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3. If L < 0 or L > 1 then you need to buy when the stock is up and sell when it is down, which is trend-following/destabilising behaviour. A recent L < 0 case is the XIV blowup and a recent L > 1 case is the Archegos blowup
4. L(L-1) is quadratic, so when L gets big, X gets really big. For Archegos if we assume L=5 then L(L-1)=20 so whenever the stock went up 5% they would need to buy 100% of their initial position size to maintain leverage -- in retrospect not surprising that VIAC was up so much.
Either big leverage (high L) or moderate leverage and volatile stocks (high R) is enough to create interesting feedback effects that can lead to blowups in less liquid markets like VIX futures or mid cap stocks. Big leverage *and* volatile stocks is spectacular :)
This should say they need to buy 100% of their initial *account* size, not position size.
This is dangerous. not only is it a quadratic, it is a logistics recursion. You are creating a fractal that is highly unstable. Given nearly any input(L = 0 and 1 are stable, others are unstable depending on multiplier) you will get a random output at some point.
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