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Why should maintaining constant leverage - symmetrically both up as well as down - be an objective function? Also, what should be relevant is the extent to which the asset return exceeds or falls short of the cost of funds used to create the leverage. R can be the difference.
In some cases it is an explicit aim of the fund (eg inverse, 2X or 3X ETFs) or it could just be the aim of the portfolio manager. To flip the question around, why would your leverage preferences change based on your recent pnl?
Cost of leverage is relevant on long time scales (and particularly relevant for determine expected return) but on short time scales like a day or week, it is completely dwarfed by fluctuations in the price of your holdings.
Thank you.
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