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A Test for the Equality of Multiple Sharpe Ratios 多个夏普比率相等性的检验
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2014-04-30 DOI: 10.21314/JOR.2014.289
J. Wright, S. Yam, Siu Pang Yung
{"title":"A Test for the Equality of Multiple Sharpe Ratios","authors":"J. Wright, S. Yam, Siu Pang Yung","doi":"10.21314/JOR.2014.289","DOIUrl":"https://doi.org/10.21314/JOR.2014.289","url":null,"abstract":"This paper provides a test for the equality of multiple Sharpe ratios. First we extend the multivariate Sharpe ratio statistic of Leung and Wong for the case when excess returns are independently and identically distributed. We then provide a test that holds under the much more general assumption that the excess returns are stationary and ergodic, making use of the generalized method of moments and heteroscedasticity and autocorrelation consistent estimation of covariance matrixes. We repeat Leung and Wong’s testing for equality of the Sharpe ratios f 18 iShares using our new tests and conclude that the hypothesis of equality cannot be rejected at the 1% level.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132502528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 28
A Note on the Cumulative Distribution Function of the Pearson Type IV Distribution for Financial Applications 金融应用中皮尔逊IV型分布的累积分布函数注记
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2014-03-10 DOI: 10.2139/ssrn.2406973
S. Stavroyiannis
{"title":"A Note on the Cumulative Distribution Function of the Pearson Type IV Distribution for Financial Applications","authors":"S. Stavroyiannis","doi":"10.2139/ssrn.2406973","DOIUrl":"https://doi.org/10.2139/ssrn.2406973","url":null,"abstract":"The cumulative distribution function of the Pearson type IV distribution is of complex form and includes a complex hypergeometric function. Although the mathematical form is complex, the resulting imaginary part is actually of the order which is attributed to the series summation of the hypergeometric function, where each term is complex, but summing up terms the complex part converges slowly to zero. This requires the use of software that can support complex hypergeometric functions, and several terms have to be summed up to achieve the negligible imaginary part. In this note we examine the transformation of the complex cumulative distribution to other hypergeometric functions that have a real contribution in each summing term, and the recurrence relation for the calculation of the expression is provided.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131215358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
How Performance of Risk-Based Strategies is Modified by Socially Responsible Investment Universe? 社会责任投资领域如何修改基于风险的战略绩效?
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2014-03-01 DOI: 10.2139/ssrn.2282372
P. Bertrand, Vincent Lapointe
{"title":"How Performance of Risk-Based Strategies is Modified by Socially Responsible Investment Universe?","authors":"P. Bertrand, Vincent Lapointe","doi":"10.2139/ssrn.2282372","DOIUrl":"https://doi.org/10.2139/ssrn.2282372","url":null,"abstract":"Risk-based allocation strategies, also known as Smart Beta allocations, define the weights of assets in portfolios as functions of the individual and common asset risk. In this paper we focus on the Minimum Variance (MV), Maximum Diversification (MD), Equal Risk Contribution (ERC) and Equal-Weight (EW) risk-based allocation strategies. The popularity of risk-based strategy is commonly justified by their good record of out-performing the cap-weighted (CW) allocation strategy. Because of the low-volatility profile of risk-based allocations this is especially true when crises occur. From March 15, 2002 to May 1, 2012 we investigate how using a socially responsible investment universe impacts performance of risk-based allocation strategies. We use different measures of performance, included risk-adjusted one (multi-factor models), and we propose to disentangle the effect of using a SRI universe from the effect of using risk-based allocations. SRI universe only contains firms that have good environmental, social and governance performance. This kind of filtering is increasingly popular among institutional investors. On the estimation period, using European stocks, we find that the use of the SRI universe has a positive contribution to risk-adjusted performance of risk-based allocations. However this contribution is not uniform among all the risk-based allocation strategies and, can represent only a small part of the total alpha that is observed.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134097602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 33
Series Primes in Binary 二进制数列素数
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2014-02-21 DOI: 10.12691/AJAMS-2-2-2
P. Mazurkin
{"title":"Series Primes in Binary","authors":"P. Mazurkin","doi":"10.12691/AJAMS-2-2-2","DOIUrl":"https://doi.org/10.12691/AJAMS-2-2-2","url":null,"abstract":"To prove the famous Riemann hypothesis, that the real part of the root is always exactly equal to 1/2, a series of 500 and the other prime numbers has been converted from decimal to binary number system. At the same time was a clear non-trivial zeros. Any prime number can be represented as quantized into binary digital signal. Quantization step to not dilute a number of prime numbers is 1. Number of levels (binary digits) depends on the power of the quantized number of primes. As a result, we get two types of zeros - the trivial and nontrivial. Capacity of a finite number of primes must be taken based on the completeness of block incidence matrix. Average statistical indicator is a binary number, and influencing variable - itself a prime number. The binary representation allows to visualize and geometric patterns in the full range of prime numbers.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"138 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125744947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
Wavelet Analysis of a Number of Prime Numbers 一组素数的小波分析
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2014-02-19 DOI: 10.12691/AJNA-2-2-1
P. Mazurkin
