Weight Determination and Portfolio Construction Based on Interval and Distributional Surface Forecasts in Financial Engineering

Yun-Kun Tu

Abstract

If portfolio optimization uses only point estimates of returns or risk, estimation error often becomes extreme weights and too much trading. Interval forecasts give ranges for parameters or returns. Distributional forecasts give conditional distributions, quantiles, and tail features. Together they give fuller inputs for choosing weights. This review studies how those inputs enter a weight rule. Interval uncertainty sets, conformal coverage, distributionally robust optimization, and conditional value-at-risk (CVaR) can be written into the objective or the constraints and then mapped into tradable weights. Interval width κ acts as a penalty on effective expected return or as a bound on the feasible set, so a wider interval shrinks active positions. Distribution shape changes risk measurement: a thicker left tail raises CVaR and lowers the weight on that asset. The two channels can be placed in one program from a point forecast μ ^ , an interval half width κ , and a conditional law F to a weight vector w under trading cost constraints. Putting interval width and distribution shape into the allocation rule can reduce overconfident concentration and improve risk budgeting and rebalancing. The argument is theoretical. It does not rest on a new backtest.

Source: semanticscholar · PDF

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