Permanent or long-term (months) market impact of large trades in stocks / equities

I need an estimate of the "permanent" long-term price impact of large institutional trades.

When an investor makes a large trade, there will be a price impact due to the trade. Institutional portfolio managers make very large trade decisions, sometimes choosing to sell \$10M, \$100M, or even \$1B at a time. I am interested in estimating the price impact of "large" trades (greater than a typical day's dollar volume), over time-spans of the "few weeks / few months / few years". The idea that I'm pursuing is "herding risk": if a few "holders" each have large positions in an illiquid asset, if one or more of them sells their position, the remaining holders will experience long-term losses (losses that won't improve with time). I'm trying to estimate what these long-term losses might be. For instance, a stock might have a \$1B market cap, a \$10M daily dollar volume, and a 2% daily volatility. Stock holders Alice, Bob, and Charley each own \$100M of the stock. Alice and Bob both sell fraction $$f \in [0,1]$$ of their positions. What is the long-term loss incurred by Charley?

Some details to give some more specificity / character / color to the question (thanks to suggestions here and arxiv searches):

• Temporary vs permanent
• Is permanent impact some fraction of peak temporary impact? Or is permanent impact completely independent of temporary impact? Somewhere in between?
• Concave or linear
• some theory suggests concave impact allows for arbitrage (free lunch), but empirical results suggest concave (in the order size) impact is reality.
• Multiple simultaneous
• how does one "sum" market impacts from Alice and Bob (multiple managers)? Do you add dollar volume or add impacts or somewhere in between?
• Duration
• If a manager sells $1B dollars, surely they will spread the orders over a large amount of time to minimize impact. Does duration affect permanent impact, or just temporary impact? • Correlation • How does correlation between signs (sell vs buy) of multiple trades affect impact? • Is permanent impact "predestined"/exogenous or "arbitrary"/endogenous • When a stock price falls permanently after a large sell order, did it fall because it was going to fall anyways, or did it fall because of the large sell order? • Market Impact: A systematic study of limit orders and Co-Impact: Crowding effects in Institutional Trading Activity – Attack68 Mar 17 at 6:57 • @Attack68: "We select metaorders whose participation rate (the ratio between their quantity and the volume traded by the market between ts and te) is smaller than 30%" If I read it right, it's the opposite of the condition in the question, no? – LazyCat Mar 20 at 2:32 • @LazyCat you may be right, but the question also discusses spreading these trades over a 'few weeks / few months' in which case \$100mm with a daily vol of \\$10 might be closer to the condition. In any case, to form an 'estimate' the links may/may not provide a useful starting point, and some validation. I didn't include it as an answer, because I didn't want to broach precisely the differences you mention. – Attack68 Mar 20 at 6:09
• @Attack68 Yes, sure. Thanks for the link. – LazyCat Mar 20 at 12:21