{"title":"Portfolio choice algorithms, including exact stochastic dominance","authors":"H.D. Vinod","doi":"10.1016/j.jfs.2023.101196","DOIUrl":null,"url":null,"abstract":"<div><p>Assume data on Nj stock (asset) returns are available for p stocks, allowing us to construct approximate density functions <span><math><mrow><mi>f</mi><mtext>(</mtext><msub><mrow><mi>x</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow></math></span>) for (j=1, 2, …, p) from p empirical cumulative distribution functions (ECDFs). Our portfolio choice is designed to rank ECDF-induced, ill-behaved <span><math><mrow><mi>f</mi><mtext>(</mtext><msub><mrow><mi>x</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow></math></span>) densities subject to multiple modes, asymmetric fat tails, dips, turns, and numerous overlaps. Older portfolio theory assumes that parameters like the mean, variance, and percentiles fully describe <span><math><mrow><mi>f</mi><mtext>(</mtext><msub><mrow><mi>x</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow></math></span>). All six of our algorithms avoid (expected) utility theory. The only available algorithm by Anderson for order-k Stochastic Dominance (SDk) needs a trapezoidal approximation. Our new exact algorithm for SDk is based on ECDFs and overcomes pairwise comparisons. We include algorithms for statistical inference using the bootstrap and one for “pandemic proof” out-of-sample portfolio performance comparisons from our R package ‘generalCorr’. We suggest a test for “zero cost profitable arbitrage” and illustrate our algorithms in action by using two sets of recent 169-month stock returns. We do not claim to suggest new optimal portfolios.</p></div>","PeriodicalId":48027,"journal":{"name":"Journal of Financial Stability","volume":null,"pages":null},"PeriodicalIF":6.1000,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Financial Stability","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1572308923000967","RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
引用次数: 0
Abstract
Assume data on Nj stock (asset) returns are available for p stocks, allowing us to construct approximate density functions ) for (j=1, 2, …, p) from p empirical cumulative distribution functions (ECDFs). Our portfolio choice is designed to rank ECDF-induced, ill-behaved ) densities subject to multiple modes, asymmetric fat tails, dips, turns, and numerous overlaps. Older portfolio theory assumes that parameters like the mean, variance, and percentiles fully describe ). All six of our algorithms avoid (expected) utility theory. The only available algorithm by Anderson for order-k Stochastic Dominance (SDk) needs a trapezoidal approximation. Our new exact algorithm for SDk is based on ECDFs and overcomes pairwise comparisons. We include algorithms for statistical inference using the bootstrap and one for “pandemic proof” out-of-sample portfolio performance comparisons from our R package ‘generalCorr’. We suggest a test for “zero cost profitable arbitrage” and illustrate our algorithms in action by using two sets of recent 169-month stock returns. We do not claim to suggest new optimal portfolios.
期刊介绍:
The Journal of Financial Stability provides an international forum for rigorous theoretical and empirical macro and micro economic and financial analysis of the causes, management, resolution and preventions of financial crises, including banking, securities market, payments and currency crises. The primary focus is on applied research that would be useful in affecting public policy with respect to financial stability. Thus, the Journal seeks to promote interaction among researchers, policy-makers and practitioners to identify potential risks to financial stability and develop means for preventing, mitigating or managing these risks both within and across countries.