Different Volatility Forecasts, Same Portfolio? Decision Equivalence Explained

Different Volatility Forecasts, Same Portfolio? Decision Equivalence Explained Why can statistically different volatility forecasts lead to identical portfolio weights? This full-length explanation covers decision equivalence, common-scale invariance, relative-risk distortions, exposure attribution, and the limits of the frozen 120-test family. Main paper — Fuli Yang: Decision-Equivalent Volatility Forecasts: Statistical Loss, Portfolio Value, and Allocation Commonality https://papers.ssrn.com/sol3/papers.cfm?ab... Paper version used: corrected v0.9. Original explanatory graphics and synthetic narration. Charts reproduce reported summaries; illustrative examples and threshold animations are labelled schematic. Full English CC available. Chapters 00:00 Different forecasts. The same portfolio. 00:41 Start with the decision rule 01:23 Double both forecasts 02:06 The scope of decision equivalence 02:54 A controlled five-asset replay 03:44 Six directions of forecast error 04:28 The placebo works to machine precision 05:14 Relative errors rotate the portfolio 06:00 Worse loss, higher historical utility 06:47 Follow the exposure change 07:37 A strong example is not familywise confirmation 08:28 Private value and commonality can diverge 09:16 Evaluate the whole forecast-to-decision map 10:03 Different scores need not mean different decisions Companion research: https://papers.ssrn.com/sol3/papers.cfm?ab... Earlier short research briefs: Decision equivalence:    • Different Volatility Forecasts, Identical ...   Forecast disagreement:    • Volatility Model Disagreement and Forecast...   GARCH QUANT | Academic research and education. This episode explains research findings and their limits; it does not present an investment recommendation or a deployed trading rule. #VolatilityForecasting #QuantitativeFinance #Econometrics