{"title":"Wavelet Analysis of a Number of Prime Numbers","authors":"P. Mazurkin","doi":"10.12691/AJNA-2-2-1","DOIUrl":"https://doi.org/10.12691/AJNA-2-2-1","url":null,"abstract":"We adhere to the concepts of Descartes, the need to apply algebraic equations directly as a final decision. The concept of wavelet signal allows to abstract from an unknown number of primes of a physical quantity. Any number of primes can be decomposed into a finite set of asymmetric wavelets with variable amplitude and frequency. For example, taken a number of A000040. The first term of the total number of model А000040 according to the law of exponential growth is the contribution of the absolute error 97,53 %. The first member of the general model of a number of А000040 on the law of exponential growth is the contribution of the absolute error 97,53 %. The remaining 35 wavelets amount to a total of 2.47 %. But their influence on the number of primes very significant. It is proved that any type of fnite-dimensional number of primes can be decomposed into a fnite-dimensional set of asymmetric wavelets with variable amplitude and frequency of oscillatory perturbations.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122289846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 15
On the Limit-Properties of Structural Change 论结构变化的极限性质
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2014-02-15 DOI: 10.2139/ssrn.2400551
Denis Stijepic
{"title":"On the Limit-Properties of Structural Change","authors":"Denis Stijepic","doi":"10.2139/ssrn.2400551","DOIUrl":"https://doi.org/10.2139/ssrn.2400551","url":null,"abstract":"Many economic theories deal with some sort of “structure” and with the changes in this structure. We provide mathematical meta-models for studying the limit-properties of continuous structural change. The limit properties of processes are important information in economic modelling. For example, they indicate whether a process can generate long-run growth effects. We show that continuous structural change is a relatively “simple” process. In most cases it is transitory or cyclical. Our meta-models cover different modelling techniques (autonomous, quasi-autonomous and non-autonomous differential equation systems) and many economic notions of structure (e.g. income-distribution, cross-sector labour allocation and investment structure).","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114961657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
On the Measurement of Economic Tail Risk 论经济尾部风险的度量
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2014-01-19 DOI: 10.2139/ssrn.2381651
S. Kou, X. Peng
{"title":"On the Measurement of Economic Tail Risk","authors":"S. Kou, X. Peng","doi":"10.2139/ssrn.2381651","DOIUrl":"https://doi.org/10.2139/ssrn.2381651","url":null,"abstract":"This paper attempts to provide a decision-theoretic foundation for the measurement of economic tail risk, which is not only closely related to utility theory but also relevant to statistical model uncertainty. The main result is that the only risk measures that satisfy a set of economic axioms for the Choquet expected utility and the statistical property of elicitability (i.e. there exists an objective function such that minimizing the expected objective function yields the risk measure) are the mean functional and the median shortfall, which is the median of tail loss distribution. Elicitability is important for backtesting. We also extend the result to address model uncertainty by incorporating multiple scenarios. As an application, we argue that median shortfall is a better alternative than expected shortfall for setting capital requirements in Basel Accords.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"68 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120866792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 80
Extraordinary Stability of Noise-Filtered Correlation Matrices 噪声滤波相关矩阵的超常稳定性
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2014-01-14 DOI: 10.2139/ssrn.2378944
A. Izmailov
{"title":"Extraordinary Stability of Noise-Filtered Correlation Matrices","authors":"A. Izmailov","doi":"10.2139/ssrn.2378944","DOIUrl":"https://doi.org/10.2139/ssrn.2378944","url":null,"abstract":"Demonstration of the extraordinary out-of-sample stability of noise-filtered correlation matrices measured in terms of simple Euclidean distance. This measure decreases 4-5 times post noise filtering implying 4-5 times improved stability.Study of the out-of-sample stability of noise-filtered correlation matrices as a function of number of securities and history horizon.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123118279","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Family of Density Expansions for Lévy-Type Processes 一类lvac型过程的密度展开式
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2013-12-27 DOI: 10.2139/ssrn.2245118
Matthew J. Lorig, S. Pagliarani, A. Pascucci
{"title":"A Family of Density Expansions for Lévy-Type Processes","authors":"Matthew J. Lorig, S. Pagliarani, A. Pascucci","doi":"10.2139/ssrn.2245118","DOIUrl":"https://doi.org/10.2139/ssrn.2245118","url":null,"abstract":"We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Levy-type martingale subject to default. This class of models allows for local volatility, local default intensity, and a locally dependent Levy measure. Generalizing and extending the novel adjoint expansion technique of Pagliarani, Pascucci, and Riga (2013), we derive a family of asymptotic expansions for the transition density of the underlying as well as for European-style option prices and defaultable bond prices. For the density expansion, we also provide error bounds for the truncated asymptotic series. Our method is numerically efficient; approximate transition densities and European option prices are computed via Fourier transforms; approximate bond prices are computed as finite series. Additionally, as in Pagliarani et al. (2013), for models with Gaussian-type jumps, approximate option prices can be computed in closed form. Sample Mathematica code is provided.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121370584","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 28
An Alternative Approach to Fast Implied Volatility Calculation 快速隐含波动率计算的一种替代方法
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2013-12-21 DOI: 10.2139/ssrn.2380749
G. Orlando
{"title":"An Alternative Approach to Fast Implied Volatility Calculation","authors":"G. Orlando","doi":"10.2139/ssrn.2380749","DOIUrl":"https://doi.org/10.2139/ssrn.2380749","url":null,"abstract":"This paper has the task of identifying an alternative approach (in terms of a mathematical algorithm) which can determine with speed (i.e. to converge within a few iterations) the value of the implied volatility for the options. This value is of particular importance since it is the main component of the option’s price. The paper after, an initial explanation of the objectives, illustrates various alternatives and proposes the adoption of an algorithm able to quickly converge to the desired solution.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114746944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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