macrocephalopod

Useful equation to remember when thinking about leverage, forced trading and impact on prices is X = L * (L - 1) * R. Here R is the return on the underlying stock/futures/whatever, L is leverage and X is the trade required to maintain constant leverage after a price move.

To get there, imagine a portfolio L:1 leverage i.e. you have $L of positions for every $1 of equity. If the stock has a return of R, you now have equity of (1 + LR) and stock worth L(1+R)

To maintain leverage of L you need the stock you hold to be worth L(1+LR) so you need to buy/sell X = L(1+LR) - L(1+R) = L + L^2R - L - LR = L(L-1)R Remember we are doing this per $1 of equity, so multiply by your initial account size to get a $ trade size.

Couple of interesting things: 1. If L = 0 (you hold cash) or L = 1 (unlevered) then you never need to trade, your portfolio automatically tracks. 2. If 0 < L < 1 then L(L-1) is negative so you sell on price increases and buy on decreases, which is stabilising