Diversification in options / BEBR No. 721 (original) (raw)

Incomplete Diversification and Asset Pricing

Advances in Finance and Stochastics, 2002

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Issues and Trends of Portfolio Diversification

International Journal of Academic Research in Business and Social Sciences, 2019

The concept of diversification has been a great importance in risk management and investment decision making in the capital market. The purpose of this paper is to examine the issues and trends of diversification of risk on capital market. In addition, the paper highlight some of the latest trends and developments in the area namely multi-asset class investment and comovement of risk and return. Moreover, in light of the basis of modern capital market theory developed by Harry Markowitz, the paper review some of the approaches developed to address the challenges encountered when using diversification strategy in practice, including the portfolio choice problem, alternative assets class and time-varying volatility assessment.

Does Risk Diversification Always Work? The Answer Through Simple Modelling

SSRN Electronic Journal, 2013

With a simple example of throwing a dice, we show how to price an insurance policy. We further study how this price decreases when many similar policies are sold. The diversification benefits increase with the number of policies and similarly the risk loading of the premium required for the risk decreases tending to zero. This is true as long as the risks are completely independent. However, when introducing in addition a biased dice played by a crooked croupier, a non-diversifiable risk does appear. Indeed, we can show analytically that, with the biased dice, there exists an additional term in the variance, which does not decrease with the number of policies in the portfolio and leads to a limit to diversification. We propose and study analytically three cases of introducing the non-diversifiable risk. For each of them, the behavior of the risk loading based on the underlying risk process is examined and a numerical illustration is provided. Then the results are discussed in view of the risk loading. Such a modelling could be used to study particular investment choices under uncertainty.

Diversification of equity investment portfolios. Application to the IBEX 35

Finance, Markets and Valuation, 2021

At present, there is no unanimity on the effects that stock diversification can have on the total risk of an investment portfolio. In this context, this paper studies some issues related to the evolution of risk in an investment portfolio made up of IBEX 35 stocks. In addition, it is tested whether conclusions drawn for other time periods and in other markets are applicable to the Spanish stock market. The methodology used consists of calculating how the two components that make up the total risk of a portfolio (systematic risk and unsystematic risk) behave as portfolios of increasing size are diversified. The study shows how an increase in the number of securities in the investment portfolio decreases the percentage corresponding to the unsystematic risk component and increases the systematic risk component. Furthermore, it also shows that the benefits of diversification become increasingly marginal as portfolio size increases. Additionally, it is shown that an increase in the numb...

The Diversification Delta: A Different Perspective

The Journal of Portfolio Management, 2017

In a 2012 article published in this Journal, Vermorken, Medda, and Schröder introduce a new measure of diversification, the Diversification Delta (DD), based on the entropy of the portfolio return distribution. Entropy as a measure of uncertainty has been used successfully in several frameworks and takes into account the entire statistical distribution rather than just the first two moments. In this article, the authors highlight some drawbacks of the DD measure and go on to propose an alternative measure based on exponential entropy which overcomes the identified shortcomings. The authors present the properties of this new measure and propose it as an alternative for portfolio optimization that incorporates higher moments of asset returns such as skewness and excess kurtosis.

The Diversification Delta: A Different Perspective

SSRN Electronic Journal, 2014

Real Options, Idiosyncratic Skewness, and Diversification

Journal of Financial and Quantitative Analysis, 2017

We show how firm-level real options lead to idiosyncratic skewness in stock returns. We then document empirically that growth option variables are positive and significant determinants of idiosyncratic skewness. The real option impact on skewness is more significant in firms with lottery-type features, small size, high volatility, distressed, low return on assets, and low book-to-market ratio. We also find that expectation on idiosyncratic skewness is associated with lower Sharpe ratios. This suggests investors are willing to sacrifice mean-variance portfolio efficiency for greater skewness deriving from real options. Furthermore, financial flexibility has a positive incremental effect, enhancing the beneficial role of asset flexibility on idiosyncratic skewness.

Taking the sting out of choice: Diversification of investments

Judgment and Decision Making, 2014

It is often the case that one can choose a mix of alternative options rather than have to select one option only. Such an opportunity to diversify may blunt the risk involved in all-or-none choice. Here we investigate repeated investment decisions in two-valued options that differ in their riskiness, looking for the effects of recent decisions and their outcomes on upcoming decisions. We compare these effects to those evident in all-or-none choice between the same risky options. The “state of the world”, namely, the likelihood of the high versus the low outcomes of the options, is manipulated. We find that aggregate allocation diverges from uniformity (i.e., from 1/n), and is sensitive to outcome probabilities, with the pattern of results indicating reactivity to the outcome of the previous decision. Round-to-round dynamics reveal that the outcome of the previous decision has an effect on the subsequent decision, on top of inertia; the aspects of the outcome that influence the next decision indicate an effect of a missed opportunity, if there was one, in the previous decision. Importantly, recent outcomes have a similar effect in diversification decisions and in all-or-none choice.

Article The Impact of Systemic Risk on the Diversification Benefits of a Risk Portfolio

2014

Risk diversification is the basis of insurance and investment. It is thus crucial to study the effects that could limit it. One of them is the existence of systemic risk that affects all of the policies at the same time. We introduce here a probabilistic approach to examine the consequences of its presence on the risk loading of the premium of a portfolio of insurance policies. This approach could be easily generalized for investment risk. We see that, even with a small probability of occurrence, systemic risk can reduce dramatically the diversification benefits. It is clearly revealed via a non-diversifiable term that appears in the analytical expression of the variance of our models. We propose two ways of introducing it and discuss their advantages and limitations. By using both VaR and TVaR to compute the loading, we see that only the latter captures the full effect of systemic risk when its probability to occur is low.

Implied correlation index: A new measure of diversification

Journal of Futures Markets, 2005

Most approaches in forecasting future correlations depend upon the use of historical information as their basic information set. Recently, there have been some attempts to use the notion of "implied" correlation as a more accurate measure of future correlation. This study proposes an innovative methodology for backing-out implied correlation measures from index options. This index reflects the market view of the future level of the market portfolio diversification. The methodology is applied to the Dow Jones Industrial Average index and the statistical properties and the dynamics of the proposed implied correlation measure are examined. The evidence of this study indicates that the implied correlation index fluctuates substantially over time and displays strong dynamic dependence. Moreover, there is a systematic tendency for the implied correlation index to increase when the market index returns decrease and/or the market volatility increases indicating limited diversification when it is needed most. Finally, the forecast performance of the implied correlation index is assessed. Although the implied correlation index is a biased forecast of realized correlation, it has a high explanatory power and it is orthogonal to the information set compared to a historical forecast.

Diversification in options / BEBR No. 721 (original) (raw)

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