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)
Show this thread
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 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.
Show this thread -
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
Show this thread -
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
Show this thread -
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.
Show this thread -
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 :)
Show this thread
End of conversation
New conversation -
-
-
Alternatively, just use =RANDBETWEEN(1 billion, 110 billion) and put it in all caps.
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
-
-
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?
- Show replies
New conversation -
-
-
If quadratic is constant necessary?. X= L^2 * R
Thanks. Twitter will use this to make your timeline better. UndoUndo
-
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.