# 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 '19 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 '19 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 '19 at 6:09
• @Attack68 Yes, sure. Thanks for the link. – LazyCat Mar 20 '19 at 12:21

IMHO there is a general shift toward algorithmic execution for institutionz over the last 5 to 10 years, and depending on your method of execution the price impact can vary, so I am not certain whether you will get meaningful results using long histories.

Some older papers look at tickets data and aggregate impact of large tickets as proxy for institutional trades, but effect size have diminished on replication.

I have measured impact of multiday VWAP orders as the integral of impact of each volume bin, but because of the magnitude and stochastic nature of volume surprise, it's difficult to measure a priori. Moreover, you see spreads and cost widen if the trade is crowded (defined here as trade order imbalance), which can be determined post hoc using various signed volume measure (e.g. VPIN). If you have access to tick level data this might be a better approach than trying to find functional forms of market impact costs.

Look for mean reversion in overnight returns as compared to the intraday (open to close) return. I believe AQR has a paper using this measure on SSRN and some AB Bernstein researchers used this measure in a paper in Quantitative Finance.