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The idea behind any of these factor models (whether it be the CAPM, Fama-French 3 Factor Model, Carhart 4 Factor Model etc...) is that expected returns are linear in covariance with variables of hedging concern to investors. The economic idea is that there are macroeconomic risks investors do not wish to hold, and to entice investors to hold these risks, ...


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The most often used additional factor is Pastor-Stambaugh. The Fama-French model is augmented with a proxy for the Pastor-Stambaugh liquidity factor. r = RF + βmkt (RM - RF) + βS x SMB + βV x HML + βL x LIQ You could check the replication issue at Critical Finance https://www.nowpublishers.com/article/Details/CFR-0074 https://www.nowpublishers.com/article/...


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I worked on volatility control funds for a few years a while back. Frequently, we would simply use the average as the threshold between high and low vol. That is because volatility is below average in normal times, but can quickly exceed the average during a correction. Mathematically, the fat right tail of an inverse-gamma distribution for an unknown ...


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