically investigate the consequences of domestic systemic risk for stock market investors. To tackle this issue, we consider two different investment strategies. One strategy is to be “crisis-conscious”, i.e., taking the possibility of systemic events into account, and the other one is to be “crisis-ignorant” and thus disregarding systemic risk. We compare the optimal portfolio choices and investment results of these strategies in an historical simulation, using almost three decades of historical stock price data. Our main findings are as follows: the crisis-conscious investor tends to choose less extreme portfolio weights for individual stocks than the ignorant investor. The overall risky investment is, however, of similar size for both. By ignoring the possibility of systemic events, the crisis-ignorant strategy performs significantly worse from the viewpoint of expected return as well as expected utility.     

A model of international asset pricing under imperfect commodity arbitrage

This paper examines the effect of imperfect international commodity arbitrage (i.e., violation of the law of one price), modeled as the existence of non-traded goods, on the structure of purchasing power risk, optimal portfolio rules of the risk-averse investors and the equilibrium yield relationship among assets. The major results of the paper include: (i) There are two separate sources of purchasing power risk, i.e., relative price risk and inflation risk; relative price risk is specific to the country in which the investor resides. (ii) In a world of n countries, investors may hold n + 1 hedge portfolios as vehicles to hedge against purchasing power risk; facing different relative prices, investors residing in different countries display divergent portfolio behavior. (iii) In equilibrium, investors are compensated in terms of excess return for bearing not only the systematic world market risk but also the systematic inflation and relative price risks.     

Is the nonlinear hedge of options more effective?—Evidence from the SSE 50 ETF options in China

The linear hedging of the options ignores the characteristic of the nonlinear change of option prices with the underlying asset. This paper establishes the nonlinear hedging strategy followed the study by Hull and White (2017) to investigate the effectiveness on the Shanghai Stock Exchange (SSE) 50 ETF options. The results show that the nonlinear hedge of the Chinese option market is less effective than the U.S option market because of the short history and the lower activity of the Chinese option market. The effect of nonlinear hedging strategy is better than the linear hedging strategy for calls in China. But for puts, the effect of the nonlinear hedging strategy is not as significant as it for calls. The difference in the trading volume between calls and puts and the high short-selling cost in the Chinese market are the main factors leading to the difference in hedge effectiveness. This paper suggests that the stock exchange could reduce margin standard of 50 ETF securities lending, promote a more flexible shorting mechanism, and accelerate the process of index options listed, so as to achieve hedging the risk of options more directly and efficiently.     

Effectiveness of Augmented Dollar-Cost Averaging

Dollar-Cost Averaging investment strategy has been widely criticized by academics for decades. This article proposes an Augmented Dollar-Cost Averaging (ADCA) strategy that conditions investment strategy to the prevailing market environment. The ADCA investment strategy is more aggressive if the economy is expanding and more conservative if the economy is contracting. Changes in market volatility, unemployment rate and capacity utilization were used to determine whether the economy was expanding or contracting. Using the Sharpe ratio, coupled with first-order and second-order stochastic dominance criteria, this study shows the risk-reducing benefits of ADCA in the U.S. stock market between 1967 and 2018.     

一种增强型指数追踪模型设计及应用

研究目标：构建了可以调节追踪误差和超额收益的增强型指数追踪模型,并给出了广义最小角度回归算法（GLARS）,用以计算调节参数作用下模型解的折中路径。研究方法：通过模拟数据和五组世界主要股票市场指数的历史数据,对本文提出的模型和算法与同类模型和算法进行了性能比较;同时追踪上证50指数构建若干稀疏且稳定的资产组合模型,通过信息比率等指标对投资组合进行评价。研究发现：本文构建的模型可用以构造权衡追踪效果和超额收益,且稀疏的资产组合,GLARS算法相对传统预设参数的算法具有良好的求解能力和计算速度。研究创新：引入调节参数平衡追踪效果和超额收益,并针对中国股票市场的特点,在增强型指数追踪模型施加非负约束;GLARS算法可遍历所有折中意义下的最优解。研究价值：本文提出的增强型指数追踪模型在国内具有较强适用性,在保证资产稀疏性的前提下可以得到超额收益,同时丰富了目前投资组合中的方法论研究。