{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T00:48:05Z","timestamp":1792111685994,"version":"4.4.0"},"posted":{"date-parts":[[2026]]},"group-title":"SSRN","reference-count":29,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>The decay in an exponentially weighted covariance estimate is often read as the market's memory. We ask whether it also reflects the decision the estimate serves. We construct equity covariance from separately weighted volatilities and correlations, and select correlation decay for either the realised risk of a global minimum-variance (GMV) portfolio or a Gaussian likelihood score. Volatility decay and regularisation strength are fixed and shared by both objectives. In U.S. equities, the correlation memory chosen for GMV responds strongly to supplied volatility memory: at the shortest volatility setting it uses about 45 effective daily observations, compared with roughly 800 for likelihood. As volatility memory grows, the portfolio's selected correlation memory increases tenfold or more, while the likelihood's choice changes comparatively little. A test specified before the 2007-2015 data were evaluated confirms the interaction, and using the likelihood's correlation choice raises held-out GMV risk by about 9% at the short volatility setting. Simulations with constant true covariance reproduce the effect closely under spectral cleaning and partly under linear shrinkage. Preferred covariance memory thus reflects the estimator and its evaluation objective, rather than market dynamics alone.<\/jats:p>","DOI":"10.2139\/ssrn.7602921","type":"posted-content","created":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T05:30:11Z","timestamp":1791869411000},"source":"Crossref","is-referenced-by-count":0,"title":["Memory for What?&amp;nbsp;How the Objective Links Correlation Decay to Volatility Decay in Covariance Estimation"],"prefix":"10.2139","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4502-3818","authenticated-orcid":true,"given":"William","family":"Smyth","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"1","key":"ref1","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/j.ejor.2017.09.028","article-title":"Estimation of the Global Minimum Variance Portfolio in High Dimensions","volume":"266","author":"Taras Bodnar","year":"2018","journal-title":"European 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